01 May Question: This problem illustrates the idea of a competitive equilibrium. Suppose there are only two agents…
This problem illustrates the idea of a competitive equilibrium. Suppose there are only two agents in the economy, whom we will call Ann and Bob. We can think of this as shorthand for an economy that has many Anns and Bobs, so that each is indeed insignificant in the market. The two people have
the following endowments of the two goods they have to consume, bananas and coconuts, as follows: The utility functions are given by:
Compute the demand functions of Ann and Bob as a function of the price of bananas pb and the price of coconuts pe. Explain why there is no loss of generality in assuming that the price of bananas pb is equal to one. Hereafter take this to be the case Find the the excess demand functions for Ann and Bob. Use these to express the market mands equal zero. Then find equilibrium prices, meaning the price of coconuts, at which excess dema solved for a competitive equilibrium -clearing conditions, which are that excess de- nds are indeed zero. You have now
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