# Suppose a consumer’s preferences are given by u(x1, x2) = x1^(3/4)x2^(1/4) and t

Suppose a consumer’s preferences are given by u(x1, x2) = x1^(3/4)x2^(1/4) and that his budget constraint is given by 3×1 + 2×2 = 10. a. Derive the consumer’s optimal consumption bundle.B. Now suppose that the price of good 2 increases to p2 = 4. Derive the consumer’s optimal bundle. How does it compare to the optimal bundle from part (a)? c. Return to the original budget constraint 3×1 + 2×2 = 10. Now suppose that the consumer’s income falls to 5. Derive the consumer’s optimal bundle. How does it compare to the optimal bundle from part (b)? Is it the same? Why or why not?d. Now suppose another consumer’s preferences are given by u(x1, x2) = x1^(1/4)x2^(3/4) and that her budget constraint is given by 3p1x1 + 2p2x2 = 10. Derive the consumer’s optimal consumption bundle. How does it compare to the optimal bundle from part (a)? Who consumes more of good 1? Why?