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P6 - ECO 310 Fall 2008 Problem Set 6 General Equilibrium...

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ECO 310, Fall 2008 Problem Set 6: General Equilibrium, Monopoly Due in class on November 25 Question 1 Consider a small country with two firms. Firm 1 produces x = min( k x , l x ) units of good x ; firm 2 produces y = p k y l y units of good y . This country has 24 units of capital and 16 units of labor. (a) Describe the production possibility frontier of this country. (b) Compute the rate of product transformation. Suppose that outputs x and y are traded internationally at prices $6 and $2 5, respectively, but the firms must buy capital through domestic factor markets at rental price $ v and labor at wage $ w . (c) Compute firm 1’s input demands and output supply as functions of v and w . (Hints: First compute the cost minimizing inputs k x and l x for given v , w , and x . Then calculate the profit maximizing output x for given v and w . Because the production function exhibits constant returns to scale, there may not exist a solution to the profit maximization problem, or, even if exists, the solution may not be uniquely determined.)
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