# w9 - b Find his optimal allocation when he can not trade to...

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Economics 11: Microeconomic Theory 1 Professor Christian Hellwig Exercises Week 9 1) The demand for portable radios is given by: Q=5000-100P. The local supply curve is given by: Q=150P. a) find the market equilibrium. b) Now suppose that radios can be imported at a price of \$10 per unit. Find the market equilibrium and the amount of radios imported. c) Now suppose that the local producers convince the government to impose a tariff of \$5 per radio. Find the market equilibrium, the total revenue of the tariff and the effect on the consumer and producer surplus. 2) Suppose that Robinson Crusoe produces and consumes fish (F) and Coconuts(C) He has 200 hours to work and he is indifferent as to whether he spends time fishing or gathering coconuts. Robinson production for fish and coconuts are given by: F=L F 1/2 C=L C 1/2 L C +L F =200 And his utility function is U=(FC) 1/2 a) Find the Production possibility frontier.
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Unformatted text preview: b) Find his optimal allocation when he can not trade to the rest of the world. c) At what relative prices this optimum can be supported as a competitive equilibrium? d) Now suppose that there is possibility for trade, and Robinson can trade fish and coconuts at a price ratio P F /P C =2/1. If he keeps the same production decision as part (b) what will be his consumption, given the possibility of trade? e) Find the new optimal production decision with trade. 3) Consider an exchange economy with two consumers (A and B) and two goods (X and Y). The initial endowments for both consumers are ( ) ( ) ( ) ( ) 15 , 20 , and 10 , 80 , = = B B A A Y X Y X . They have the following utility functions: B B B A A A Y X U LnY LnX U = + = a) Find each consumers demand function b) Find the market-clearing price ratio. c) Find the contract curve....
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