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Unformatted text preview: GENERAL EQULIBRIUM with ASSETS and TIME The general equilibrium model is timeless. Fisher showed, however, that by rein- terpreting the commodities, one could introduce time into the general equilibrium model without changing anything. An entire new world of f nancial problems sud- denly can be understood with the same mathematical apparatus used to deal with simple timeless trade. We make this explicit by starting from a genuinely intertemporal two-period model with a stock and bond. We de f ne f nancial equilibrium, noting that that the budget set now becomes more complicated, consisting of many (two) constraints, since at every period each agent is constrained to spend no more than he has. We show that nevertheless f nancial equilibrium can be reduced to a standard (timeless) general equilibrium model with one budget constraint, provided there is no uncertainty. Thus (timeless) general equilibrium can be reinterpreted as if it were always about f nancial questions. The crucial idea is that if we think of commodities not as apples X and oranges Y, but rather as apples today X and apples tomorrow Y, then we can proceed ex- actly as before. The (timeless) general equilibrium prices p x and p y now have to be reinterpreted as present value prices. In other words, p y is the price you would need to pay today in order to get delivery of an apple tomorrow. One very important and practical conclusion is that the easiest way to look at an agent’s sequential budget constraints is to consolidate them into one present value budget constraint. On the right hand side one puts the present value of all current and future income. We shall see the bene f ts of this way of looking at things in the next few lectures. The most important implication of Fisher’s analysis is that the trade-o f between consumption today and consumption in the future is exactly on a par with the trade- o f between consumption of pork and beans today. They both involve the determina- tion of a relative price by supply and demand. Fisher called the relative price between today and tomorrow the real rate of interest, to distinguish it between the trade-o f between a dollar today and a dollar tomorrow, which he called the nominal rate of interest. We study the rate of interest in the next chapter. The connection between in F ation, and the real and nominal interest rates is called Fisher’s equation. The connection between a stock’s price, and its real dividends, and the real interest rate is called the fundamental theorem of stock pricing. The connection between a stock’s price, and its nominal dividends, and the nominal interest rate is called the present value theorem of stock pricing....
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This note was uploaded on 12/08/2009 for the course ECON 251 at Yale.