04b_GE_Assets1

04b_GE_Assets1 - GENERAL EQULIBRIUM with ASSETS Fisher made...

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GENERAL EQULIBRIUM with ASSETS Fisher made three major contributions to f nance by extending the equilibrium model to include f nancial questions. He introduced assets into the equilibrium model (leading him to formulate the idea of the fundamental value of an asset and implicitly the idea of arbitrage). He introduced time into the analysis. And he formulated the impatience theory of interest. We shall introduce these new elements in exactly that order, concentrating on assets in this chapter and time in the next chapter. The most basic questions about f nance are: what should stock prices be, and what should the interest rate be? As we shall see in the next section, interest rates are like inverse asset prices, so the basic question (not the only question, by any means) of f nance is simply, what should the prices of various assets be? Unfortunately, the general equilibrium model does not include assets. Fisher added assets to the model in order to study f nance. The simplest and most abstract way to introduce assets is by de f ning an asset by the dividends it pays, or promises to pay. Some people care about owning assets for the joy of owning them. But for most people, assets only have value because they pay dividends. By identifying an asset exclusively by what it pays, we are ignoring the f rst class of people. Fornowwesupposethata l lde l iver iescanbeperfect lyforeseen ,sowea lsoignore the possibility of default. Naturally, this is an unrealistic assumption, which we shall drop later. But assuming it now will, as Ricardo said in a di f erent context almost a century before Fisher, be very illuminating. Assets are of two types: one kind is physical, like land or trees or factories. Another kind is promises, like an IOU note or a bond. What it pays depends on somebody keeping his promise. Since we ignore default for now, the only di f erence between these is that the former are in positive supply (so many acres of land actually exist today), while the latter are in zero net supply, since a promise sold by somebody is a promise bought by somebody else. Identifying assets with their payo f s naturally led Fisher to the conclusion that asset prices should be equal to the value (prices times quantities) of their dividends. This is now called the fundamental theorem of asset pricing. If asset prices were di f erent from the value of their dividends, there would often be an arbitrage, where one could sell the asset and buy the dividends directly, thus turning a pro f toverand over, contradicting the hypothesis we are in equilibrium. This insight enabled Fisher to quickly reduce a general equilibrium economy with assets to a standard general equilibrium model without assets. 1A s s e t s Fisher began by introducing a new element into the model, namely assets. An as- set delivers some combination of goods. For example, a tree might produce fruit and leaves, of di f ering quantities. The tree itself might give no utility, but what it 1
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produces could be of value. The price of the tree would then be explained by what
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This note was uploaded on 12/08/2009 for the course ECON 251 at Yale.

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04b_GE_Assets1 - GENERAL EQULIBRIUM with ASSETS Fisher made...

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