Consider a currency-issuing government that requires itself either to deduct taxes from non-government accounts or to issue debt to non-government before it spends. This is quite typical of governments today. At first glance, these requirements may seem problematic. From inception, it would clearly be impossible for a currency issuer to receive tax payments in its own currency or to auction off public debt in the form of treasuries in exchange for its own currency before the currency itself had actually been issued. The resolution to this apparent conundrum is that government can always (and currently does) advance to non-government the currency it requires to purchase newly issued public debt.

More specifically, the central bank, as the monetary arm of government, issues currency in the form of reserves (by crediting reserve accounts) while requiring collateral in the form of previously issued treasuries. Non-government is then in a position to purchase newly issued treasuries, with reserve accounts debited in settlement.

Typically, there will be a bidding process at a Treasury auction. The treasuries will go to the participants with successful bids – all those bids that offer an interest rate on government debt that is at or below the cutoff. If the central bank is prohibited from purchasing treasuries directly from the Treasury (which may or may not be the case, depending on the country in question), it will be necessary to auction off all newly-issued treasuries to non-government. In that case, the cutoff between successful and unsuccessful bids will be determined in the auction itself.

Considering that the sale of public debt is typically subjected to a bidding process, it may be wondered how government can nonetheless maintain control over the terms on which it spends. In particular, it may be unclear what prevents the rate of interest on public debt from rising above the rate that government actually wants to pay.

The answer is simple. The central bank can always purchase financial assets in the secondary market (the market for previously issued financial assets) so as to drive down the interest rates (yields) on those assets. The more the central bank’s actions drive down interest rates, the more attractive newly issued treasuries become in comparison. Since the central bank can credit reserve accounts without limit, there is never any risk whatsoever of the government somehow being forced to pay an interest rate on its debt that it is not fully prepared to pay. If the government wants the interest rate on newly issued treasuries to be lower than it otherwise would be, the central bank will simply inject more reserves into the system in exchange for financial assets purchased in the secondary market, thereby driving down the interest rates applicable to financial assets seen as close alternatives to newly issued treasuries.

Since both reserves and newly issued treasuries have zero default risk, and since reserves offer less interest than treasuries, there will be a willingness within non-government to exchange reserves for interest-bearing treasuries.

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**Behavioral Assumption**

As was emphasized in the earlier post, a key behavioral assumption of the income-expenditure model is that, in setting production levels, firms attempt to eliminate unplanned investment, defined as the unanticipated change in inventories. Equivalently, unplanned investment can be defined as excess supply. In response to excess demand or supply, firms are assumed to vary the level of production in an effort to cater to the level of demand. The model presupposes that there is sufficient slack for output to be adjusted to demand in the assumed way.

In the context of a continually growing economy, the elimination of excess demand or supply requires firms not only to react to what has happened in the immediate past (as reflected in any unexpected change in inventories) but also to anticipate how fast demand is likely to grow in the immediate future. This suggests the following decision rule:

This says that firms will adjust actual output (Y) by an amount (ΔY) that is intended to cover the expected change in demand (ΔY_{d}^{e}) as well as eliminate part or all (a proportion λ) of unplanned investment (I_{u}).

If growth is taken to be continuous, with time divisible into tiny increments, the process can be represented in terms of elementary calculus. The above decision rule becomes:

The dots indicate time derivatives. Y dot (= dY/dt) is the instantaneous change in output. Y_{d}^{e} dot is the expected change in demand. It equals the expected growth rate of demand (g_{d}^{e}) multiplied by the level of total demand: Y_{d}^{e} dot = g_{d}^{e }Y_{d}. The level of unplanned investment (I_{u}) – or excess supply – is the difference between actual output and total demand: I_{u} = Y – Y_{d}. Substituting these alternative expressions for Y_{d}^{e} dot and I_{u} into the decision rule and rearranging gives:

**Expectations**

At times it is necessary to specify how expectations are formed. For present purposes, the simplest form of adaptive expectations will do. According to this assumption, firms expect demand in the present to grow at the same rate as it was growing in the recent past:

Here, g_{d}^{e} is the expected growth rate of demand at time t and g_{dt–θ} is the actual growth rate of demand at an earlier time t – θ, where θ is a phase of time.

Adaptive expectations result in systematic errors. When the actual growth of demand is accelerating, so that demand is growing faster now than in the recent past (g_{d} > g_{dt–θ}), firms that form expectations in the assumed way will underestimate the growth rate of demand. Conversely, when the growth of demand is decelerating, firms will overestimate the growth rate of demand. Expectations will only turn out to be correct when the growth rate of demand stabilizes for long enough that g_{d} = g_{dt–θ} = g_{d}^{e}.

This simple form of adaptive expectations implies that, whenever there are errors, expectations are adapted according to the rule:

The difference between g_{d}^{e} and g_{d} is the error in expectations. It is assumed that firms respond by adjusting expectations in the opposite direction to the error. For example, if firms overestimate the growth rate of demand prevailing at time t, the error will be positive. Expectations will be adjusted downwards. This is a special case of a more general rule of adjusting expectations by the amount -β(g_{d}^{e} – g_{d}), where the positive reaction parameter β is set to one.

A different assumption could be made, such as basing expectations on a weighted average of past outcomes, allowing for slower adjustment of expectations in the event of errors, or opting for rational expectations, which would allow for quicker correction of random, unbiased errors, but none of these choices would alter the basic results of the model. One way or another, expectations have to be modeled to give determinate results, but the precise choice does not matter much in the present context as long as the assumed rule is at least somewhat sensible. Accordingly, a simple option is preferred.

**Growth of Actual Output**

Expression (2), which describes the way firms respond to excess demand or supply, implies a growth equation for actual output. This is obtained by dividing both sides of the expression by actual output (Y) and noting that Y dot / Y is the instantaneous growth rate of actual output (g).

If there is excess demand, the fraction Y_{d }/ Y exceeds one and actual output grows faster than expected demand (g > g_{d}^{e}). Under excess supply, the reverse is true. Equilibrium requires that demand equal supply (Y_{d }/ Y = 1). In that case, the growth rate of actual output will coincide with the growth rate of expected demand (g = g_{d}^{e}).

As has already been noted, expectations can only become correct if the growth of total demand (g_{d}) first stabilizes. Otherwise, if g_{d} keeps changing, expectations will also keep changing (with a time delay of θ) and result in variations in the growth rate of actual output.

For equilibrium to persist, firms’ demand expectations would need to become – and then remain – correct (g_{d}^{e} = g_{d}). If this occurred, actual output would grow at the same rate as total demand (g = g_{d}) until firms made an error in predicting the trajectory of demand. Starting, hypothetically, from a point of equilibrium, any error would cause actual output to deviate from total demand (Y_{d }/ Y would differ from one) and result in diverging growth rates for actual output and total demand.

**Other Key Assumptions**

As has been discussed, the growth equation for actual output given by (5) is predicated on the behavioral assumption that firms, through their production decisions, attempt to eliminate unplanned investment and keep pace with demand. Two other key assumptions of the income-expenditure model are that: (i) there is a positive level of autonomous demand (A > 0); and (ii) there is a positive, and stable, marginal propensity to leak (α > 0) to taxes, saving and imports.

On the basis of these three assumptions, there is a tendency, within the model, for both actual output and demand to converge, at any point in time, toward a particular (but, in a growth context, evolving) level of output (Y*) at which supply would equal demand.

The characterization of this equilibrium level of output will depend on what is assumed about demand. As always, total demand can be considered as the sum of two parts: induced demand and autonomous demand. Here, all demand other than net induced consumption is assumed to be autonomous. This makes induced demand (1 – α)Y. Autonomous demand is A. Therefore:

**Equilibrium Output**

With the determinants of actual output and total demand specified, the level of output (Y*) to which supply and demand converge can be established. With actual output equal to total demand, Y and Y_{d} can be replaced with Y* in (6):

Solving for Y* gives:

Output level Y* is a particular multiple (equal to 1_{ }/_{ }α) of autonomous demand. It is a notional level of output (changing over time) that the economy does not necessarily reach. Its relevance hinges on it being an ‘attractor’ for both actual output and total demand. In the income-expenditure model, Y* does in fact play the role of an attractor under most circumstances. A way to verify this point is presented later.

**Growth of Equilibrium Output**

The growth rate of Y* can be obtained from (6′). The first step is to differentiate with respect to time:

All terms involving Y* dot can be collected to the left-hand side:

Dividing through by αY* will convert the left-hand side to a growth rate (Y* dot / Y*). Multiplying A dot by A / A will also enable this derivative to be converted to a growth rate:

Rewriting the expression in terms of growth rates and noting that A / α = Y* gives:

Under present assumptions, the growth rate of Y* simply follows the behavior of autonomous demand (g* = g_{A}), which is taken as exogenously given.

**Growth of Total Demand**

The growth behavior of total demand is implicit in (6). Following the same procedure as in the previous section, the expression can be differentiated with respect to time:

Dividing through by Y_{d} and multiplying Y dot and A dot by Y / Y and A / A, respectively, gives:

Expressed in terms of growth rates:

Here, g_{d}, g and g_{A} are the growth rates of total demand, actual output and autonomous demand, respectively. The growth rate of total demand is basically a weighted average of the growth rates of actual output (g) and autonomous demand (g_{A}). The first term on the right-hand side describes endogenous demand growth. The second term describes autonomous demand growth.

Substituting for g, using (5), and rearranging yields the following expression for the growth rate of total demand:

Terms 1 and 2 can be considered briefly in turn. If there is excess demand, Y / Y_{d} is less than one and term 1 will be greater than (1 – α) g_{d}^{e}. As Y / Y_{d} increases toward one, the term approaches (1 – α) g_{d}^{e}. If Y / Y_{d} actually equals one, the term will equal (1 – α) g_{d}^{e}. Now, it has already been mentioned, in relation to (5), that when Y / Y_{d} equals one, the growth rate of actual output equals both the expected growth rate of demand (g = g_{d}^{e}) and, by (8), the growth rate of autonomous demand (g = g_{A} = g*). So the tendency of term 1 is to approach (1 – α) g*.

Turning to term 2, in equilibrium A_{ }/_{ }Y_{d} equals α. This is clear because, from (7), the equilibrium level of income is Y = Y_{d} = Y* = A_{ }/_{ }α, implying A_{ }/_{ }Y = A_{ }/_{ }Y_{d} = α. When there is excess demand, both Y and Y_{d} are less than Y*, implying Y_{d} < A_{ }/_{ }α or, upon rearrangement, A_{ }/_{ }Y_{d} > α. So term 2 exceeds αg_{A} when there is excess demand but tends toward αg_{A} as A_{ }/_{ }Y_{d} shrinks toward α. In equilibrium, term 2 equals αg_{A}. And since g_{A} is the equilibrium growth rate, term 2 tends toward αg*.

Considering the right-hand side of (10) as a whole, the growth rate of demand (g_{d}) tends to approach (1 – α)g* + αg* = g*.

**Dynamic Stability**

The discussion so far has highlighted certain characteristics of ‘equilibrium’ – or what is often referred to as ‘steady state’ – growth. In a nutshell, a steady state would require actual output continually to equal total demand (Y = Y_{d} = Y* = A / α). Under these circumstances, autonomous demand would be a stable fraction (α) of actual output and total demand (A / Y = A / Y_{d} = α). In terms of growth rates, all key variables would be growing at the same rate (g = g_{d}^{e} = g_{d} = g_{A} = g*).

Of course, it is one thing to identify features of steady-state growth. It is another to establish whether the system has a tendency to move toward such a state. Basically, the question is this: if the exogenously given growth rate of autonomous demand is held constant for long enough, will the assumed behavior of firms and households tend to push the economy toward a situation in which actual output and total demand converge on output level Y* with all key variables growing at the same rate as autonomous demand?

It should be stressed that this is an exercise more in logic than empirical reality. There is no suggestion that autonomous demand would in fact grow at a constant rate for any significant length of time or that a real-world economy could ever attain a steady state. The purpose of the exercise is to establish the results and tendencies that follow, logically, from the stated assumptions of the model.

To consider the issue of dynamic stability, let:

Variables y and z, both ratios, are measures of excess demand. Variable y is greater than, equal to, or less than one depending on whether demand is greater than, equal to, or less than output. When Y = Y_{d} = Y*, y = 1.

Variable z, the share of autonomous demand in income, is an alternative indicator of excess demand. It has already been observed that when demand and supply are both at the level Y*, z = α. If, starting from a steady state, autonomous demand subsequently grows at a different rate than output, there will be excess demand or supply, with z diverging from α. Under excess demand, z > α; under excess supply, z < α.

It follows from the definitions of y and z that the share of autonomous demand in total demand (A / Y_{d}) is z / y. As with z, this share is greater than, equal to, or less than α depending on whether there is excess demand, equilibrium, or excess supply.

Most of our focus can be on variable y (= Y_{d }/ Y). Dynamic stability requires y to tend toward one and, if it gets there, to remain at one unless there is an exogenous change in either the growth rate of autonomous demand (g_{A}) or the marginal propensity to leak (α). Clearly, whether y will behave in the required way will depend on the growth behavior of total demand (Y_{d}) and actual output (Y). This can be made explicit by differentiating y with respect to time (applying the quotient rule):

The fractions in brackets on the far right are growth rates and Y_{d }/ Y is variable y. Modifying the expression accordingly gives:

This is a differential equation. It relates the instantaneous change in y (y dot = dy/dt) to the growth rates of demand and output (g_{d} and g) as well as to y itself.

For a steady state to persist, it is not enough that y = 1 at a given moment. It is also necessary for y to remain unchanged (y dot = 0). As (12) spells out, this can only occur if demand and output happen to grow at the same rate (g_{d} = g = g*).

Equation (12) is missing details that are needed to assess stability. One way to fill in these details is to express the equations for g_{d} and g in terms of y and substitute the resulting expressions into (12). An alternative way, which turns out to be a bit simpler, is to substitute an equation for g into an equivalent expression for y dot, making use of the definition of z. The first step is to differentiate z ( = A / Y) with respect to time to obtain:

It can then be observed that

Since both 1 and α are constants, it follows that y and z both change at the same rate:

This means that the expression for z dot in (13) can be substituted into the right-hand side of (12) to obtain:

To eliminate z, it can be noted from rearrangement of (14) that z = y + α – 1. Upon substituting for z, (12) becomes:

Since (12) and (12′) are equivalent expressions, either can be used to check stability.

It is still necessary to substitute an expression for g in (12′). Writing (5) in terms of y gives the required expression:

Substituting this into (12′) gives:

Formulated in terms of (12”), the question of dynamic stability comes down to how y dot responds to a small change in y. Starting from a situation in which y = 1 and y dot = 0, it is necessary that changes in y away from 1 set in motion forces that tend to cause y to move back toward 1. In considering this question, expectations will be taken as given. At time t they are already formed, based on what happened at time t – θ. And in a steady state, the expected growth rate of demand will equal the other growth rates under consideration. The other elements in (12”) are either parameters (α, λ) or an exogenous variable (g_{A}) and so can also be taken as given. Accordingly, we take the derivative of y dot with respect to y. Dynamic stability requires that the derivative be negative when evaluated at the critical point y = 1.

In undertaking this exercise, it is important to mention that equation (12”) is nonlinear in y because of a y-squared term (if the expression is expanded out). This means that taking the derivative with respect to y serves only as a test of ‘local stability’ as opposed to ‘global stability’. Basically, the derivative represents the best linear approximation to the behavior of y near the point y = 1.

Taking the relevant derivative (applying the product rule) gives:

Evaluating the derivative where y = 1 and g_{d}^{e} = g_{A} = g* reduces the expression to:

The derivative is negative provided:

Therefore, the modeled behavior is locally stable provided the growth rate of autonomous demand (g_{A} = g*) exceeds -λ, where λ is the positive reaction parameter that indicates the intensity of firms’ response to unanticipated changes in inventories. For positive growth regimes, the model always exhibits local stability.

To get an idea of the global characteristics of the model’s behavior, the relationship between y dot and y can be represented graphically, once again taking expectations and the growth rate of autonomous demand as given and equal to each other. In the diagram below, g_{d}^{e} = g_{A} = 0.02, λ = 1 and α = 0.5.

In reference to the diagram, we can take an arbitrary value for y and consider whether it is a stable point, and then ask the same question for other arbitrary values of y.

Not all values of y are permissible because of the assumption that the level of autonomous demand must be positive. This implies, in turn, that z (= A_{ }/_{ }Y) must also be positive. Since, by (14), z = y + α – 1, it follows that y must exceed 1 – α. In the diagram, y must exceed 0.5, reflecting the value chosen for α.

If there is excess supply, y is less than one. In the scenario considered, if y is between 0.5 and 1, y dot is positive, meaning that the assumed behavior of households and firms will push y higher, toward 1. This is indicated by the arrows pointing to the right. Conversely, when there is excess demand, y is greater than 1 and y dot is negative. The arrows situated to the right of y = 1 and pointing left indicate that y, when above one, is pushed lower, toward one. The only stable point is y = 1. This is indicated by the black dot.

There is another point at which y dot is zero, indicated by the white dot. But in most scenarios, this point is unstable. On and to the left of this dot, y is below the minimum permissible value. To the right of the white dot, y is pushed toward y = 1.

Assigning different values to the parameters (α and λ) affects the diagram in certain ways. As has been discussed, the value of α determines the minimum permissible value of y. Choosing a smaller value for λ flattens the curve, reflecting slower adjustment, without altering the positions of the two critical points. However, for some extreme cases, the positions of the white and black dots can switch.

The result that local stability requires g* > -λ comes into play in these extreme cases. If the growth rate is very negative and λ is small, it is possible for the point y = 1 to be unstable. For example, if the values of g_{d}^{e} and g_{A} are both set to -0.2 and λ is reduced to 0.1, with α kept at 0.5, the critical point y = 1 is unstable and repels the system, which is pushed either toward infinity (if y > 1) or toward y = 1 – α (if y < 1).

In extreme cases such as this, the model suggests that stability can be restored through an exogenous change in policy that lifts the growth rate of autonomous demand.

**Description of the Model’s Growth Behavior**

Provided the condition for dynamic stability holds (g* > -λ), and y is quite close to 1, the behavioral assumptions ensure a tendency for actual output and total demand to converge on Y*. Conceptually, the growth process depicted in the model can be described as follows. Starting from a steady state, an exogenous increase in the growth rate of autonomous demand (g_{A}) creates a situation in which actual output and, to a lesser extent, total demand temporarily grow less rapidly than Y*. This results in excess demand (y > 1), a delayed upward revision of expectations (since g_{d} > g_{dt–θ}), and an acceleration of output growth (g) that brings with it further endogenous acceleration of demand growth (g_{d}). So long as g remains below g_{A}, it also remains below g_{d}. At this stage, y is still rising further above one.

At a certain point, g catches up to g_{d}. This occurs at the same time as g catches up to g_{A}. It then overtakes both g_{d} and g_{A}. The deviation of g above g_{A} is greater than g_{d}‘s deviation. This is partly because endogenous demand growth accounts for only a fraction of total demand growth (which is a weighted average of endogenous and exogenous growth) and partly because leakage to taxes, saving and imports occurs throughout the process.

In the convergence of y toward 1, there can be some oscillation (fluctuation) around the critical point. This is due to the lag in firms’ response to excess demand and supply, including in the adjustment of expectations. If the growth rate of autonomous demand (g_{A}) is held constant throughout the adjustment process, the oscillation is damped (declining in amplitude). This is illustrated in the first diagram below. In the second diagram, random variations in g_{A} cause more sporadic behavior. In both diagrams, the growth rate of autonomous demand is exogenously increased from 0.01 to 0.03 at time t = 5, though with random variation around these levels in the second diagram.

The next two diagrams illustrate the convergence of growth rates. Once again, the growth rate of autonomous demand is exogenously increased from 0.01 to 0.03 at time t = 5. In the first diagram, the process is entirely deterministic. In the second diagram, the growth rate of autonomous demand is subjected to random disturbance.

The way in which g interacts with g_{d} and g_{A} can be verified working from the expression for g_{d} in (9). Subtracting g from both sides of the expression gives:

This can be rewritten

In the first fraction on the right-hand side, the difference between total demand Y_{d} and induced demand (1 – α)Y is simply autonomous demand A. Modifying the expression accordingly gives:

If g is less than g_{A}, the right-hand side is positive. Since the left-hand side must then also be positive, g will clearly be less than g_{d}. Conversely, when g is greater than g_{A}, it must also be greater than g_{d}. This confirms that g deviates further from g_{A} in both directions than g_{d} deviates. The expression also shows that the growth rates of actual output and total demand coincide when equal to the growth rate of autonomous demand (g = g_{d} = g_{A}).

**Growth as Such**

Economic growth entails an ongoing expansion of output. Output, when defined in terms of National Accounting conventions, is a monetary measure. This is true whether the figure for Gross Domestic Product (or related measures) is reported in nominal terms (at market prices) or in so-called ‘real’ (meaning constant-price) terms. Growth of output, when output is defined in this way, can occur with or without environmental risk and social harm. In this sense, growth is neither inherently good nor bad.

Clearly, the desirability and sustainability of growth depends on the nature of that growth. In principle, if our measure of output is sufficiently broad, an economy geared toward learning (through education, research and development, science and technology, the arts and humanities), restoration and regeneration of the natural environment, provision of first-rate health and care services, construction of quality infrastructure, development of socially harmonious institutions and processes, as well as the fostering of creativity and play, can grow just as well as an economy geared toward military adventurism, plunder of natural resources and the proliferation of social and psychological maladies. When an economy produces more knowledge, for example, with the same expenditure on education, science and research, that should really be counted as an addition to ‘real’ output, appropriately conceived, though of course difficulties can arise in evaluation and measurement.

A key implication of Modern Monetary Theory is the capacity we have, if served by a suitably empowered and accountable currency-issuing government, to select sustainable activities and development paths.

Even so, the question might still be asked, why the need or desire to grow? Why not just satisfy ourselves with a stationary economy, or perhaps even shrink things a little?

Well, strictly speaking, nothing in a consideration of economic growth necessarily requires that we prioritize high or even positive rates of growth. Especially if we are thinking in terms of a future society with a job guarantee, full employment could be maintained with or without positive rates of growth. We can attempt to understand characteristics of an economy’s growth behavior, whether that growth is quantitatively positive or negative. But, having said that, it seems likely that most people will consider growth to be a positive, provided it is the right kind of growth. Ultimately, growth can and should be about the sustainable development of humans and other species in the fullest sense. Such growth might become less and less about the production of widgets and more and more about the attainment of knowledge, peace and understanding, social cohesion, an expanded scope for individual expression and creativity, and so on.

**Demand-Led Growth**

A motive for considering the possibility that growth is demand led is the implication that this would carry for macroeconomics in general. The central idea of demand-led growth lends credence to a key assumption underlying the Kaleckian or Keynesian view of output determination. In this view, a change in demand is assumed to induce variations in the level of production (real output) more or less independently of changes in (some index of) the price level. A critical assumption underlying this position is that there is spare capacity and spare reserves of labor-power and other resources making it possible for output to adjust to demand in the suggested way.

Demand-led growth theory makes sense of the idea that spare capacity is not merely a short-run assumption but one that is normally valid over any time frame. Arguably, it is even more applicable to the long run than to the short run. The reason – as demand-led growth theory highlights – is that output can respond to demand not only through a fuller utilization of existing capacity but, via investment, an expansion of capacity itself. Modern economies are almost always operating far below the physical maximum capacity. Average utilization rates of somewhere between 80 to 85 percent seem to be typical. In the US, for instance, the rate of utilization has fluctuated between about 67 and 90 percent since records began to be published in 1967.

How is this possible?

It is possible because long before full capacity is reached, firms will find themselves operating beyond the rates of utilization that they consider ‘normal’ – meaning beyond the utilization rates that they consider appropriate to the levels of demand that they expect to face on average – and this entices them to undertake further capacity-expanding investment.

Why do firms want to operate below full capacity?

They want to do this mostly because of uncertainty over what levels of demand they, in fact, will confront at any given time. Planned margins of spare capacity give them leeway, enabling them to respond to fluctuations in demand with variations in output rather than risk losing customers to rivals. In short, spare capacity gives flexibility.

It is not critical to this view of demand-led growth that prices be assumed constant. It is only necessary that real output respond to demand in the suggested way. In the short run, a strengthening of demand may well give rise to temporary price effects in those sectors that are operating nearer to full capacity than others. These price pressures may persist until new capacity has been installed, whether by new firms or through existing firms expanding their operations. As long as, in aggregate, the level of production responds to demand in the supposed way, there is no difficulty for demand-led growth theory, since its focus is on the behavior of real output. At the same time, the possibility of temporary price effects actually makes a working assumption of independence between the price level and output more plausible in the long run than in the short run, because the longer time frame allows for investment to have its full effects on capacity.

Surplus reserves of labor-power are also a normal feature of the system. Partly this is because expansion of capacity is achieved not only through an extension of scale at given technical efficiency but through technical progress that enables the same level of output to be produced with less labor. In addition, it is partly because capitalists can and do exploit previously untapped sources of labor-power located in non-capitalist spheres of the global economy (whether these individuals reside in so-called developed or developing economies). There is also a tendency for the size of the labor force to expand in periods of strong demand due to individual labor-supply decisions. Some individuals who become discouraged in their job search during periods of stagnation re-enter the labor force when prospects improve. As with plant and equipment, which will typically be utilized at different rates in different sectors on the basis of unbalanced growth, the supply of some types of labor-power can dry up before other types. Here, too, there can be price effects in affected sectors. As with spare capacity, the assumption of excess labor-power is actually more plausible rather than less over longer time frames. In the long run, there is time to train up new workers or innovate to reduce the need for certain types of labor-power.

The most pressing constraint is the environmental one. As already stressed, remaining inside the limits set by natural resources requires being cognizant of the type of growth and kinds of activities we prioritize. Here, currency-issuing governments have the capacity to encourage or undertake the right kinds of activity and discourage or proscribe ecologically harmful production.

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*Ugh* … I lurched toward the window. Not good.

I glared down at the crowd.

Leaning out the window it was all I could do not to spit the ghastly brew all over their unsuspecting heads.

*Damn and blast you all to hell*, I thought.

I pulled sharply away from the window, slamming it shut with the anguish of a young man in confusion and pain.

It was an intense, existential pain.

Physically I was okay, though. (Absolutely tip top.)

I glared down at the brown liquid, a dirty circular pond, withdrawing into myself, leaving my once cherished Study Mug on the emotional outer, unloved. Any sense of oneness it may once have shared with its holder and the crowd below had since crashed down upon the hardwood surface of the table, its contents not hot – nor even warm – but tepid. Unforgivably tepid.

Moments later my glare was redirected toward the moka pot, perched in all its feigned innocence on the kitchen stove. I was about to reach for something breakable to throw at it when the microwave clock came into view. It conveyed the surprising news that two full hours had elapsed since the discredited brew had come fresh off the production line. Sensations of universal oneness had apparently left me incapable of keeping track of time. Deflated, I rested against a wall to take stock, exhaling a slow, steady breath. Letting it go. Letting it all go.

Lukewarm coffee had spilled on lecture notes that awaited revision. Tactfully, courteously the notes had waited, but so far with little reward.

Fetching a cloth from the kitchen sink, I mopped up.

A stack of playing cards sat aloof on a bookshelf – mockingly, haughtily, difficult to ignore forever. Their presence oppressed me, too, like unstudied lecture notes. Procrastination only added to the burden. I approached them gingerly. Grabbed a pile in one hand and sized it up. Checked the last card in the pile (they were numbered on the back). Repeated the exercise.

Some time later I was out the door.

*****

“Dealer has six, sixteen, too many!”

Players at the table roared their approval, happy, on a winning run. The young dealer, Chintana, made the payouts. She was currently very popular with the table, a popularity that was, perhaps in part, of the “what have you done for me lately?” variety. Some say it’s the best kind of popularity.

“Shuffle time.”

I stood by a nearby table. There was a German couple, tourists, or so they said. Also a sleepy looking Indian guy pretending to be sleepy. And a twenty year old international student I recognized from class chatting in Cantonese to Enlai, the sharply dressed dealer, about how much the stockbroking game had changed over the course of his long career. I chatted to some guy playing box one, who said he was from the suburbs, while affecting disinterest in Chintana’s table, waiting for the shuffle.

I’d been in the casino for a few hours by now, pretending to drink beer, nibbling on snacks, hard at work, occasionally placing a bet, mostly just watching, mingling, joking with dealers and winning players, commiserating as losses began to mount. It was fun, really, apart from the need to wager.

At the happy table Chintana presented cards for the players’ cut. A messy-haired guy in T-shirt and jeans cut about a deck from the bottom of the eight decks. A bit more than a deck, really. About fifty-seven cards. Not more than fifty-nine, anyway. Maybe as few as fifty-five. Best guess fifty-seven.

I studied Chintana’s hands for a moment, and the stack of cards she held, rested against the baize. The bottom card faced her, away from the players, but angled somewhat to my point of view. I caught the identity of that card. It was the bottom card prior to the players’ cut, but the fifty-seventh card post cut, once Chintana had placed the cut cards to the front of the shoe, and the fifty-sixth card once she burned the first card, placing it face down in the discard tray. It could be a go.

I turned back to watch Enlai’s table, a spectator only, engaging in a bit of encouraging banter with the international student (we pretended not to know each other) and the box one suburban guy who had decided to “chip up”, pressing his luck, as if he really was from the suburbs. I cheered them on, but kept an eye on the happy table. With three boxes open, the players and dealer would typically consume about a fifth of a deck of cards per round. The sixth round was the one of possible interest. But only if it panned out as hoped. The situation could just as easily dissolve into nothingness if the card came a round earlier, but too late in the round to be useful. Or maybe another player would arrive and mess things up. Hopefully peer pressure would prevent it.

With hope still alive at the end of the fifth round. I wandered over to the happy table, lingering behind box three, a beer in one hand, a clutch of gaming chips in the other. Players eyed me anxiously, fearing that I’d open a new box and mess with The Flow. The Flow was – still is – a concept embraced by the superstitious and scientific alike. The former as true believers. The latter as a pretense, a way of discouraging new players from joining a game at inopportune moments.

They needn’t have worried. I placed a “back bet”. The players nodded their approval and relaxed, glad, or pretending to be glad, that The Flow had been preserved.

“Eight hundred dollars on box three,” said Chintana. Three hundred and twenty five of those were mine. Or, at least, used to be mine. They were up for grabs now. The remainder of the eight hundred used to belong to a happy-go-lucky corporate guy. His girlfriend turned and grinned. Said they were in marketing and due back at the office. Maybe it was true. It was not impossible.

The pit supervisor nodded approval to Chintana, then laughed at the marketers’ truancy. “More money to be made in here,” he joked.

“Yeah, right!” said the marketer, in good humor.

Chintana ran her hand across the baize – “no more bets” – and wished everybody luck.

Tipsy and easygoing on the outside, sober and queasy on the inside, I pushed clenched fists into jacket pockets, hoping for the best. The wager amounted to a sizable chunk of my still pitiful bankroll, a few thousand dollars plus change built up from a measly initial thousand. I knew that until that got up to perhaps a hundred thousand or so the game was always going to be a slog. A hellish, never-ending kick in the guts, placing back bets to appease other punters and avoiding costly waiting bets by resisting the comfort of a chair. Slog was right. I still sweated the turn of each card. The psychology of it all should have been conquered by this point, but had not been.

The wager as a proportion of bankroll was more or less justified. With a margin for error of five cards, my theoretical advantage on the round was about ten percent, and the standard deviation on the wager only a bit more than the bet itself. Optimal betting theory called for roughly the bet placed.

On the dealing of box three’s first card by the amazing Chintana, my spirits soared. An ace of diamonds, as hoped for! No, not as hoped for. As intended, and expected. I was a pro, damn it, or at least on the way to becoming one.

*Oh, Chintana, thank you! You are wonderful and your popularity thoroughly deserved.*

With the appearance of the ace as first card the advantage had now spiked to about fifty percent. I tried to conjure a sense of optimism to mask the gnawing in the deep dark pit of my stomach that said this was all going to end in calamity.

I longed for a picture card to go with the ace, for blackjack. Nothing but that three-to-two payoff would do now. A nice add to my small but growing – yes growing, damn it – bankroll.

Chintana showed an eight as up card. Box three, unfortunately, soon showed a seven for its second card, giving a mediocre soft eighteen. The marketers correctly stood.

I cursed the universe inwardly. *Typical*. And it *was* typical. It typically happened twenty-four times out of every four hundred and fourteen attempts that a seven would be drawn to an ace when the lovely Chintana showed an eight as up card from an eight deck shoe. Roughly one in thirteen times. The temporary fifty percent edge had eighty percent evaporated, though the situation was not terrible. There was still hope. I was reduced, once again, to hope.

Hope, that is, until Chintana revealed a seemingly heartless three of hearts for eleven and a ten of clubs – for clubbing players over the head – for three-card twenty-one, swiftly banishing eight hundred dollars, three hundred and twenty-five of them formerly mine, down the chute.

Chintana shrugged sympathetically. I gave my best impression of a good-natured roll of the eyes, commiserated with the marketers and strolled off in the direction of a bar. (The nearest high cliff was some distance away and peak hour traffic would frustrate any attempt to reach it in a hurry.)

Soon after, I headed for an exit.

*****

Back at the apartment, I brooded, waiting for the moka pot to work its magic. The lecture notes, for their part, still waited in dignified, non-judgmental silence on the table.

With Study Mug in hand, fresh and forgiven, I resumed my earlier vantage point by the window, gazing at the crowds below. Such beautiful, crazy crowds. How they wandered to and fro. Happy. Unhappy. Rich. Poor. Amazing. Wonderful. Crazy beautiful crowds.

I muttered to no one in particular, “Damn and blast you all to hell.”

The door opened.

It was Chintana. She was beautiful, eyes sparkling, changed out of her work clothes. She gave me a look. Quizzical.

I shrugged.

“It didn’t work?” she asked.

“It worked perfectly,” I assured her. “You did great. It was not obvious, but clearly visible.”

She crossed the room and nestled close. “The ace,” she said, “but it was no good.”

“Just unlucky.”

We kissed and went to the bedroom. Later, we got a ton of study done and, that semester, caned finals.

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A first step is to consider the disequilibrium behavior of an economy that, for simplicity, is taken to be stationary (non-growing) when in equilibrium. This approach is adopted in the present post. The exercise is really preparation for considering a continually growing economy – a task that is left for a possible future post.

The material in this post is somewhat technical but hopefully not difficult. Even so, the post is long (about 4000 words) and, for readers not already familiar with similar material, possibly a stretch to read all in one go. I considered separating the post into numerous shorter ones but felt that the loss of continuity would require too much repetition in setting up the discussion each time.

The post is divided into sections that provide natural stopping points for readers who wish to take breaks. The section titles are:

1. Macroeconomic Equilibrium

2. Disequilibrium Behavior

3. Adjustment Process

4. Adjustment in Simple Algebra

5. Convergence as a Power Series: λ = 1

6. Convergence as a Power Series: λ < 1

7. Adjustment of Growth Rates

Some background information relating to 1 can be found in the ‘Short & Simple’ series (mainly here). A very helpful reference for some of the material covered in later sections is Ronald Shone’s book, *An Introduction to Economic Dynamics*, Cambridge University Press. The edition I have was published in 2003. In particular, the third chapter provides more sophisticated – but still highly accessible – treatments of 3 and 4. The purpose of 7 is to lay some groundwork for a possible future post on a continually growing economy.

**1. Macroeconomic Equilibrium**

The notion of macroeconomic equilibrium relates to plans (or desires). Although, under National Accounting conventions, actual output equals actual expenditure by definition, equilibrium will only occur if actual output equals planned expenditure.

The sum of planned expenditures constitutes total demand. Actual output represents total supply. Accordingly, the equality of demand and supply requires that actual output and actual expenditure equal planned expenditure. This only occurs when unplanned expenditure is zero.

Unplanned expenditure is possible because of the way actual expenditure is defined. Included in actual expenditure is the **change in inventories**, meaning the change in unsold stocks of goods held by firms. The change in inventories is treated, in the National Accounts, as expenditure by firms to themselves.

From a theoretical standpoint, intended changes in inventories are part of planned investment. Unintended changes in inventories amount to **unplanned investment**.

Defined in this way, unplanned investment is identically equal to **excess supply**. It is the amount of output that firms intended to sell but were unable to sell within the period. In other words, unplanned investment is the excess of supply over demand.

In symbols:

Here, I_{u} is unplanned investment (the unanticipated change in inventories). Y is actual output (supply). Y_{d} is planned expenditure (demand).

Equilibrium occurs if unplanned investment is zero (I_{u} = 0) so that:

where Y* is the equilibrium level of output.

Total planned expenditure (Y_{d}) can be grouped into two broad categories. ‘Autonomous demand’ (A) is considered exogenous and independent of income. It includes the planned exogenous spending of households, firms, government and foreigners and is defined net of exogenous imports. ‘Induced demand’ is endogenous and depends on income. It is defined net of endogenous imports. In general, endogenous spending can be undertaken by households, firms or government. But to keep the present discussion as simple as possible, all expenditure other than net induced consumption (defined as induced consumption minus endogenous imports) will be considered exogenous and part of A. If the marginal propensity to leak to taxes, saving and imports is denoted by α – assumed to be a constant fraction between zero and one – there will be induced demand of (1 – α)Y.

Total demand, then, is the sum of the induced and autonomous components of planned expenditure:

Actual output, which is identically equal to actual expenditure, includes not only planned expenditure but also unplanned investment:

When unplanned investment is zero, actual output (Y) equals planned expenditure (Y_{d}) and is at the equilibrium level (Y*). Substituting the expression for Y_{d} in (3) into equilibrium condition (2) gives:

Solving for Y:

Since both autonomous demand (A) and the marginal propensity to leak (α) are taken as given, equilibrium output (Y*) is stable unless there is an exogenous change in A or α.

Although, for given A and α, Y* is stable, actual output (Y) and planned expenditure (Y_{d}) only equal Y* in equilibrium. Our present concern is with what happens out of equilibrium.

**2. Disequilibrium Behavior**

In the income-expenditure model, it is assumed that firms respond to unexpected changes in inventories (excess demand or supply) by varying levels of production. The model is valid provided there is sufficient spare capacity, underutilized labor-power and resources for firms to respond in this way.

In a situation of excess supply, unwanted inventories mount (I_{u} > 0) and firms are assumed to cut back production. This initiates a multiplier process that causes actual output (and to a lesser extent demand, through the effects on induced demand) to decline toward the equilibrium level.

Conversely, when there is excess demand, firms are assumed to step up production in an attempt to replenish dwindling inventories. This sets off a multiplier process in which actual output (and to a lesser extent demand) rise toward the equilibrium level.

So, in a situation of excess demand:

An expansion of production will induce consumption and cause both actual output and planned expenditure to rise toward the equilibrium level of output.

In a situation of excess supply:

and the reverse process occurs.

**3. Adjustment Process**

Suppose the economy is initially out of equilibrium. We can consider the process of adjustment.

Throughout the exercise, both autonomous demand (A) and the marginal propensity to leak (α) will be held constant. This means that the equilibrium level of output (Y*) will also remain constant throughout the adjustment process as actual output and planned expenditure converge on Y* = A_{ }/_{ }α.

A well known diagram is often used to illustrate the situation. It is shown below. In the diagram, expenditure (E) is measured along the vertical axis. Output and income (Y) are measured along the horizontal axis.

The level of planned expenditure associated with each level of output is indicated by the Y_{d} schedule. At points off this schedule, actual expenditure differs from planned expenditure by an amount corresponding to unplanned investment.

The 45-degree line shows all the points at which actual output equals actual expenditure; that is, all the points at which Y = E.

As has already been established, equilibrium requires that planned expenditure (Y_{d}) equals actual output (Y). This occurs at the point of intersection between the Y_{d} schedule and the 45-degree line. Since actual output equals actual expenditure by definition, the point of intersection also represents a situation in which planned expenditure equals actual expenditure.

All points on the Y_{d} schedule to the left of the 45-degree line show situations of excess demand (Y_{d} > Y), whereas points on the Y_{d} schedule to the right of the 45-degree line indicate excess supply (Y > Y_{d}).

Suppose initially that actual output is at the level Y_{0}. This is a situation of excess demand. Planned expenditure E_{0} exceeds actual output Y_{0}.

The difference between demand and supply, which defines unplanned investment, is represented by the horizontal distance from output Y_{0} to output Y_{1}. It is also measured by the vertical distance between the Y_{d} schedule and the 45-degree line at output Y_{0}.

In the present situation, unplanned investment is negative because demand exceeds supply (Y_{d} > Y).

Although only output of Y_{0} is actually produced in period zero (denoted t = 0), firms are able to satisfy demand of E_{0} by running down inventories.

The unexpected depletion of inventories acts as a signal for firms to expand production in the next period (t = 1) to the level of output Y_{1}.

The diagram is drawn on a simplifying assumption that firms make the full adjustment from Y_{0} to Y_{1} in a single period. In general, they might only make part of this adjustment within the period. (They might even make more than the full adjustment, but this possibility will be ignored in the present discussion.) The basic logic of the model is not affected by the strength of reaction to excess demand or supply, but the convergence process will take a bit longer in the case of partial adjustment.

Even the full adjustment from Y_{0} to Y_{1} does not immediately result in equilibrium, because the additional income (ΔY = Y_{1} – Y_{0}) induces extra private consumption. This is represented as a movement up along the Y_{d} schedule.

So, at output Y_{1}, planned expenditure is still greater than actual output. This can be seen by the fact that, at output Y_{1}, the Y_{d} schedule is still above the 45-degree line.

Importantly, though, there is less excess demand at time t = 1 than at time t = 0. The reason for this is that the slope of the Y_{d} schedule is flatter than the 45-degree line. Demand rises more gradually than supply as both increase toward the equilibrium level of output.

Specifically, the Y_{d} schedule’s slope is less than one. (Its slope is 1 – α, which is less than 1 because α > 0.) In contrast, the slope of the 45-degree line is equal to 1. The difference in slopes makes it possible for supply to catch up to demand as firms attempt to adjust actual output to demand.

Within the model, the relative flatness of the Y_{d} schedule is actually one of two conditions that, when satisfied, ensure convergence of actual to equilibrium output, or what is called ‘dynamic stability’.

Both conditions for dynamic stability relate to the Y_{d} schedule and are depicted in the diagram. They are that:

(i) there is a positive level of autonomous demand (A > 0), which means that the Y_{d} schedule must have a positive vertical intercept; and

(ii) the marginal propensity to leak is positive (α > 0), which means that the slope of the Y_{d} schedule (1 – α) must be less than one.

The first condition – a positive vertical intercept – ensures that if the Y_{d} schedule crosses the 45-degree line at an equilibrium point, it will do so at a positive level of output. This is important because only positive levels of output make economic sense.

The second condition – a positive marginal propensity to leak – ensures that the two schedules will cross, because it means the Y_{d} schedule is flatter than the 45-degree line.

Provided the conditions for dynamic stability are satisfied, the convergence process will eventually cause output to reach (asymptotically) the level Y*, where supply equals demand (Y = Y_{d} = Y*).

The process is indicated by the arrows. Each time firms respond to a deficiency of inventories by stepping up production, this induces extra demand, but not as much demand as the additional income that has been created, because of a positive marginal propensity to leak from the circular flow of income.

A similar process would occur from a position of excess supply at which the point on the Y_{d} schedule happened to be to the right of the 45-degree line. There would be a multiplied decline in actual output as each contraction in the level of production shrunk induced demand, but not by as much as the reduction in income.

**4. Adjustment in Simple Algebra**

The adjustment process just described can be expressed in simple algebra.

Recall, from (1), that unplanned investment is identically equal to the amount of excess supply in the economy:

It has been assumed that, out of equilibrium, firms attempt to eliminate part or all of the unplanned investment in the next period. This suggests that, in the next period, firms will adjust production by the amount

where λ is a positive fraction. The minus sign in (7) indicates that firms adjust actual output in the opposite direction to the change in unplanned investment. For example, if demand is 990 and actual output only 980, implying unplanned investment of -10, it is assumed that output in the next period will be increased by some fraction (λ) of 10.

The expression for unplanned investment in (1) can be substituted into (7):

This says that the change in actual output (ΔY) can be expressed as a fraction (λ) of excess demand (Y_{d} – Y).

From (3), we know that Y_{d} = (1 – α)Y + A. Substituting for Y_{d} in (8) and rearranging gives:

This expression makes it possible to work out actual output for the next period as the sum of current-period output and next period’s change in output (Y + ΔY). To do so, we can add Y to both sides of (9) and rearrange:

If we are considering periods t and t+1, this can instead be written:

This is a recursive equation. We can repeatedly substitute the value of actual output in one period (Y_{t}) to obtain actual output of the following period (Y_{t+1}).

For example, suppose in period t = 0 that autonomous demand is 500, with the marginal propensity to leak a constant 0.5. The equilibrium level of output will be Y* = A_{ }/_{ }α = 1000. But perhaps firms have only produced actual output of 980 in the period.

According to the behavioral assumption, firms will increase production each period until equilibrium is restored. In the simplest case of full adjustments (λ = 1), actual output in successive periods will be:

The squiggly equals sign in the final row says that Y_{n} is ‘asymptotically equal’ to the equilibrium value. That is, actual output approaches the equilibrium level asymptotically.

The logic of the adjustment process just outlined can also be considered in a slightly different way by assuming, as an alternative exercise, that the economy is initially in equilibrium and then working through the effect of a one-off exogenous change in autonomous demand.

Suppose A = 490, α = 0.5, and the economy is initially in equilibrium with both actual output and total demand equal to 980. If autonomous demand then increases by 10 to 500 (giving ΔA = 10), this will result in excess demand and call for an expansion of production by firms. If we take the change in autonomous demand to have occurred in “period 0”, then the disequilibrium adjustment process will be an exact replica of the one shown above.

If λ happens to be less than 1, the adjustment will be more gradual. The following table, which continues with the same example, shows the sequence of actual output and total demand for various values of λ. Total demand is calculated each step by substituting the most recent value for actual output into (3), which says that Y_{d} = (1 – α)Y + A.

In the table, autonomous demand is held constant at A = 500, the marginal propensity to leak is α = 0.5 and a situation of excess demand is assumed to exist in period 0.

Here are a couple of cases represented in graphical form:

**5. Convergence as a Power Series: λ = 1**

We have observed that actual output and demand both tend to converge to a level that is a multiple of autonomous demand. In equilibrium, Y = Y_{d} = Y* = A_{ }/_{ }α.

As is well known, the expenditure multiplier (1_{ }/_{ }α) can be interpreted as the sum of a power series:

When α takes a value between zero and one, which is always the case under the assumptions of the income-expenditure model, the above series asymptotically approaches 1_{ }/_{ }α as n becomes large.

The power series can be interpreted as tracing out each step of the adjustment process in which actual output adjusts to its equilibrium level.

Starting from a position of equilibrium, reconsider the consequences of a one-off exogenous change in autonomous demand, denoted ΔA.

The change in autonomous demand will cause a multiplied change in equilibrium output of:

Here, the sum of the power series given in (11) has been substituted for the multiplier 1_{ }/_{ }α.

Continuing with the example, if actual and equilibrium output were initially 980, the marginal propensity to leak 0.5 and the change in autonomous demand 10, then equilibrium output would eventually increase by 20. Applying (12), with α = 0.5 and ΔA = 10:

If it is assumed that firms make a full adjustment each period (meaning λ = 1), then each step in the convergence process toward equilibrium will correspond to one of the terms in the infinite series shown above.

The initial change in autonomous demand (ΔA = 10) causes a situation of excess demand. Actual output is 980, whereas total planned expenditure has suddenly increased to 990. Firms meet the higher demand by running down inventories by 10. This represents unplanned investment of -10.

By assumption, firms respond by trying to eliminate the unplanned investment. In step 0 of the adjustment (t = 0), firms expand production by 10. This is equal to the first term in the power series: 10 x 1 = 10(1 – 0.5)^{0}.

The increase in actual output of 10 induces extra expenditure of 5, equal to (1 – α)ΔY. As a result, there is still excess demand, but now only of 5 rather than 10.

In step 1 (t = 1), firms expand production again, this time by 5. This corresponds to the second term in the power series: 10(0.5) = 10(1 – 0.5)^{1}.

More generally, the adjustment that firms make in step t of the convergence process will be given by the *(t+1)*th term in the series: ΔA(1 – α)^{t} = 10(1 – 0.5)^{t}. For instance, in step 3, firms adjust output by 10(1 – 0.5)^{3} = 1.25.

The sum of the adjustments made over n steps asymptotically approaches 20, with both actual output and planned expenditure converging on 1000.

Visually, this adjustment has already been illustrated in the graph provided earlier for the case of λ = 1.

**6. Convergence as a Power Series: λ < 1**

We have seen that if λ takes a value less than 1, the adjustment process will be more gradual. The power series needs to be modified to:

This is a more general version of (12). In the special case of λ = 1, the above formula reduces to the earlier one. The effect of λ < 1 is to spread the adjustment process over more steps. The adjustment in the initial step is smaller, but the size of the adjustment each period shrinks less rapidly than when λ = 1.

The value of λ affects the speed of adjustment but, within the model, not the level to which actual output and demand converge. Since Y* = A_{ }/_{ }α, the point of convergence depends only on autonomous demand (A) and the marginal propensity to leak (α).

The rest of this section can be skipped without missing much economic content. But for readers who may be curious, it is pretty easy to arrive at the formula given in (12′). Each step of the adjustment process can be described algebraically, beginning with t = 0, until a clear pattern emerges. Since this kind of scenario arises quite frequently in economics, perhaps it is worth spelling out the working.

The sequence of events begins with a one-off change in autonomous demand, or ΔA. This creates excess demand of ED_{0} = ΔA. In response, firms begin to adjust actual output to demand by trying to eliminate unplanned investment.

Let Δ_{t}Y be the change in actual output at step t of the adjustment process. The change in actual output (and income) will induce additional private consumption (net of endogenous imports) of Δ_{t}C. Specifically, a fraction (1 – α) of the extra income will go to induced demand. This constitutes excess demand, but less than was created in earlier steps.

The excess demand of period t (ED_{t}) will be reduced in period t+1 to the extent that extra output is produced in the new period, but will be increased to the extent that extra demand is induced. That is, ED_{t+1} = ED_{t} – Δ_{t}Y + Δ_{t}C.

Putting all this together, a pattern emerges within a few steps:

The adjustment of actual output in step t will be equal to λΔA(1 – αλ)^{t}. When t = 0, this reduces to λΔA. When t = 1, the expression reduces to λΔA(1 – αλ).

The total change in actual output over the entire adjustment process will be the sum of all these step adjustments, which is what (12′) says.

**7. Adjustment of Growth Rates**

It is also possible to represent the adjustment process in terms of growth rates. This will be useful if considering an economy with a continual tendency to grow over time (a task left for another time).

At the moment, we are considering a simpler economy that only grows (or shrinks) in the process of adjustment to equilibrium. So, in the present context, the growth rate will settle at zero once equilibrium is reached.

Recall that unplanned investment, as defined earlier in (1), is identically equal to the amount of excess supply in the economy:

We have expressed the change in actual output as a function of excess demand. Combining (7) and (8) from earlier:

If, conceptually, we break down the steps of the adjustment process into tiny enough increments of time, we can think of the adjustment process as a continuous one and recast (8) as:

Here, Y dot is the derivative of output with respect to time (dY_{ }/_{ }dt).

The growth rate of actual output (g) is found by dividing Y dot by Y:

This growth rate diverges from zero whenever the economy is out of equilibrium. In situations of excess demand, Y_{d }/_{ }Y is greater than one and the actual growth rate rises above zero. The growth rate will remain positive until equilibrium (Y_{d }/_{ }Y = 1) is attained. Conversely, the actual growth rate is negative in situations of excess supply, and remains that way until convergence is complete.

Under present assumptions, the equilibrium growth rate (g*) is determined by the exogenously given growth rate of autonomous demand. This can be seen by differentiating the expression for equilibrium output (Y* = A_{ }/_{ }α) with respect to time and dividing by Y*:

Since autonomous demand is being held constant throughout the adjustment process, g_{A} and g* are both zero over the relevant time horizon.

In more elaborate versions of the model, the behavior of the equilibrium growth rate can be more complicated. The simplicity, in the present context, is due to: (i) all demand other than net induced consumption being treated as exogenous; and (ii) the marginal propensity to leak being assumed strictly constant. Introducing more endogenous elements to demand will complicate the behavior of g*. (Examples involving endogenous investment and an endogenous component to government spending are discussed in a previous post.)

The convergence of the actual growth rate (g) to the equilibrium growth rate g* (and g_{A}) is illustrated below for a couple of values of λ.

The growth behavior of total demand is also illustrated in these diagrams. Like actual output, demand grows at a rate other than zero outside equilibrium. Its growth rate (g_{d}) does not diverge as far from the equilibrium growth rate as g does, because the required adjustment of demand is less than the required adjustment of output. By the logic of the model, whenever there is disequilibrium, production needs to “catch up” to demand. To do so, it needs to grow (or shrink) faster than demand during the process of adjustment.

The growth behavior of demand is implicit in (3), which defines planned expenditure as the sum of induced and autonomous demand:

Differentiating this expression with respect to time gives:

Dividing through by Y_{d} and multiplying Y dot by Y_{ }/_{ }Y and A dot by A_{ }/_{ }A gives:

The expression for g in (13) can now be substituted into the growth equation for demand. Upon rearrangement:

Since the level of autonomous demand is held constant throughout the adjustment process, the growth rate of autonomous demand (g_{A}) is zero, making the second term on the right-hand side of (14) also zero:

The sign of g_{d} simply depends on whether the fraction Y_{ }/_{ }Y_{d} is greater than, equal to, or less than one. When there is excess demand, Y_{ }/_{ }Y_{d} is less than one and g_{d} is positive. This is consistent with the behavior depicted in the diagrams above. In the reverse case of excess supply, Y_{ }/_{ }Y_{d} is greater than one and g_{d} is negative. In equilibrium, the term on the right-hand side of (14′) vanishes and g_{d} equals zero, as expected.

It has been stated that, out of equilibrium, the divergence of g from the equilibrium growth rate (g* = g_{A} = 0) is greater than the divergence of g_{d}. This can be verified working from the expressions for g and g_{d} provided by (13) and (14′), respectively:

The growth rate of actual output (g) will be greater in absolute value than the growth rate of total demand (g_{d}) provided:

From (4), Y = (1 – α)Y + A + I_{u}, which implies that I_{u} = αY – A. This can be substituted for I_{u} in the above inequality to obtain the following condition:

This is one of the two conditions for dynamic stability already discussed. Since, within the model, there is always a positive amount of autonomous demand, the condition A > 0 automatically holds. This verifies that, out of equilibrium, the absolute value of g will exceed the absolute value of g_{d}. In other words, g will take more extreme values than g_{d} during convergence to equilibrium.

It is possible to say more about the growth behavior of actual output, total demand and equilibrium output, but this is perhaps better left for a discussion of a continually growing economy.

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**The Basic Framework**

The level of ‘real’ economic activity – as measured in the National Accounts as Gross Domestic Product at constant prices – will be considered demand determined along the lines of Keynes and Kalecki. It is assumed that normally there are reserves of labor-power and other resources as well as spare productive capacity in the form of underutilized plant and equipment. So long as this assumption holds, it is possible for output to be adjusted to demand through variations in the level of activity.

Inside resource and capacity limits, the level of output is regarded as being determined more or less independently of prices. In exceptional circumstances, when demand outstrips the capacity of the economy to respond in real terms, there would be demand-side price pressures and/or non-price rationing. But, for the most part, the economy is considered to be demand constrained, inside ultimate supply-side limits.

This is regarded as true over any time frame. In a period so short that capacity is treated as fixed, output is adjusted to demand through variations in the rate of capacity utilization. In response to stronger demand, firms utilize their given facilities more fully. Over longer time frames, in which capacity should be considered variable, output can be adjusted to demand not only through variations in the utilization rate but by altering capacity itself, investment being the means for doing this.

Both the level of activity and the growth rate of the economy are in this way considered to be demand led.

This perspective on output and growth is intentionally left open in terms of other key economic questions, such as value, price and distribution. This leaves space for competing theories on these matters. If distribution, for instance, is thought to impact systematically on the level of output, it can be introduced through explicit assumptions about the determinants of variables or parameters that, in the present discussion, are simply taken as exogenously given. A well known example is Kalecki’s adoption of the classical assumption that workers, in aggregate, consume all their wages, which makes the size of the multiplier dependent on the distribution between wage and profit income.

The perspective presented here is also open when it comes to the roles of money and finance, although the natural fit with endogenous money and state money theories will probably be evident.

Cumulative developments in the sectoral balances that are thought to impact on private consumption could be worked into an explanation of that part of consumption that here is simply treated as autonomous. Within the framework to be discussed, this would also have an impact on private investment.

**Keynesian Output Determination**

We can start with the standard Keynesian model of output and income determination (although Kalecki’s framework would serve just as well). Total output (Y) is equal to the sum of expenditures. In the simplest versions of the model, all expenditures other than the greater part of private consumption are assumed to be exogenous. Induced consumption is taken to equal c(1 – τ)Y, where c and τ are the marginal propensities to consume and tax, respectively. For simplicity, both are assumed constant. Supposing a closed economy, also for simplicity, exogenous demand includes autonomous private consumption, private investment and government spending. These categories of demand can be grouped together as autonomous expenditure (A). Output will equal the sum of induced consumption and autonomous expenditure:

All variables are taken to be functions of time. Unless there is risk of ambiguity, time subscripts will be omitted. If we let α = 1 – c(1 – τ) represent the marginal propensity to leak to taxes and saving, which implies that c(1 – τ) = 1 – α, the above expression can instead be written as:

This notational choice will simplify some of the algebra later.

If (1) is viewed in terms of actual output, it is merely an identity. The identity holds because of the National Accounting convention of treating changes in inventories, whether anticipated or not, as part of investment. Over time, however, unanticipated variations in inventories can be expected to induce an output response. These inventory changes, to the extent that they are unexpected, amount to unplanned investment. A key assumption of the Keynesian income-expenditure model is that firms expand or cut back production in an attempt to eliminate unplanned investment or disinvestment. Granted this output response to the emergence of excess supply or demand, and given the level of exogenous variables and parameters, there will be a tendency for actual output Y to converge on output level Y* (obtained by solving (1) for Y):

This notional level of output is usually referred to as ‘equilibrium output’. In what follows, it will be the focus of attention. It is possible to delve into the relationship between Y and Y*, but this exercise is left for another day.

The term ‘equilibrium’ is often taken to have quite negative connotations in heterodox circles. With that in mind it is perhaps worth stressing that the requirements of equilibrium, as defined by (2), are far less onerous than those pertaining to some other notions of equilibrium. In particular, there is no implication that all markets must clear. Equilibrium, in the present sense, simply refers to a situation in which planned leakages (in a closed economy, taxes plus saving) happen to equal planned injections (government spending plus private investment) so that the sum of all monetary demand (planned expenditures) equals the sum of output supplied (also measured in monetary terms). There may be mismatches of supply and demand in many markets, but if the excess demands and supplies happen to sum to zero, actual output will be at Y*.

If capacity is taken as fixed – as is often the case in short-run models – Y* will be stable until there is a change in one of the exogenous variables or parameters (summarized as A and α). As will be apparent by the end of the post, over longer time frames, in which capacity is free to vary, neither Y* nor the growth rate of Y* will necessarily be stable other than in the simplest versions of the model that take all expenditure other than induced consumption as exogenous. Over longer time frames, a stable growth rate requires more than an equality of planned leakages and injections. In particular, capacity would need to be fully adjusted to demand.

Importantly, the model does exhibit ‘dynamic stability’ provided that: (i) there is a positive level of autonomous demand (A > 0); and (ii) the marginal propensity to leak is greater than zero (α > 0). The property of dynamic stability is a consequence of the key behavioral assumption that firms seek to eliminate unanticipated changes in inventories. Dynamic stability ensures that there is a continual tendency for Y to converge toward Y*.

The model’s property of dynamic stability perhaps provides some justification for focusing, at least in certain analytical contexts, on the behavior of Y*, rather than explicitly dealing with the distinction between actual and equilibrium output. In what follows, the asterisk in Y* will be dropped unless ambiguity seems likely, with output Y* simply referred to as Y. But it should be kept in mind that discussion pertains to the behavior of notional output Y* rather than actual output Y.

**A Growing Economy**

The growth behavior of this notional level of output, which we are simply denoting Y, can be considered by differentiating (1) with respect to time:

Here, Y dot is the derivative of output with respect to time (dY/dt). Similarly, A dot = dA/dt. Collecting terms involving Y dot to the left-hand side gives:

Dividing both sides by αY and multiplying the right-hand side by A/A (= 1) modifies this to:

A time derivative of a variable divided by the variable itself gives the variable’s instantaneous growth rate. In our case, Y dot/Y is the instantaneous growth rate of output Y, which can be denoted g. Likewise, A dot/A is the instantaneous growth rate of autonomous spending A, which can be denoted g_{A}:

Recalling from (2) that Y = Y* = A / α, the fraction on the right-hand side reduces to one. So, in this simple version of the model, equilibrium output grows at the same rate as autonomous demand:

The growth rate of equilibrium output remains constant so long as the growth rate of autonomous demand remains constant (which, of course, may not be for long at all).

**A First Complication: Endogenous Private Investment**

In terms of growth behavior, the model as presented so far is as simple as it gets. The reason for this is that: (i) all expenditure other than induced private consumption has been assumed exogenous and part of autonomous expenditure; and (ii) the only endogenous component of spending (induced private consumption) has been treated as a constant fraction of income, because of the simplifying assumption that the marginal propensities to consume and tax are both constant. The behavior of equilibrium output becomes a little more complicated once we allow for the idea that private investment is induced by growing output and income. The basic rationale here is that higher rates of capacity utilization, which occur when output is expanded relative to capacity to meet rising demand, will encourage additional investment as a means for firms to adjust capacity to demand.

Following the supermultiplier theory, this situation can be represented by a simple modification of expression (1). Output will now equal the sum of induced consumption, endogenous private investment and autonomous demand:

The second term on the right-hand side, hY, is endogenous planned investment (I = hY). Unlike the marginal propensity to leak, the ‘marginal propensity to invest’ h, while also a fraction between zero and one, is not considered to be a constant. Instead, h is assumed to rise when the rate of capacity utilization is above ‘normal’ and to fall when the utilization rate is below normal. In the present context, the marginal propensity to invest can also be thought of as the investment share in income, because I = hY implies h = I/Y. It is supposed that investment rises and falls as a proportion of income in response to variations in the rate of utilization.

The final term in (1′) is also somewhat altered compared with (1). Z, like A, refers to autonomous expenditure. But this expenditure now also has the characteristic that it does not directly add to private-sector productive capacity. In the literature, this category of expenditure is sometimes referred to as ‘non-capacity-enhancing autonomous demand’. In a closed economy, Z includes autonomous private consumption and government spending. In an open economy, it would also include exports.

Solving (1′) for Y enables us to express equilibrium output as a multiple of autonomous demand Z:

Dynamic stability now requires Z > 0 and α > h. The fraction 1/(α – h) is known as the ‘supermultiplier’. It is larger than the regular multiplier because of the inclusion, in its denominator, of the marginal propensity to invest. (At the same time, compared with (2), a term for investment has been removed from the numerator, so the supermultiplier operates on a level of autonomous expenditure that is smaller than in the simpler version of the model.) For example, if α (the marginal propensity to leak to taxes and saving) is assumed to be 1/2 and, at a given point in time, the marginal propensity to invest happens to be 1/6, the regular expenditure multiplier will be 2 whereas the supermultiplier will be 3. An exogenous increase in Z will cause an expansion of output and income that induces further private consumption and investment.

Differentiating (1′) with respect to time, we have:

Here, the product rule [d(uv)/dt = u’v + uv’, where u’ and v’ are the time derivatives of u and v, respectively] has been applied to the term hY because both h and Y are functions of time. Collecting all the terms involving Y dot to the left-hand side and factorizing gives:

Following the same basic procedure as earlier, we can divide both sides by (α – h)Y and multiply Z dot by Z/Z to obtain:

Referring back to (2′) we can see that Z/(α – h) = Y, which makes the last fraction in the above expression one. After reordering terms and noting that g = Y dot/Y and g_{Z} = Z dot/Z, we have:

Growth of equilibrium output now depends not only on the instantaneous growth rate of autonomous demand but also on the instantaneous growth rate of the supermultiplier, which is the second term on the right-hand side of (3′). This last point can be seen by differentiating the supermultiplier 1/(α – h) with respect to time [applying the quotient rule, which says d(u/v)/dt = (u’v – uv’)/v^{2}] and dividing this derivative by the supermultiplier itself. The result is the second term on the right-hand side of (3′).

It is possible to say more about this growth behavior by fleshing out the notion of induced investment, its relationship to the behavior of the utilization rate, and the ongoing attempts by firms to adapt capacity to demand. For now, suffice to note that unless capacity is fully adjusted to demand, h dot (the instantaneous change in the investment share) will be nonzero (other than possibly momentarily when switching sign). As a consequence, equilibrium output will grow more or less rapidly than autonomous demand, according to whether the investment share is rising or falling (h dot is positive or negative). In contrast to the simplest version of the model, the growth rate of equilibrium output is variable rather than constant – even though it pertains to a situation in which supply continually equals demand – unless the investment share has stabilized.

For readers who may be interested, a few earlier posts (for example, here and here) discuss aspects of growth under the assumption of endogenous private investment.

**Another Complication: A Job Guarantee**

It is possible to endogenize other components of spending. Doing so will further modify the growth behavior of equilibrium output. An example that has been touched on in a couple of earlier posts concerns a job guarantee. Under this program, a part of government spending would respond endogenously to variations in output and employment in the broader economy (by which is meant the non-job-guarantee sector). Strictly speaking, this spending would adjust in response to fluctuations in the composition of employment between the two sectors. But it is possible to consider the spending as endogenous with respect to output and income as well, because of the close connection between output and employment.

Modifying expression (1) once more, output for the economy as a whole is now the sum of induced private consumption, endogenous private investment, endogenous job-guarantee spending and autonomous demand:

Here, jY represents government spending on a job guarantee (G_{j}), where j is the proportion of income spent on the program. Like h, j is variable rather than constant. But unlike h, j varies countercyclically rather than procyclically. It automatically rises in economic downturns and falls during upturns. A couple of earlier posts (here and here) discuss the behavior of job-guarantee spending. In those posts, job-guarantee spending was denoted G_{g}. From now on, I intend to opt for G_{j} instead (j for ‘job guarantee sector’) so that g can be reserved for growth rates. Since G_{j} = jY, it follows that the job-guarantee spending share in income is j = G_{j}/Y. An expression for j can be derived from the expressions for G_{j} and Y that are presented in the earlier posts. This is left for a possible future post.

Solving for equilibrium output gives:

Dynamic stability now requires Z > 0 and α – h – j > 0. The supermultiplier has become 1/(α – h – j). An exogenous increase in autonomous demand Z will boost output as well as employment in the broader economy. One consequence is that h will tend to become bigger due to a strengthening of the inducement to invest. Viewed in isolation, this will tend to make the supermultiplier larger. But another consequence of stronger autonomous demand is that j will tend to shrink, because rising output implies a stronger employment outcome in the broader economy, reducing the need for job-guarantee spending. This, viewed in isolation, tends to make the supermultiplier smaller. The overall impact on the supermultiplier will depend on the combined impact of stronger autonomous demand on the investment share (h) and job-guarantee spending share (j).

Adopting the same procedure as we have already adopted twice in earlier sections of the post enables the derivation of an expression for the growth rate of equilibrium output:

Here, time derivatives are denoted with the prime (‘) symbol rather than dots, because j already has a dot. Expression (3”) says that the growth rate of equilibrium output deviates from the growth rate of autonomous demand to the extent that there are variations in the investment and/or the job-guarantee spending shares in income. As before, the growth rate of equilibrium output will equal the sum of the growth rates of autonomous demand and the supermultiplier.

**Concluding Remark**

Even though we have abstracted from the distinction between actual output Y and equilibrium output Y*, which amounts to assuming that the economy is continuously operating at a level of output that equates aggregate supply with aggregate demand (or planned leakages with planned injections), this does not imply a constant rate of growth (let alone a constant level of output) other than in the simplest versions of the model. In the presence of endogenous investment and/or a job guarantee, stability in the equilibrium growth rate would further require that capacity had fully adjusted to demand (stabilizing the investment share h) and/or the composition of employment had settled at a particular sectoral configuration (stabilizing the job-guarantee-spending share j). Needless to say, there is little reason to expect that such stability in the equilibrium growth rate would ever be maintained for long, or even be attained at all.

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For the principle of effective demand to make sense, it is necessary: (i) that the economy is operating within the limits of its productive capacity (defined by the plant and equipment that can currently be brought into use); and (ii) that there is sufficient availability of labor-power and natural resources for production to be expanded in response to rising demand. If either of these conditions were violated, the economy would be supply (rather than demand) constrained. The Keynesian or Kaleckian view is that normally the economy is operating inside the ultimate supply limit to a degree that is determined by demand. The economy is therefore regarded as demand constrained under normal circumstances.

The demand-led growth process can be regarded as proceeding largely independently of the price level. In the context of a variable productive capacity, it is conceivable (though not inevitable) that output and capacity could respond to rising demand without creating excessive pressure on prices from the demand side. This would not mean a constant price level. It would simply mean that changes in the price level would mostly be the result of factors operating on the supply side, through changes in financing and production costs and the aggregate markup over money wages.

Such a scenario is at least plausible because of a characteristic feature of capitalist economies that is especially evident in the manufacturing and services sectors; namely, firms typically operate with planned margins of spare capacity. In the US, for instance, average rates of capacity utilization have varied from a low of 67 percent to a high of almost 90 percent since 1967, when measurements began. This behavior is not out of the ordinary. Across industrialized economies, average utilization rates of somewhere between 80 and 85 percent seem typical. A strategic factor driving this behavior would appear to be a competitive imperative to meet intermittent peaks in demand through an expansion of output. A firm’s failure to do so, due to insufficient capacity, could see it lose market share to competitors.

There also appear to be technical factors at work, basically of an engineering nature. Much plant is such that, inside physical capacity limits, average variable cost (relating to wages and materials) can remain approximately constant when output is varied. If anything. falling average variable costs seem more likely than rising average variable costs in many contexts, because of the common practice of “hoarding” workers in downturns and delaying the hiring of new workers in the early stages of recovery. This results in pro-cyclical variations in productivity. On the other hand, the prices of raw materials are more sensitive to demand than other prices, and could rise with output.

In general, nothing very precise can be said about the relationship between costs and output. Some demand-led growth theorists, rather than making a simplifying assumption about the behavior of costs, prefer instead to treat price determination as analytically separable from output determination and growth. Others suggest that the most appropriate simplifying assumption is a constancy in average variable costs over the relevant range of capacity utilization. This assumption implies that any firm with fixed costs will face falling unit costs (falling average costs) as output expands. Under either approach to pricing, normal pricing can be regarded as reflecting the cost associated with meeting the average level of expected demand. This average level of demand will correspond to an expected average rate of capacity utilization.

Within fairly wide limits, firms in the manufacturing and services sectors will adjust output to demand without necessarily altering cost-determined prices. Even where firms do alter prices as well as output in response to demand, these price effects are likely to be short-lived. Over a longer time frame, either the alteration in demand will prove to be a temporary fluctuation, in which case its effects will reverse, or the change in demand will turn out to be persistent. If the change in demand is persistent, it will call for an alteration in productive capacity and so have implications for the rate of investment. Once the additional capacity comes on line, the price pressures will dissipate.

In other words, a sustained growth in demand that pushes the economy toward full capacity is likely to induce capacity-enhancing investment. Increasingly, firms will find that they are mostly operating beyond their intended average or ‘normal’ rates of utilization. This is also likely to manifest as a higher realized rate of profit (because, for given distribution of income and capital-to-output ratio, the actual rate of profit and utilization rate move together). If the growth in total demand persists for some time, it becomes increasingly profitable for firms to install additional plant and equipment.

If it were not for the presence of spare capacity and the possibility of adding to capacity over time, the acceleration in investment would cause demand to outstrip supply limits. Whereas the impact of investment on demand is immediate, its capacity effects only register with a delay. It takes time to construct new plant and equipment. But because the economy normally operates with spare capacity, the demand effects of stronger investment can usually be accommodated through variations in output without an emergence of excessive demand-side inflationary pressures.

It should be kept in mind, though, that this argument relates to the average rate of utilization for the economy as a whole. There can be bottlenecks due to some sectors hitting full capacity before others. If so, in reality there are likely to be some price effects mixed with the output effects before capacity has had time to adjust.

The continual, gradual process in which firms attempt to adapt capacity to demand is carried out partly through the expansion or contraction of existing industries, including by entry or exit of firms, as well as through the emergence of new industries and the disappearance of declining ones. At a disaggregated level, there will be fledgling industries with capacity temporarily far below expected demand and declining industries with lots of unwanted capacity.

In this conception of growth, there needs to be a source of demand that is independent of endogenous, capacity-enhancing investment so as to induce that investment. In the approach considered here, the key role is played by components of autonomous demand that do not directly add to private-sector productive capacity. Government spending, autonomous private consumption expenditure and, for open economies, exports are the main examples of this kind of demand. The significance of this demand is that it promotes fuller capacity utilization. It calls for expansion of output without directly adding to private-sector capacity. Persistent growth of this demand tends to push the economy towards fuller rates of utilization and so encourages investment in additional capacity.

**Related Posts**

A comparison between the Keynesian or Kaleckian view that the economy is normally demand constrained with the opposing view is provided in:

Institutions, Monetary Operations and a Demand-Led Global Economy

Demand-led growth is considered in a bit more depth in:

The Role of Government Spending in Fostering Global Growth

Demand-Led Growth With Cycles – A Simple Model and Illustration

Demand-Led Growth – Government Spending and the Investment Share

]]>Or similarly it could be asked, if the robots ever became better than us at everything, what would be the point of life?

I don’t know the limits of artificial intelligence, but one answer to these questions is that we would be freer to focus on learning, exploration, self and group development, social interaction and play. If these robots ever became so amazing that they could compose better music than us, create more captivating movies, engineer sturdier bridges, devise smarter phones, play a more riveting style of football and produce superior widgets of all kinds in next to no time, then by learning from the robots, their activities and their output, we could be educated in all sorts of ways that would enable our own human improvements. We might never match the robots, but our own understanding and appreciation of life and the universe would expand tremendously.

Such a prospect need not be daunting so long as we manage the social transition. It would be necessary either to disassociate income from labor time or to re-envisage the nature of paid employment to encompass a far richer set of human activities.

If the transition can be accomplished, the prospects seem bright.

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Although the finer points of MMT can get quite involved, the most basic takeaway is very simple. For societies with currency-issuing governments:

If something can be done, it is “affordable”.

If we have access to the raw materials, the labor power, the skills, the equipment and the facilities needed to produce something, then we can afford to produce it. The cost of doing so is not financial. The cost is a real cost: the exertion of human effort and know-how, the wear and tear on facilities and equipment, and the depletion of natural resources.

On one level, it is bizarre that this basic takeaway of MMT is not already mainstream. If the idea is heterodox, it is only because we are currently living in a very topsy-turvy world, in which up is presented to us as down, black as white, with everything reversed. In reality, it should be much harder to believe the opposite: that what we are capable of is impossible.

A kind of collective dementia has developed, so much so that, as the linked article observes, MMT initially strikes many of us as:

one of those Alice in Wonderland, down the wormhole kind of concepts that neutralises every received wisdom … prepare to be blown away and forget what you think you knew about money.

But what did most of us think we knew about money before encountering MMT or related ideas? Chances are, money seemed confusing, its basic mechanics hazy. In the mental fog, all kinds of superstition could take hold. Fantasies of a currency somehow arising spontaneously out of nature.

It is obvious, once freed from the mental fog, that somebody has to create the currency. It does not grow in the ground or answer to the cycles of the moon. For a currency to exist, it must be issued by its issuer.

It is so obvious, the concept must be heterodox.

But perhaps this will not be the case for much longer. We may be witnessing the early stages of the obvious going mainstream.

From the article:

It therefore appears that Theresa May’s oft-repeated refrain attacking Corbyn on the grounds that there is no such thing as a magic money tree is not exactly true. So if money can basically be created with the press of a button, then suddenly our world appears to be (pace Panglossian disciples) the craziest of all possible worlds.

It is not crazy, of course. It just seems that way to minds conditioned by forty years of neoliberal thinking. The craziest of all possible worlds would be one in which a currency did not originate from its issuer.

In effect, the usual dictum of “tax and spend” is inverted to “spend and tax” with spending stimulating jobs and growth, which can later be taxed. … Taxation is not therefore a way of raising revenue …

Since taxes are settled only in the government’s currency, the settlement of taxes cannot occur before the currency has been issued. Something cannot be destroyed (taxed) before it has been created (issued). Accordingly, taxes cannot be a revenue source for a currency-issuing government. Government spending (or lending) creates the currency that is needed for taxes to be paid.

This in no way implies a reduced significance for taxes. To the contrary, taxes are crucial.

At the most fundamental level, imposition of a tax that can only finally be settled in the currency ensures a willingness, within the community, to accept the currency in exchange for goods and services. This is what makes it possible for government to hire staff or purchase goods and services with its own currency.

The effect is most obvious in the case of taxes unrelated to income. For example, a simple head tax of a fixed amount would require everybody to obtain the currency in order to pay the tax.

But the effect also works when taxes are imposed on income. This is because, for tax purposes, income is assessed in terms of the government’s currency. Income received by members of the community will be assessed in the currency and, above a certain threshold, be subject to tax. Since most people need an income to survive, or depend upon somebody who has an income, the imposition of an income tax ensures demand for the currency in much the same way as the imposition of other taxes.

Taxes also play an important role in moderating the overall level of spending in the economy and can be used to influence behavior.

At this point, you might understandably be asking why on earth we do not just spend our way out of the current mess. And while we are at it – give the NHS more money, shelter the homeless and feed the poor of the world. This is where we come up against the ideological edifice of neoliberalism.

Yes, the obstacle is political, partly due to a collective failure to comprehend the capacities of a currency issuer.

It is not spending, as such, that gets us out of our mess. It is the actual doing of what needs to be done that gets us out of the mess. Running the NHS, sheltering the homeless and feeding the poor are achieved through the employment of appropriately trained staff and use of real resources. But, in a monetary economy, at least in the monetized sectors, the doing fails to occur in the absence of an expenditure of money. A refusal to spend prevents the doing. It is not that the doing is impossible. It can be done, provided the necessary workers and resources are available, as soon as the expenditure is made.

Therefore:

Public spending cannot be unlimited and must be commensurate to the capacity of the economy…

The limit to public spending is the amount of useful things we are capable of doing with the resources we have. Spending beyond that point – the point where we are fully employing our productive capabilities – would be useless, because it would add nothing to production, and would also create excessive inflationary pressure. This is true of any spending, whether public or private. But inside this real constraint, there are no limits other than our capacity for clutching defeat from the jaws of victory (political obstacles).

In other words, a currency-issuing government can always purchase what is available for sale in its own currency. It may or may not be in a position to purchase goods and services available in some other currency. And, of course, things that are currently impossible to supply cannot be purchased in any currency.

But in any case, if we can do it, it is “affordable”.

**Related Posts**

Why Do We Accept Fiat Currency?

Pain of Austerity Brings No Future Gain

Short & Simple 2 – Establishing a National Currency

Who Will Accept it? Currency-Issuing Govts are Constrained by Resources, Not Money

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**The Model**

In the basic income-expenditure model, total output (Y) converges on the level Y = A/α, where A is net autonomous expenditure and α is the marginal propensity to leak from the circular flow of income to taxes, saving and imports. Introducing a job guarantee into the model modifies this to:

where G_{g} is the government’s spending on the job guarantee. The main preoccupation of the earlier post was to find an expression for this component of government spending, which adjusts automatically to variations in the number of people who accept the standing offer of a job. It was shown that within the model:

In this expression, L_{F} is the level of employment associated with full employment. This level of employment is determined exogenously by workers themselves in the sense that a job at the living wage can always be obtained in the job-guarantee sector. (A more sophisticated approach might also allow for endogenous changes in the level of L_{F} by explicitly recognizing that some people unwilling to accept job-guarantee jobs will exit employment in a downturn, due to layoff, and re-enter in an upturn.) The cost of the job-guarantee program per unit of labor is w_{L}/ϕ, where w_{L} is the living wage paid per unit of job-guarantee employment and ϕ is the share of wages in total job-guarantee costs. Productivity in the broader economy is denoted ρ_{b}. As discussed in the earlier post, productivity in the job-guarantee sector can be interpreted as being equal to the living wage (ρ_{g} = w_{L}). The difference in productivity between the job-guarantee program and the broader economy implies that average productivity for the economy as a whole (ρ) varies with the composition of employment between the two sectors (assuming ρ_{b} > ρ_{g}).

Since the present focus is on total output and employment, it is convenient to substitute the expression for job-guarantee spending given by (2) into (1). Rearrangement (eventually) gives:

Of the economy’s total output, Y_{b} is the output produced within the broader economy and Y_{g} = ϕG_{g} is the amount produced in the job-guarantee sector. An expression for output of the broader economy can be obtained by subtracting ϕG_{g} (= Y_{g}) from both sides of (1), substituting for G_{g} and solving for Y_{b}. An expression for Y_{g} can be obtained simply by multiplying the expression for G_{g} in (2) by ϕ.

Expressions (3) to (5) show that, once a job-guarantee is introduced, Y, Y_{b} and Y_{g} can be affected by exogenous changes on both the demand and supply sides of the economy. On the demand side, there is the familiar effect of exogenous changes in autonomous expenditure (A) or changes in the marginal propensity to leak from the circular flow of income (α). On the supply side, an exogenous change in the level of total employment (L_{F}) will directly bring about changes in Y_{g} and hence Y and subsequently Y_{b}. Exogenous changes in other supply-side factors – the living wage (w_{L}), the wage share in job-guarantee costs (ϕ) and productivity in the two sectors (ρ_{b} and ρ_{g} = w_{L}) – make themselves felt through their impact on the size of the multipliers applying to A and L_{F}.

**Demand Stabilization**

Like other automatic stabilizers, a job guarantee would somewhat moderate fluctuations in total demand and output. In the following diagram, fluctuations in output are generated by arbitrarily letting private investment cycle between a high of 35 and a low of 25, beginning and ending at 30. The marginal propensity to leak is assumed to be 0.5, productivity in the broader economy 2, and the wage share in job-guarantee costs 0.67. Full employment is set at 100. Net autonomous spending other than private investment is set to 67 in the absence of a job guarantee, 64 when the job-guarantee wage is 0.5 and 58 when the job guarantee wage is 1. These values for net autonomous spending other than private investment are chosen to ensure that the initial and final levels of output are the same for the three scenarios, since the focus here is on illustrating the dampening of fluctuations.

Within the model, the stabilization effects are stronger when the living wage paid to job-guarantee workers is increased relative to productivity in the broader economy. This does not account, though, for the possibility that a higher living wage might encourage some employed workers to switch from the broader economy to the job-guarantee sector.

Fluctuations in the economy as a whole (represented by Y) are dampened more than fluctuations in the broader economy (represented by Y_{b}). The greater volatility of Y_{b} is illustrated in the next diagram. The values for the parameters and private investment are the same as in the previous diagram. Net autonomous spending other than private investment is set to 62 (rather than 58) when the living wage is 1, but given the same settings as before in the other scenarios.

To a significant degree workers would be sheltered from the volatility in the broader economy through variations in job-guarantee employment:

**A Supply-Side Effect**

From a Keynesian or Kaleckian perspective, a mere increase in potential output (such as through an increase in labor-force participation or an improvement in productivity) does not necessarily bring about an automatic increase in output and employment. The greater productive potential is only realized if demand happens to be sufficient to sustain the higher level of output.

The job guarantee introduces a mechanism through which an increase in labor-force participation directly initiates an expansion of demand, actual output and employment. The causation, in these instances, runs from individual decisions to enter the labor force to accept the job-guarantee offer, to an increase in employment, to an activated expenditure by government on the program and increased income and output, to multiplier effects in the broader economy.

Similar effects can be partially present under some other policy measures, though the effects are likely to be weaker and less direct. For instance, when government pays an unemployment benefit that is not contingent on prior employment (this occurs in Australia, for instance), a decision by a jobless person to enter the labor force activates, subject to administrative checks and with a delay, a benefit payment. This does not represent a direct addition to demand because the benefit payment is treated as a ‘transfer’ (or negative tax) in the National Accounts. Even so, to the extent the benefit payment is used for consumption expenditure (and mostly it will be), there will be an impact on demand with a subsequent multiplier impact on the economy. Such a policy therefore does enable a supply-side change to have an impact on demand, actual output and employment, though the channel is less direct. If the benefit is means-tested (this is the case in Australia), the channel will be narrower than otherwise.

Under a job guarantee, exogenous growth of the labor force would cause an increase in output and employment. The increase in output would be enabled by an automatic expansion of job-guarantee spending and an inducement of additional private consumption. Suppose, initially, that there is no change in the assumed behavior of other exogenous variables or parameters. In that case, although employment in the broader economy would expand, it would not keep pace with the expansion of the job-guarantee sector. This is illustrated in the next two diagrams. It is assumed that the level of employment associated with full employment (L_{F}) grows by 1 percent each period. The other exogenous variables and parameters take the same values as in earlier examples except that the living wage paid to job-guarantee workers is always 0.5 in the following scenarios.

For employment in the broader economy to grow in line with total employment, it would be necessary for autonomous spending to keep pace with the growth in the labor force. In the next two diagrams, it is assumed that autonomous spending other than private investment grows by the same rate as the labor force. Growth in private investment is also assumed to occur, but with an arbitrary delay of four periods.

**Concluding Remark**

The automatic translation of extra supply potential into actual demand, output and employment seems quite an interesting feature of the job guarantee.

**Academic Treatments of the Job Guarantee’s Macro Effects**

A more sophisticated and comprehensive empirical analysis of a job guarantee’s macro effects, which employs the Fair model (an econometric model developed in the tradition of the Cowels Commission by Ray Fair), is provided by Scott Fullwiler in a 2005 paper.

A recent paper by Warren Mosler and Damiano Silipo focuses on price-stabilizing features of the job guarantee.

**Introductions to the Income-Expenditure Model**

For newer readers, an introduction to the income-expenditure model is provided in:

Bill Mitchell – Spending Multipliers

Earlier heteconomist posts on the topic, with the easiest posts listed first, include:

Short & Simple 16 – The Expenditure Multiplier and Income Determination

Short & Simple 18 – Income Determination in a Closed Economy

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