Exercise 3Casper consumes cocoa and cheese. Cocoa is scarce and its pricing regulated by the government, which has imposed tiered pricing to discourage excessive consumption. In particular, the total price for x2 units of cocoa is $x22. Cheese is sold at a uniform price of $2 per unit. Casper’s income is $40 and his preferences are representable by the utility function u(x1, x2) = x1 + 2×2, where x1 ? 0 is his consumption of cheese and x2 ? 0 is his consumption of cocoa.(1) Sketch Casper’s budget set.(2) Sketch several indifference curves and label Casper’s demand.(3) Calculate Casper’s demand.Exercise 4Alex doesn’t care about where he lives, but he does care about what he eats. Alex spends all his money on restaurant meals at either American or French restaurants.His firm offers to transfer him from its Austin office to its Paris office. Alex notices that the relative prices for American and French meals differ in Paris versus Austin.Luckily, the firm will adjust his salary so that he can afford the same bundle of goods in Paris that he is currently buying in Austin. Would he be better off taking the offeror remaining in Austin? (Assume Alex’s preferences are monotone and strictly convex,with well-defined MRS everywhere, and that he currently consumes a positive number of meals at both American and French restaurants.)Exercise 5Optimize f(x, y) = x + y subject to the constraint x^2 + y^2 = 1.
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