Utility function: U (x; y) = 10x + p y

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

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