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ps5 - ECO 310 Fall 2007 Problem Set 5 Equilibrium Analysis...

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ECO 310, Fall 2007 Problem Set 5: Equilibrium Analysis Due in class on November 20 Question 1 In this problem we will consider the fish industry on the island of San Serife. For this purpose we will aggregate all the other goods into one composite, and measure it in units of the island’s currency Arial. Thus the price of the other good is 1. (a) There are 160 consumers, each with the utility function U ( x, y ) = 10 x - 5 x 2 + y, where x is the consumption of fish and y the consumption of the other good. Let P denote the price of fish. Find one consumer’s demand func- tion ( x expressed as function of P ). Be careful about boundary solutions with x = 0, but ignore boundary solutions with y = 0, i.e., assume that each consumer has suﬃciently high income. Find the market demand for fish. Show this in a graph with P on the vertical axis and the market quantity Q on the horizontal axis. (b) The fishing industry consists of several firms. Each firm, to produce and sell a positive amount of fish, must get a boat and hire a market stall.

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ps5 - ECO 310 Fall 2007 Problem Set 5 Equilibrium Analysis...

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