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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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 Winter '14
 Economics

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