05_Impatience

05_Impatience - Econ 251a Fall 2006 Irving Fishers...

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Econ 251a Fall 2006 Irving Fisher’s Impatience Theory of Interest Irving Fisher reduced intertemporal economics without uncertainty to timeless general equilibrium, putting future goods on the same footing as current goods. Fisher’s insight had at least four important consequences. One implication is that the real rate of interest (the relative price of apples to- day vs apples tomorrow) is just like any other relative price, morally equivalent, Shakespeare nearly said, to the price of pork (the relative price of pork and money). Limiting interest, for example by anti-usury laws, would have the same deleterious e f ects as other price controls. Second, Fisher concluded that the reason the real interest rate is positive is re- duced to the reason the marginal utility of goods tomorrow is less than the marginal utility of goods today. And that is because people are impatient. More precisely, the real interest rate relative money price of good now and good later: p 2 p 1 = 1 1+ r Fisher’s comparative statics theory of the real interest rate implied that: (1) Impatience ↑⇒ real r (2) Optimism about future endowments ↑⇒ real r (3) Redistribution of wealth from rich to poor real r (4) New technology real r These comparative statics can be proved to hold under special (Cobb-Douglas) assumptions about utility. They are not true in general. But probably they are true in practice, most of the time! One important di culty with Fisher’s notion of the real rate of interest is that it presumes a single good today and tomorrow. If there are multiple goods, then which price ratios should denote the real interest rate? To answer this question, Fisher became the world’s greatest authority on price (and hence) in f ation indices, and the Fisher ideal index is now considered the best index ever invented. But we shall ignore multiple goods in these lectures. A third implication of Fisher’s reduction of intertemporal economies to timeless general equilibrium is that, by no-arbitrage, one can reduce all the di f erent interest rates, bond prices, and stock prices, today and in the future, to the same number of prices as there are periods. In a two-period model, bonds, stocks, and promises are become perfect substitutes. 1
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A fourth implication is that one can summarize the wealth of an individual by the product of present value prices and the current and future goods in the endowments, which is called the individual’s present value. 1 Introducing Time into General Equilibrium Consider an economy with two goods x and y, with welfare functions of the form W i ( x, y )= u i ( x )+ d i u i ( y ) . Fisher realized that one could use the theory of general equilibrium to understand f nance. He began by reinterpreting the good X as consumption today and the good Y as consumption tomorrow, or consumption next year. Since it was important to him to put consumption tomorrow on the same footing as consumption today, it is not surprising he was one of the pioneers in replacing the constant marginal utility
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This note was uploaded on 12/08/2009 for the course ECON 251 at Yale.

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05_Impatience - Econ 251a Fall 2006 Irving Fishers...

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