Suppose that a consumer's utility function isU=xywithMU_x=yandMU_y=x. Suppose the consumer's income is $480.

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 thatprice of x increases to $8andwe find thatthe optimal bundlefor the consumerisx*=30andy*=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?