The Determinants of Consumption

The marginal propensity to consume is less than the average propensity to consume because of errors in measuring permanent income. True or False? Explain your answer.

True because current income is not a good measure of permanent income. Increases in observed current income levels in the economy are typically part permanent and part transitory. Permanent increases in income affect consumption but transitory increases do not. Thus, even though consumption will typically be a more or less constant fraction of permanent income and thus vary in roughly the same proportion as permanent income, it will vary less than proportionally with changes in current income because only a portion of changes in current income are typically permanent. If consumption is a constant fraction of permanent income, the marginal propensity to consume out of permanent income will equal the ratio of consumption to permanent income. This ratio of consumption to permanent income is also the average propensity to consume out of permanent income. The marginal propensity to consume out of current income, on the other hand, will typically be less than the ratio of consumption to current income (or average propensity to consume out of current income) as indicated by the Keynesian consumption function

(1) C = a + b Y,

where C is consumption, Y is income, and b, the marginal propensity to consume, is less than the ratio C/Y, which is in turn less than unity. Note that in the current-income consumption function above, the average propensity to consume out of current income (C/Y) will fall as current income increases.

The relationship between the current and permanent income consumption functions can be seen from FIGURE 1.

The average level of both current and permanent income income is given by Yo. When current income is above Yo, permanent income (denoted with a P superscript) is also above Yo, but by a smaller amount. Consumption depends on permanent income according to the consumption function

(2) C = kYp.

Consumption varies less than current income because permanent income varies less than current income. As a result, the current-income consumption function, given by equation (1), is flatter than the permanent-income consumption function, given by equation (2). The marginal propensity to consume out of current income, which is equal to the slope b, is less than the marginal (and average) propensity to consume out of permanent income, which is equal to the slope k. The average propensity to consume out of current income is given by the slope of a line (not shown in FIGURE 1) drawn from the point on the current income consumption line associated with the amount of consumption to the origin. The slope of such a line will be smaller, and the average propensity to consume will therefore be smaller, the greater the level of consumption.

Zero time preference implies that consumption is the same in all years regardless of income. True or False? Explain your answer.

False! Zero time preference would only lead to equal consumption in all years if the interest rate were zero. In a two-period model, consumption will be the same in both years if the rate of time preference equals the real rate of interest. Assume that the individual's two-period utility function is of the time-separable form

U = U(C0) + [1/(1 + p)] U(C1)

where C0 and C1 are the levels of consumption in year 0 and year 1 respectively and p is the rate of time preference. It can be shown that -(1 + p) is the slope of the individual's indifference curves where they cross the 45 degree ray from the origin (along which C0 equals C1). If the individual is endowed with incomes Y0 and Y1 in the two years and and can borrow and lend at the constant real interest rate r, his two-period budget line will have a slope equal to -(1 + r). The indifference curve and the budget line will therefore be tangent at the 45 degree ray from the origin, and consumption will be the same in both years, when (1 + p) = (1 + r) ---that is, when p = r. If p is zero but r is not zero, the positive r will result in the individual consuming less in year 0 than in year 1. This is shown in FIGURE 1 below.

Given zero time preference (p = 0), the slopes of all indifference curves where they cross the 45 degree ray from the origin are equal to -1. If the interest rate is positive, the slope of the consumer's budget line will be steeper than -1. The individual will consume the combination C0 and C1 in the respective years. Since this combination is to the left of the 45 degree ray, more is consumed in year 1 than in year 0.

For consumption to be the same in both years the interest rate would have to equal the rate of time preference. Since the rate of time preference is the slope of the indifference curves where they cross the 45 degree ray, equality of the rate of time preference with the rate of interest would imply that the indifference curves and the budget line have the same slope along the 45 degree ray from the origin. Tangency of the two curves would then occur where consumption in the two years is the same.