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 ismore 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 bundle (4,1)? Give economic interpretation of this MRS.g. Does the utility exhibit a diminishing marginal rate of substitution?
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 ismore preferred?c. Are the preferences convex?d. Find the
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