Irving Fisher and Intertemporal Choice The basis for much subsequent work on consumption. Assumes consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction. Consumer’s choices are subject to an intertemporal budget constraint, a measure of the total resources available for present and future consumption

The basic two-period model Period 1: the present Period 2: the future Notation Y1 is income in period 1 Y2 is income in period 2 C1 is consumption in period 1 C2 is consumption in period 2 S = Y1 - C1 is saving in period 1 (S < 0 if the consumer borrows in period 1)

Deriving the intertemporal budget constraint Period 2 budget constraint: Rearrange to put C terms on one side and Y terms on the other: Explain the intuition/interpretation of the period 2 budget constraint. If students understand it, then everything else follows nicely. Finally, divide through by (1+r ):

The intertemporal budget constraint present value of lifetime consumption present value of lifetime income If your students are not familiar with the present value concept, it is explained in a very nice FYI box on p.439.

The intertemporal budget constraint The budget constraint shows all combinations of C1 and C2 that just exhaust the consumer’s resources. Saving Consump = income in both periods Borrowing Y1 Y2 The point (Y1, Y2) is always on the budget line because C1=Y1, C2=Y2 is always possible, regardless of the real interest rate or the existence of borrowing constraints. To obtain the expression for the horizontal intercept, set C2=0 in the equation for the intertemporal budget constraint and solve for C1. Similarly, the expression for the vertical intercept is the value of C2 when C1=0. There is intuition for these expressions. Take the vertical intercept, for example. If the consumer sets C1=0, then he will be saving all of his first-period income. In the second period, he gets to consume this saving plus interest earned, (1+r)Y1, as well as his second-period income. If the consumer chooses C1<Y1, then the consumer will be saving, so his C2 will exceed his Y2. Conversely, if consumer chooses C1>Y1, then consumer is borrowing, so his second-period consumption will fall short of his second-period income (he must use some of the second-period income to repay the loan). C1

The intertemporal budget constraint The slope of the budget line equals -(1+r ) 1 (1+r ) Y1 Y2 The slope of the budget line equals -(1+r): To increase C1 by one unit, the consumer must sacrifice (1+r) units of C2. C1

Consumer preferences Higher indifference curves represent higher levels of happiness. An indifference curve shows all combinations of C1 and C2 that make the consumer equally happy. C1 C2 IC2 IC1

Consumer preferences C1 C2 The slope of an indifference curve at any point equals the MRS at that point. Marginal rate of substitution (MRS ): the amount of C2 consumer would be willing to substitute for one unit of C1. IC1 1 MRS

Optimization C1 C2 The optimal (C1,C2) is where the budget line just touches the highest indifference curve. At the optimal point, MRS = 1+r O All points along the budget line are affordable, including the two points where the orange indifference curve intersects the budget line. However, the consumer prefers (and can afford) point O to these points, because O is on a higher indifference curve. At the optimal point, the slope of the indifference curve (MRS) equals the slope of the budget line (1+r).

How C responds to changes in Y An increase in Y1 or Y2 shifts the budget line outward. C1 C2 Results: Provided they are both normal goods, C1 and C2 both increase, …regardless of whether the income increase occurs in period 1 or period 2.

Keynes vs. Fisher Keynes: current consumption depends only on current income Fisher: current consumption depends only on the present value of lifetime income; the timing of income is irrelevant because the consumer can borrow or lend between periods.

How C responds to changes in r An increase in r pivots the budget line around the point (Y1,Y2 ). A A B As depicted here, C1 falls and C2 rises. However, it could turn out differently… Y1 Y2

How C responds to changes in r income effect If consumer is a saver, the rise in r makes him better off, which tends to increase consumption in both periods. substitution effect The rise in r increases the opportunity cost of current consumption, which tends to reduce C1 and increase C2. Both effects  C2. Whether C1 rises or falls depends on the relative size of the income & substitution effects. Note: Keynes conjectured that the interest rate matters for consumption only in theory. In Fisher’s theory, the interest rate doesn’t affect current consumption if the income and substitution effects are of equal magnitude. After you have shown and explained this slide, it would be useful to pause for a moment and ask your students (perhaps working in pairs) to do the analysis of an increase in the interest rate on the consumption choices of a borrower. In that case, the income effect tends to reduce both current and future consumption, because the interest rate hike makes the borrower worse off. The substitution effect still tends to increase future consumption while reducing current consumption. In the end, current consumption falls unambiguously; future consumption falls if the income effect dominates the substitution effect, and rises if the reverse occurs.

Constraints on borrowing In Fisher’s theory, the timing of income is irrelevant because the consumer can borrow and lend across periods. Example: If consumer learns that her future income will increase, she can spread the extra consumption over both periods by borrowing in the current period. However, if consumer faces borrowing constraints (aka “liquidity constraints”), then she may not be able to increase current consumption and her consumption may behave as in the Keynesian theory even though she is rational & forward-looking

Constraints on borrowing The budget line with no borrowing constraints Y2 Y1

Constraints on borrowing The borrowing constraint takes the form: C1  Y1 C1 C2 The budget line with a borrowing constraint Y2 Similar to Figure 16-8 on p. 445. Y1