Question

3. Assume that a household has the following utility function: U = 100q1 +242 a) (10 points) Suppose the household has an income of Y - $800, and a per unit price of food pi $5 and price of clothing p2 - $0.1. What is the utility- maximizing bundle? b) (5 points) Suppose the price of the first good increases to $6 per unit. What is the utility maximizing bundle?

Answer 1

From the utility function we find that MUq1 = 100 and MUq2 = 2. Also p1 = 5 and p2 = 0.1

At the utility maximizing choice, MUq1/p1 should be equal to MUq2/p2

Here MUq1/p1 = 100/5 = 20 and MUq2/p2 = 2 / 0.1 = 20

a) Since MUq1/p1 = MUq2/p2, consumer will experience his budget constraint coinciding with the indifference curve. Hence, there is no unique bundle but any combination of q1 and q2 that satisfies the budget equation 800 = 5q1 + 0.1q2 will generate same utility

b) Now p1 is 6. Here MUq1/p1 = 100/6 = 16.67 and MUq2/p2 = 2 / 0.1 = 20. Since MUq1/p1 < MUq2/p, consumer will consume only q2 since it generates more additional utility. Hence q1 = 0 and q2 = 800/0.1 = 8000 units. This is the optimal bundle