1. You are given the utility function:
U (x; y) = 10x + p y
a. If x = 10; what must y equal to be on the U = 200 indi§erence curve?
b. What is the MRSx;y at the point found in (a)?
c. Consider the logarithmic transformation of the utility function:
g (x; y) = ln [U (x; y)]
what is the general expression of MRSx;y of this transformed utility function, g (x; y)?
2. A consumer with the utility function u (x; y) = 3x 0:9py faces the prices Px = 2 and Py = 3: What is his optimal consumption basket if his income is I = 84?
3. The price elasticity of demand for x is 1:9: If the price of x increases by 10% what happens to:
a. the demand for x?
b. the total revenues from x?
4. What is MRSx;y from the following utility functions? Is it diminishing with x?
a. U (x; y) = p x + y
b. U (x; y) = ln x + ln (xy)
c. U (x; y) = y 2x + y