Hmk3 - home work assignment PDF

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Intermediate Microeconomics Homework Set 3: Optimal Choice Due 09/21 (Beginning of class)

Exercise 1 Max has utility function u(x1 , x2 ) = x1 (x2 + 1). The price of x1 is $2 and the price of x2 is $1. Income is $10. How much x1 does Max demand? How much x2 ? If his income doubles and prices stay unchanged, will Max’s demand for both goods double? Exercise 2 Max has a utility function u(x1 , x2 ) = 2x10.3x0.3 2 + 1. The price of x1 and x2 are both $1 and Max has an income of $20. (1) How much of each good will he demand? (2) A tax is placed on x1 so that x1 now costs Max $2 while his income and the price of x2 stay the same. How much of good x1 does he demand now? (3) Would Max be as well-off as he was before the tax if when the tax was imposed, his income rose by an amount equal to $1 times the answer to part (2) Exercise 3 Casper consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the higher the price you have to pay per unit. In fact x2 units of cocoa will cost Casper x22 dollars. Cheese is sold in the usual way at a price of $2 per unit. Casper’s income is $40 and his utility function is u(x1 , x2 ) = x1 + 2x2 , where x1 is his consumption of cheese and x2 is his consumption of cocoa. (1) Sketch Casper’s budget set. (2) Sketch some of his indifference curves and label the point that he chooses (3) Calculate the amount of cheese and the amount of cocoa that Casper demands at these prices and this income (hint: Write down the Lagrangean for this problem and solve the maximization program). Exercise 4 Alex 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 (xA ) or French restaurants (xF ). His firm offers to transfer him from its Austin office to its Paris office, where he will face different prices. The firm will pay him a salary in euros such that he can buy the same bundle of goods in Paris that he is currently buying in Austin. (1) Will Alex be better off in Paris if the relative prices between American and French meals (pA /pF ) are lower in Paris than Austin? Why? 1

(2) Will Alex be better off in Paris if the relative prices between American and French meals (pA /pF ) are higher in Paris than Austin? Why? Exercise 5 Maximize the function f (x, y) = x + y subject to the constraint x2 + y 2 = 1. Sketch the constraint first, and then maximize.

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