Lecture 10

4 2 units in state 1 and 2 the general point here

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Unformatted text preview: ng the Arrow securities and the securities above: that is, form the portfolio: 2 , 8 , With this portfolio, we obtain: 6 10 8 units in State 2. , , 4 . 2 units in State 1, and 2 The general point here is that an Arrow security is easier to work with, and accomplishes much the same thing as ordinary securities. The above discuss assumes the financial markets are complete the markets are not complete . Then: . What if 1. Trade between some states are not possible. The allocation will, in general, fail to be Pareto efficient. 2. It generally is not possible to determine a unique set of equilibrium relative prices. The degree of indeterminacy of the relative prices is equal to . To see this last point, note that we can normalize all prices, and the prices of the , ,… relative to some good ‐ say, Good 1 in State 0. This then assets leaves K‐1 relative prices (goods at Date 0) to determine at Date 0, along with the prices of the K units of goods at each state , 1,2, . . . , , for a total of 1 1 1 relative prices to determine. On the other hand, we have 1 independent clearing conditions at Date 0 and K‐1 independent clearing conditions for each state s, s=1,2,...,S, for a total of 11 clearing conditions. The difference is: 1 1 11 . When the asset payoff matrix indeterminacy. is of full rank, and there is no relative price Problem: Suppose we have a world with 1. 2 Dates, Date 0 and Date 1 2. At Date 1, there are 2 possible states, s = 1, s = 2. 3. We have 2 agents. 4. We have complete Arrow securities. 5. Preferences are: 6. Endowments are , ,...
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