Short & Simple 17 – A Notion of Macroeconomic Equilibrium

At the macro level, equilibrium requires that total demand in product markets equals total supply. This could occur at high or low levels of output and employment. Equilibrium implies stable output, but it does not ensure full employment.

Equilibrium is conceived as a position of stability at which the plans of economic agents (for example, households and firms) are fully ‘realized’ or compatible, so that no one desires to change their behavior.

In particular, equilibrium requires that firms sell what they expect. Otherwise, they would find it necessary to change their production levels and/or prices in an effort to rectify the situation. Their plans would be unrealized (or incompatible with the demand behavior, or plans, of their customers) and they would alter their behavior.

We have previously encountered the national accounting identity:

Total Output = Total Spending

In symbols:

Y = C + I + G + X – M

This identity does not imply equilibrium.

To understand why, recall that the identity follows from the way private investment is defined. Investment includes changes in inventories (unsold output). A change in inventories can be intentional or a mistake.

If firms sell what they expect, any change in inventories will be planned (or desired). However, if sales differ from the expected level, there will be an accumulation or depletion of inventories that is unanticipated (or unplanned or undesired).

For theoretical purposes, it can be useful to distinguish between planned and unplanned investment. This enables us to distinguish between equilibrium and disequilibrium situations. This distinction can be useful because it has ramifications for future behavior. Disequilibrium will encourage a change in behavior. Equilibrium will encourage a continuation of current behavior (unless there are known reasons to expect things to change in the future).

In making the distinction, ‘actual investment’ can be defined to include both planned and unplanned elements. ‘Planned investment’ differs from actual investment in that it excludes unanticipated changes in inventories. Unanticipated changes in inventories constitute ‘unplanned investment’:

Actual Investment = Planned Investment + Unplanned Investment

In symbols:

I = IP + IU

Unanticipated changes in inventories (IU) relate closely to equilibrium and disequilibrium.

Unexpectedly high inventories (IU > 0) are the result of excess supply. The unanticipated change in inventories is evidence that actual output (aggregate supply) exceeds planned spending (aggregate demand). For example, if firms expect to sell $100 billion of output but only sell $98 billion, there will be unplanned investment of $2 billion and an excess supply of the same amount.

Conversely, unexpectedly low inventories (IU < 0) are the result of excess demand. Inventories deplete as firms run down stocks to meet the unexpectedly strong demand.

It is still always true that actual output equals actual spending (Y = C + I + G + X – M). But whenever unplanned investment differs from zero, actual output will differ from planned spending. If we call actual spending AE (for ‘aggregate expenditure’) and planned spending AEP, we have:

Y = AE = C + IP + IU + G + X – M

AEP = C + IP + G + X – M

Equilibrium requires:

Y = AEP = C + IP + G + X – M

This only occurs when IU = 0.

Strictly speaking, all categories of spending involve planned and unplanned components. For example, households might consume less (save more) than intended because of a temporary shortage of output or interruption in production. Government might intend to spend a certain amount on public hospitals but confront a temporary shortage of qualified staff or materials. And so on. For simplicity, we will assume that most spending is at its planned level and any divergence of aggregate supply from aggregate demand is the result of unplanned investment.

The distinction between planned and actual spending is relevant to the idea of demand-determined output. In the previous post, it was supposed that output depends on autonomous spending (including private investment) and the marginal propensity to leak. Strictly speaking, the level of output that is determined by demand, in this framework, is the equilibrium level, not the actual level.

Call equilibrium output Ye, planned autonomous expenditure AP and the marginal propensity to leak α. Then:

This says that equilibrium output is a multiple of planned autonomous spending.

In situations of disequilibrium, firms are assumed to respond to excess demand or supply by altering the level of production in an attempt to eliminate unplanned investment.

This behavior will tend to bring output toward the equilibrium level. It is only in equilibrium that firms would have no reason to change behavior.

It perhaps should be emphasized that equilibrium can be thought of in relation to the level of output or the growth rate.

In reality, growth is the normal situation. In an economy that grows on average, a “continuation of current behavior” would mean an expansion of production in line with the current rate of growth. A “change in behavior” would mean an acceleration or deceleration in the rate of growth.

In the present context, we are considering production within a given period. Accordingly, the definition of equilibrium relates to the level of output. But the emphasis would need to change to the economy’s growth rate when considering how the level of production changes over time.

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10 thoughts on “Short & Simple 17 – A Notion of Macroeconomic Equilibrium

  1. Hi Pete

    In situations of disequilibrium, firms are assumed to respond to excess demand or supply by altering the level of production in an attempt to eliminate unplanned investment.

    This behavior will tend to bring output toward the equilibrium level. It is only in equilibrium that firms would have no reason to change behavior.

    Say we determined Ye.

    But Ye is not what the statistics show. In fact, we have

    Y = C + (Ip+Iu) + G + X – M > Ye

    (say, Iu > 0)

    This means that the economy is not in equilibrium. Supply exceeds demand, unplanned investment accumulates. Firms, therefore, reduce output, until Iu = 0 and Y = Ye.

    Does this tendency ensure the economy reaches equilibrium? I guess I can reformulate the question in these terms: is that equilibrium an attractor?

    Further, that equilibrium is stable, right? After all, once the economy reaches it, “the plans of economic agents (for example, households and firms) are fully ‘realized’ or compatible, so that no one desires to change their behavior”.

  2. Excellent questions, Magpie.

    I’ll get to your specific points, but first a general observation. The notion of macro equilibrium described in the post is sometimes resisted in heterodox circles because it can be perceived as going against a due recognition of time (temporality) and the non-equilibrium behavior that is central to some heterodox approaches. For example, it might seem to conflict with the temporal single-system interpretation of Marx’s value theory, which is temporal and non-equilibrium in its understanding of value and prices. Or it might seem to conflict with Post Keynesian notions of dynamic, non-equilibrium behavior.

    IMO any supposed inconsistency is only apparent, not actual. First, the notion of macro equilibrium implies only a stability in output or, more realistically, the growth rate, given no change in (i) the behavior of autonomous spending (A) and (ii) the marginal propensity to leak (α). Whenever there is a change in either A or α, the notional equilibrium level of output (or rate of growth) changes. Second, implicit in the first point is that there is no requirement that equilibrium entails either full employment or equilibrium prices. In fact, the notion of equilibrium described says nothing about pricing behavior if the analysis, as is usually the case, is conducted in real (i.e. price-deflated) terms. Nor does the notion of equilibrium require that sectoral supplies equal sectoral demands, because stability of output at the aggregate level could be due to the response to unplanned investment in excess-supply sectors being offset by the response to unplanned disinvestment in excess-demand sectors. Third, the purpose of the distinction between equilibrium and disequilibrium is to enable a focus on the behavior out of equilibrium and to say something about causation. The economy is rarely if ever in equilibrium, even in the quite unrestricted sense that it is described here.

    Turning to your specific questions:

    Does this tendency ensure the economy reaches equilibrium? I guess I can reformulate the question in these terms: is that equilibrium an attractor?

    It is conceived as a tendency. Hypothetically, if A and α (and hence the expenditure multiplier) remained constant for a sufficiently long time, and the output response to variations in unplanned investment is granted (i.e. the behavioral assumption is accepted), then output would converge on its equilibrium level. However, in practice, A and α will change before such convergence could take place. So the conception is more of a moving equilibrium to which the economy tends but never reaches.

    Similar observations can be made about macro equilibrium in terms of growth rate. However, in the context of growth, the key behavioral assumption concerns firms’ responses to variations in rates of capacity utilization. Hypothetically, if α and the growth rate of A remained constant for a sufficiently long time, then granted the behavioral assumptions, the economy’s growth rate would converge on the growth rate of so-called Z (which is that part of A that does not directly add to private-sector productive capacity). I’ve discussed this in a few earlier posts (for example, here) on the notion of demand-led growth.

    Further, that equilibrium is stable, right? After all, once the economy reaches it, “the plans of economic agents (for example, households and firms) are fully ‘realized’ or compatible, so that no one desires to change their behavior”.

    Dynamic stability requires (1) A > 0 and (2) 0 < α < 1. If these two conditions are met, then the economy will tend to converge to an output level or growth rate determined by the behavior of A and α. If (hypothetically) the economy were given enough time to converge to equilibrium, behavior (under the behavioral assumption specified) would then remain unchanged until one or both of A and α changed.

  3. As anyone who has been involved in business knows, both price and quantity are tweaked to maintain the desired level of inventory on an ongoing basis.

    There are “surprises” on both sides when behavior departs significantly from expectations. Either selling opportunities are lost owing to insufficient inventory, or unplanned inventory builds up.

    Usually firms initially institute sales (temporary priced reductions) to reduce unplanned inventory. Quantity is not the first tool most firms turn to in dealing with inventory issues, which are ongoing. Successful firms closely monitor inventory in an environment of just on time delivery to reduce carrying cost.

    Most economists have never been anywhere near a management position in a firm, so they are clueless about how firms actually work and how they compete to maintain and increase market share in a highly competitive environment, that is, unless they are protected by artificially constructed scarcity, which every firm aims at through intellectual property rights, for instance.

  4. Yes, Tom, agreed that both price and output are likely to adjust.

    The model does not preclude a price response. Rather, the analysis is conducted in price-deflated (“real”) terms. It is assumed that, below full capacity, there will be an output response to an increase in demand.

    The model is consistent with a view, for instance, that price variations will play a larger role in short-term adjustments than they will in long-term adjustments, once capacity has had time to adjust to demand.

    In the context of ongoing growth, short-run variations in capacity utilization enable output to adjust to demand (along with any price adjustment, especially in cases where capacity is constrained). whereas over a longer time frame, the capacity effects of investment adjust capacity to demand.

  5. Thanks Pete,

    Just one further question.

    If (hypothetically) the economy were given enough time to converge to equilibrium, behavior (under the behavioral assumption specified) would then remain unchanged until one or both of A and α changed.

    Can I take that to mean that “yes, the equilibrium Ye would be stable”?

  6. Of course, models simply for tractability. The aim is to capture the right of amount of information for the model to be useful as a tool for the purpose of its design.

    But what is the criterion from determining the “right” amount. If it’s science, it must be outcomes.

    While economists admit that their assumptions are not completely realistic, they point out that they don’t have to be for the purpose of the model as a tool. No problem if the outcomes corroborate.

    But then many economists do argue from models at least tacitly presuming they are realistic representations, even though when pressed with will admit they are not. Regardless, they then continue to argue that reality must be fit to the model based on purely formal grounds. “See, the math says so.”

    I have no problem with modeling as such. The problem I have as someone whose job is teaching critical thinking skills is employment of tools beyond their scope of application.

    From this standpoint, much of economics is irrelevant to most practical discussions. This is even true of micro, let alone applying macro to policy formulation. For example, business school use the case method and only require an intro course in econ, if they require one at all.

    Economic modeling is not particular instructive for firms, or they would be hiring economists, which they generally do not outside of finance. And in finance, its the computer science, math and physics people that get the choice jobs in constructing propriety trading algorithms (“algos”).

    Funnily enough, Ian Haztius, chief economists of Goldman, brought in Wynne Godley to advise on the sectoral balances model. Godley was not an academic economist but a Treasury man. Godley was a major influence on MMT though his development of the stock-flow consistent accounting approach to macroeconomics instead of the neoclassical approach based on formalism.

    From the point of view of SFC modeling, economic entities, whether firms or nations, and even the global economy are always “in equilibrium” dynamically from the POV of accounting, and when an entity gets “out of equilibrium,” it becomes insolvent and is either sold, re-capitalized, or liquidated, or the debt is otherwise wiped out, e.g, debt forgiveness.

    The way economists generally use the term “equilibrium,” it is a squishy metaphysical concept since major factors are not specified operationally. That is to say, the modeling hangs in the aether rather than being grounded in observable reality.

    I would use Occam’s razor and dump the term, or do something like Jason Smith with is doing with his information transfer economics, where equilibrium makes sense based on data and without ideology.

  7. Magpie, yes, for constant α between 0 and 1 and positive A, there is a tendency within the model to equilibrium and, if equilibrium is reached, the level of output is stable until either A or α change exogenously.

  8. Thanks for your thoughts, Tom.

    I think the main usefulness of math in economics is as a check of logic. It can’t do much more than verify that, given your behavioral assumptions, and given any identities that must hold, the argument that you think follows does actually hold up logically. That doesn’t make it right, of course. It is just a check on internal consistency. I agree, though, that there is a danger of making hidden assumptions without realizing it because of not understanding what the math is actually saying.

    I think in the case of the income-expenditure model, the use of math is quite appropriate and kept to a level that is both very simple and tractable. Basically, it is taking the accounting identity for GDP and making some explicit behavioral assumptions. As you are well aware (but for the benefit of readers who may not be), the key behavioral assumption is that the consumption function (and also leakages) are in a fairly stable relation to income. Without the assumed stability of these relations, we could no longer talk about a fairly stable multiplier effect of autonomous expenditure. Perhaps there are some heterodox economists (I don’t have any in mind) who would prefer to take the view that all spending is essentially autonomous, rather than treating consumption as induced in a fairly predictable fashion by income. Keynes justified a stable marginal propensity to consume by reference to a supposed psychological propensity of the community. I think there are institutional and systemic reasons for a degree of stability in the relationship between consumption and income (allowing of course that autonomous consumption is also a reality).

    To give just one example where a bit of simple math can help with a logical point, the opponents of fiscal policy have sometimes used the specious argument that (1) sustained economic growth is more rapid when investment is a higher proportion of income (true), therefore (2) government should cut back its spending (this conclusion does not follow from 1). If we make the behavioral assumptions of the income-expenditure model and add an assumption about how investment responds to variations in the rate of capacity utilization, then it follows logically (according to some simple algebra) that within resource limits, a faster growth of Z (meaning autonomous expenditure that does not directly add to private-sector capacity) results in a higher investment to income ratio and a lower Z to income ratio. Since government spending is part of Z, it is quite possible that a faster growth in government spending will result in both a higher investment to income ratio and a lower government spending share in income, given the behavioral assumptions. In a simplified model in which government spending is the only component of Z, the investment to income ratio rises and the government spending share in income falls the faster government spending grows so long as the economy remains inside resource limits. IMO that is not an obvious point to see — or at least to verify — without a bit of algebra to check that the conclusion does actually follow from the behavioral assumptions. (An earlier post explains this point. In doing so, it follows recent papers that are cited in the post.)

  9. I agree, Peter. My beef is with continuing to use ideologically-laden terms “equilibrium,” which is foundational in neoclassical (“marginalist”) economics, where it is a weasel word that is used to sneak in ideology.

    For example, in thermodynamics, equilibrium in a state space is defined as maximum entropy — no lumpiness. The corresponding state in economics would be equal distribution. This is even suggested by perfect competition where profit would be competed away. The existence of profit is evidence of economic rent that indicates the system in not “in equilibrium.” Since profit is assumed to bring forth investment in a capitalistic economy, capitalism depends on disequilibrium as a foundational assumption. Conventional economics was arguably developed to conceal that, and people are John Bates Clark are identifiable as its originators and conventional economists as its propagators.

    Another good example is the Cambridge capital controversy. Heterodoxy won but it didn’t change anything. The conventional economists were powerful enough in the discipline to ignore it.

    Heterodoxy really needs to refrain from using key concepts of conventional economics and especially foundational ones like “equilibrium.”

    Time to practice “rectification of names” (ht Confucius).

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