Consider a market with two goods, x and z that has the following utility function
U = (x^.8)(z^.2)
a. What is the marginal rate of substitution
b. As a function of the price of good x (px), the price of good z (pz) and the income level (Y), derive the demand functions for goods x and z
c. Suppose px=4, pz=2 and Y=50. What is the optimal bundle consumed?
d. Suppose the price of good x increases to px=8. Now what is optimal bundle?
e. Calculate the decomposition bundle associated with price change
f. Calculate the income effect, substitution effect and total effect