Simple Model of Income Determination



The first step to constructing a model is to specify which variables are exogenous vs. endogenous. It is incorrect to treat a variable as exogenous if it can be affected by other variables within the model. The simple model treats the price level as exogenous. The price level is determined by PT+1=(1+INF)PT. Since we are building a short-run model, the price level is PT – even if some other price level may be reached in future periods, in the short run the price level is not affected by GNP or other endogenous variables. In the short run, the price level has been determined by previous events. Endogenous variables in this model, particularly the actual GNP, will affect how the price level will change in the future, but not in the short run.

The assumption  that the price level is exogenous in the short run is a key element of Keynesian economics. Prior to Keynes, economists generally treated the price level as endogenous in the short run. Keynes showed that if the price level is considered exogenous in the short run, the model behaves in a radically different manner and is better able to explain observed real world events. The validity of this argument is still in debate.

Further assumptions are made: The economy has no government or international sectors, the only actors are private firms and households, all savings are undertaken by households and all investment by firms; and potential output is taken to be fixed.

The level of national icome achieved has been shown above to depend on the level of aggregate demand, which in this closed model depends upon consumption demand (C) and investment demand (I). We shall initially assume I to be fixed at all levels of income and attempt to determine the behavior of C.

Consumption demand may be influenced by many factors, including: Level of income; distribution of income and wealth; tastes, habits and social conventions; advertising; law and regulation. In a model that included a government sector, taxation, welfare, etc., would also play a part. Of all these influences, the level of income is taken to be the most significant. In our simple model, because there are no taxes or transfers, total income and disposable income are the same. Both casual introspection and empirical data suggest a direct relationship between consumption and disposable income across all households in the long run. This relationship, called the consumption function, determines how consumption will behave for a given level of income. The exact nature of the consumption function is subject to debate. A simple long run consumption function is: C=bYD where 0<b<1.

In the short run, however, the behavior is different. The evidence suggests that there is a time lag before consumption responds to changes in income. This time lag may result from habit, existing institutional arrangements, and/or the desire to ensure that any given change in income is permanent rather than temporary. After a period of time, consumption adjusts to match the new level of income as per the long-run consumption function. But in the short run, the behavior is different. The simple short run consumption function is: C=aN+bNYD where bN<b. This function permits values where consumption is higher than income, which is based on the assumption that given a decline in income, some dissaving will occur while consumption behavior adjusts.

The short run change in consumption resulting from a given change in income is called the “marginal propensity to consume.” Given an increase in income, a relatively small increase in consumption will occur, followed in the long run by a shift in the consumption function (a new, higher value for aN) and an accompanying long-run increase in consumption. The relative flatness of the short-run consumption function, combined with the fact that the timing of shifts in the function may be difficult to predict, means that short-run consumption per income is not nearly as predictable as it is in the long term.

 It is important to distinguish between the average propensity to consume APC=C/YD and the marginal propensity to consume MPC=DC/DYD. Average propensity to consume is the proportion of income consumed overall, while marginal propensity to consume is the change in consumption that results from a change in income.

In the long run, APC=MPC. In the short run, however, MPC is quite different from APC, because of the presence of the aN term in the consumption function. MPC is important in determining how the economy will react to a change in a component of aggregate demand. If the MPC is high, then a large portion of the initial change is “passed on” and a high multiplier exists. If the MPC is low, then more of the initial change winds up in savings and a lower multipiler is in effect.


When national income is in equilibrium it will equal aggregate demand, as described above. The line Y=D shows all such points. At the same time, aggregate demand is represented by consumption and investment demand, C+I. Equilibrium national income is the point where the lines Y=D and C+I intersect. This is also the only point where the plans of savers and the plans of investors are the same.

Suppose the economy is in equilibrium and a series of new inventions promises to make investment in capital goods more profitable for investors. This increase in profitability means that firms will want to make greater investment expenditure than before. As a result the investment function, which has so far been simply I=I0, will shift upwards. The investment function is still an exogenous variable, so the new function will be I=I0+DI. This indicates an increase in aggregate demand of at least DI. However, this increase in demand will trigger a multiplier effect: The increase of DI will result in additional income for households, who will now consume the additional amount bDI (where b is the marginal propensity to consume), in a cyclic series, so that the final change in national income will be some multiple of the initial DI. This can be seen graphically:


The multiplier is the sum of an infinite series of smaller and smaller increases in demand. The series is convergent for 0<b<1 and can be found by: Multiplier = 1/(1-MPC). MPC=0.75 produces a multiplier of 4; MPC=0.5 produces a multiplier of 2. This leads to a statement of the relationship between exogenous changes in investment and national income: DY=DI/(1-MPC).

It is important to note that the multiplier process can only occur when there are sufficient unemployed resources to meet the new demands. If the economy were operating at full employment, then any exogenous increase in demand would simply result in inflation. No additional resources would be available to produce output to meet the new demand; supply would not be able to increase; and prices would rise, as shown here:


Initially, the economy is in equilibrium at point A. Some exogenous event causes aggregate demand to shift from D1 to D2. In order for the full multiplier effect to occur, the economy would have to reach point C. This is not possible because potential output, Q, would be exceeded. As a result, the economy is stuck at point B and an inflationary gap exists.

The marginal propensity to consume (MPC) must be in the range 0<MPC<1. If MPC were zero, the multiplier would be one and no consumption would occur. If MPC were 1, then the multiplier would be infinity and the economy would swing wildly between zero and full employment output. These situations are not observed to occur, so 0<MPC<1 must be true. However, calculating the value of MPC for a real-world economy is quite difficult and subject to interpretation and debate. As a result it is not an easy task to guide the economy to full employment output without creating inflation. In addition, the presence of government and international sectors will complicate the task in the real world (and in more complex models, below).

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