Suppose that a consumer’s utility function is U=xy with MU_x=y and MU_y=x. Suppose the consumer‘s income is $480. For this question you may need to use the following approximations: sqrt(2) is approximately 1.4, sqrt(3) is approx. 1.7 and sqrt(5) is approx 2.2.

a) Initially, the price of y is $4 and the price of x is $6. What is the consumer’s optimal bundle?

b) What is the consumer's initial utility?

Now suppose that price of x increases to $8 and we find that the optimal bundle for the consumer is x*=30 and y*=60.

c) What is the change in the consumer’s demand for good x?

d) What is the change in the consumer’s demand for good y?

e) Using this information, what the cross price elasticity of demand for good y with the price of good x?

f) What is the substitution bundle?

g) What is the substitution and income effect on good x?