A consumer in an exchange economy has a vector of endowments given by e Rⁿ++. Prices in the

economy are given by the vector p Rⁿ+.

(a) Define the consumer's indirect Utility functionV (p,p .e)

(1)

(b) Show that the consumer's indirect Utility function is homogeneous of degree zero in prices. (1)

(c) Suppose the price of good i increases. Show that the consumer is better offif and only if her endowment of the good (ei )exceeds her

current consumption of the good (x*i) given prices p. (3)

(d) Given this price increase, is the consumer's compensating variation positive or negative. Explain (2)

(e) In a two good economy (e R²++), use a well labeled diagram with indifference curves andbudget lines to illustrate the impact of an in-

crease in p1 on a consumer's optimal choice of goods 1 and 2 given the consumer initial has

x*1