Z-D Model

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Z-D Model

The Z-D model refers to the analysis contained in chapter 3, “The Principle of Effective Demand,” of John Maynard Keynes’s The General Theory of Employment, Interest, and Money (1936). It was in this early chapter that Keynes first unveiled what he considered a revolutionary new approach, defining the range of possible levels of employment that could (and in the West in the 1930s, did) characterize a market economy in equilibrium. At this early stage of his book, his task was to outline the path his argument was to take. He used what has since become known as the Z-D model to accomplish this task.

Keynes’s model is based on the expectations of producers and demanders as to how much employment-generating aggregate activity they can profitably either engage in (the producers) or purchase the output of (the demanders) in the short period. The short period is defined by the time necessary to realize the results of the aggregate of producers’ decisions (whether these were maximally profitable or not) for demand and supply. Crucially, demand for consumer goods can be known within this period, but the demand for investment goods cannot, since the value of such goods to demanders depends on an expectation of return over a longer time horizon than just the short period. In practice, this reduced to the assumption that the following are fixed: (1) the existing level of technology; (2) capital and labor; (3) the existing propensity to consume or save out of income; and (4) the expectations of the return on newly produced investment (what Keynes termed long-period expectations).

With this in mind, we can understand Keynes’s basis for declaring—as he did many times after the General Theory was published—that his theory of short-period employment is most easily understood under the assumption that short-period expectations are always fulfilled; that is, given their assumptions, producers’ output is the profit-maximizing one for each of them in this situation. Notice this leaves the state of long-term expectations, and so the level of investment, as given, and not necessarily at the level required for full employment.

A Z or aggregate supply function is then posited to capture producers’ short-period expectations as to what level of production and employment will be profitable, given the relevant ceteris paribus conditions (above) and their expectations of demand (which can be assumed to be correct in equilibrium). Thus Z is a function of the proceeds producers expect, given the costs of producing a level of output. Hence: Let Z be the aggregate supply price of the output from employing N men, the relationship between Z and N being written Z = Φ (N ), which can be called the aggregate supply function (Keynes 1936, p. 23).

Similarly, a D or aggregate demand function is posited to represent the sectoral demands, namely, the consumption

function for goods and services by households (later in the chapter, D ₁), and the demand for newly produced capital by investors (D ₂). Hence: Similarly, let D be the proceeds that entrepreneurs expect to receive from the employment of N men, the relationship between D and N being written D = f (N ), which can be called the aggregate demand function (Keynes 1936, p. 23).

Due to diminishing returns to employment, N, in the short period, we may expect the supply function, Φ (N ), to rise at an increasing rate in N. We also expect D ₁ to rise at a constant and eventually less-steep rate than Φ (N ) as N increases (with growing output) because the household marginal propensity to consume (X ) is less than one (or, amounting to the same thing, the marginal propensity to save out of increased income is positive); and that D ₂ is fixed by long-term expectations as to the amount a community is currently willing to spend on investment. Thus, where the increasingly rising Z function intersects a constantly rising total D function, employment will be determined.

This is the point of expected profit maximization. To the left of the intersection, producers can expect to make increased profits by employing more workers; to the right, the expected proceeds do not justify the additional expected cost.

“Hence the volume of employment in equilibrium depends on (i) the aggregate supply function, Φ, (ii) the propensity to consume, X, and (iii) the volume of investment, D ₂ . This is the essence of the General Theory of Employment” (Keynes 1936, p. 29).

Thus does Keynes stake out his question. Those factors that determine the marginal propensity to consume and the volume of investment become the keys to what level of employment a market economy will generate in short-period equilibrium (i.e., the time frame in which we live).

SEE ALSO Aggregate Demand; Aggregate Demand and Supply Price; Aggregate Supply; Economics, Keynesian; Investment; Keynes, John Maynard; Long Period Analysis; Propensity to Consume, Marginal; Propensity to Save, Marginal; Returns, Diminishing; Short Period