Consider an economy of two consumers, i = A,B, and two goods, x1 and x2. Consumer A has income mA and utility function

uA(x1,x2) = lnx1 +lnx2. Consumer B has income mB and utility function

uB(x1,x2) = 2lnx1 +lnx2. The price of x1 is p1. The price of x2 is p2.

a. Write down the utility maximization problem of each consumer. 2

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b. Solve the utility maximization problems of two consumers. Denote the solution as x1i (p1, p2,mi), x 2i ( p 1 , p 2 , m i ) .

c. What are the market demand functions for x1 and x2? (The market demand for x1 is simply the summation of the quantities demanded by consumer

AB A, x1 , and consumer B, x1 .)

d. Does income distribution affect the market demand for goods? Specifically, fix a total income at M = mA + mB. For different combinations of mA and mB, are the market demands the same or not? Use an example to support your argument.