Charlie has utility function U(x1, x2)= x1x22 over two goods. This is a special case of the Cobb-Douglasutility function.

a. Write the equation of the indifference curve with utility value C. Hint: Set U(x1, x2) to Cand solve this equation for x2.

b. Draw two indifference curves passing through points (4,1) and (9,1/3). Which bundle is more preferred?

c. Are the preferences convex?

d. Find the marginal utilities for good 1 and good 2. Hint: compute the partial derivatives.

e. Write the formula for the marginal rate of substitution between goods 1 and 2.

f. What is the MRS for the bundle (4,1)? Give an economic interpretation of this MRS.

g. Does the utility exhibit a diminishing marginal rate of substitution?