The transmission of information through prices

Economist von Hayek asserted that one of the main roles of prices in a market economy is to aggregate information that individuals privately have. In this part, you are going to show whether or not prices reveal the information that some traders have.

There is a market system for the exchange of two physical goods, ‘wheat’ and ‘leisure’, and two payoff-relevant states of uncertainty, s = 1, 2. There are two types of traders with Bernoulli state- dependent utilities

uixi ,xi ,silogxi (1i)logxi 1,s2,s s 1,s s 2,s

and endowments wi 1,1, independent of i or s, and with 1  2/3, 1 1/3, while s12

2 1/3, 2  2/3 (so traders i are those who prefer wheat over leisure in state i). Traders do 12

not care about consuming today, nor they receive an endowment at s = 0. There is a (large) number N of each type of traders in the market. Each trader i = 1 is perfectly informed of the state of nature before trading, receiving a signal y = 1, 2. Type i = 2 traders are totally uninformed. There are no financial assets for trading today, and state-contingent spot markets for the exchange of wheat and leisure will open after traders i = 1 receive their information.

1. (a) Is this market informationally efficient?
2. (b) Suppose that endowments were incorrectly measured. They actually are wi 1,1, wi 1,1, with  0 small, and exogenously fixed. Does your 12 conclusion at point (i) still hold true?
3. (c) Draw conclusions regarding von Hayek’s assertion in this market (explain why you get your conclusions).