2. (25 points) A bakery uses both domestically-sourced and imported eggs. If the bakery buys d cartons of domestically-sourced eggs, each of these cartons costs 45 32 dollars. If the bakery imports i cartons of eggs, each imported carton costs 3 32' dollars. In total, the bakery will bake (15 d# + it) + cakes and sell each cake for $16. The government imposes an import quota of Q cartons (i.e. the bakery cannot import more than Q cartons of eggs). a) (4 points) Does the price per carton of domestic eggs rise or fall as the bakery buys more of them? Justify your answer mathematically. With economic intuition, why might the price change this way? b) (4 points) Formally write the bakery's profit maximization problem. c) (5 points) List the cases implied by complementary slackness, as well as their equations and checks. d) (6 points) When does importing below the quota yield a critical point? For the rest of the problem, suppose the firm optimally imports exactly the quota amount. e) (4 points) How does the bakery's optimal number of domestically- sourced cartons change as the quota allowance @ falls? Justify your answer mathematically. f) (2 points) Based on your answers to the previous parts, why might domestic egg farmers lobby for a low import quota (i.e., a low Q)