Consider a consumer who consumes only two products X and Y . (for example, X may

Question

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- sisting 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

Explanation / Answer

1.If she again consumes 500 units of both X and Y. then she is equally well off as in 1990. But this might not always be the case. In case she decides to buy more of Y keeping X same or more of X keeping Y same, then she would be worse off in 1991 as compared to 1990

2. The cost of living adjustment she should receive such that she would be equally well off in 1991 (relative to 1990) would definately be more than 500$ in case she deviates from her consumption of 500units of both X and Y.$500 is the minumum living adjustment she should receive to be able to  afford to buy her earlier consumption bundle X = 500; Y = 500.Any deviation from earlier consumption bundle X = 500; Y = 500 would need a higher cost of living adjustment (i.e more than $500)

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