Illustration of Dynamic Adjustment with a Job Guarantee

In some recent posts, a job guarantee has been considered within the income-expenditure framework. One post in particular suggested a possible conceptualization of the dynamics of the model. It was shown that these dynamics are consistent with the model’s steady state requirements. Demonstrating this took a fair bit of algebra, which may have obscured for some readers the simplicity of the actual model. Much of the algebra was only needed for the specific purpose of verifying that the suggested dynamics are valid. At least for the version of the model presently under consideration, this task has now been accomplished. It is justifiable just to focus on the basic model which is really quite simple while still allowing for somewhat complicated behavior. Below, an example of this behavior is provided. First, though, it seems worth putting things into context with a quick summary of the key variables and parameters.

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Some Aspects of a Steady State with a Job Guarantee

The first section of the previous post outlined basic steady state relationships in a simplified economy with a job guarantee. There are various ways of expressing the same relationships that shed light on what is going on in the model. Here, a few ways of thinking about the levels of total income and job guarantee spending are noted.

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Quantity Dynamics with a Job Guarantee

A job guarantee would be a standing offer of a publicly funded job, with spending on the program adjusting automatically and countercyclically in response to take-up of positions. The likely feedback between spending on the program and activity in general is interesting and can be considered within the income-expenditure framework. In what follows, the standard model is modified to find the steady state levels and compositions of income and employment and other key variables. Attention then turns to how the system might behave outside a steady state. A way of conceptualizing the dynamics of the system is suggested and formulas developed to describe that behavior. The suggested dynamics are shown to be consistent with steady state requirements.

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Condensed Income-Expenditure Model

The following is mostly intended as background for a possible post (or posts) on quantity effects of a job guarantee in which the standard income-expenditure model is taken as a base. It is desirable to work from as simple a starting point as possible as the exercise can complicate pretty quickly. To minimize unnecessary complications, the base model will be presented in highly abbreviated form. This will not cause anything important to be lost because it is always possible to switch back to the more detailed version of the model when desired. The abbreviation has already appeared here and there in earlier posts, but to avert possible confusion it seems advisable to spell out exactly how it corresponds to the more familiar version of the model.

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