Consider a consumer who consumes only two products X and Y. (for example, X may be housing and Y may represent a "composite commodity" con- sifting of all other goods). Assume that this consumer's utility function is rep- resented by U(X; Y ) = XY . Suppose in 1990, px = 1, py = 1 and I = $1000. Observe that in this year the consumer buys 500 units of X and 500 units of Y: 1
1. Suppose in 1991, px = 1, py = 2. However, in 1991 she receives a cost of living adjustment of $500, so that she can afford to buy her earlier consumption bundle X = 500; Y = 500. (of course, she is not restricted to buy X = 500; Y = 500). Is she better or worse o¤ in 1991 (relative to 1990)? Justify your answer.
2. What is the amount of cost of living adjustment she should receive such that she would be equally well off in 1991 (relative to 1990)? Is this amount more than or less than $500