Econ11Fall2007ProblemSet_5AnswersDue19Nov2007

- A Yezer THE GEORGE WASHINGTON UNIVERSITY Department of Economics Fifth Problem Set Answers in Econ 11 Fall 2007 1 Steel can either be produced

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THE GEORGE WASHINGTON UNIVERSITY Department of Economics A. Yezer Fifth Problem Set Answers in Econ 11 Fall 2007 1. Steel can either be produced from iron ore at traditional mills or from scrap at mini-mills. Assume that the marginal cost per ton of steel produced at traditional mills is MC T = 100 + 0.1 Q, where Q is output in tons and that the marginal cost per ton of steel produced at mini-mills is MC M = 150 + 0.2Q. Assume (for simplicity) that average variable cost is constant and equal to $100 per ton at traditional mills and equal to $140 per ton at mini-mills. 1a. Assume there is only one mill of each type and that steel mills are price takers. If market price is $200 per ton, how much steel is produced at each mill. If market price rises to $240 per ton, how much steel is produced at each mill? If Price = $200/ton, then the profit maximizing output of the traditional mill is found where MC = 200 = 100 + 0.1Q and hence Q = (200 - 100)/0.1 = 1,000 while profit maximizing output at the mini mill is at MC = P = 200. Therefore Q = (200 - 150)/0.2 = 250. If price rises to 240, output at traditional mills rises to MC = P = 240 and traditional mills will produce Q = (240 - 100)/0.1 = 1,400 and mini- mills produce Q = (240 - 150)/0.2 = 450. Note that, in either case, price exceeds average variable cost and both types of mills will operate. 1b. Now assume that there are 10 traditional mills and 20 mini-mills. Add horizontally and find the market supply curve of steel. Plot this curve carefully. If market price is $200 per ton, how much steel is produced at each mill. If market price rises to $240 per ton, how much steel is produced at each mill? Problem 1a provides the answer to this question. 10 traditional mills produce ten times the output of one mill, or output of 10,000 at price of $200 and 14,000 at price of $240. For mini-mills output of 20 mills will be 5,000 at price of $200 and it rises to 9,000 when price is $240/ton. 1c. Now assume that the demand for steel in tons is given by Q = 20,000 - 20P, where P is price in $ per ton. What is the price of steel, total output of steel, and how much is produced at each type of mill? If you plot the supply curve, you know that total supply is 5,000 + 10,000 = 15,000 when price = $200 and output is 24,000 when price = $240/ton. Supply and demand intersect when price = approximately $205 per ton. You may observe this on the supply and demand graph that you have drawn. Output at a traditional mill is Q = (205 - 100)/0.1 = 1,050 and total output at the 10 traditional mills is 10,500 while output at a mini-mill is Q = (205 - 150)/0.2 = 275 and total output at 20 mini-mills is 5,500 so total steel output is 16,000. 1d. Now assume that a tax of $10 per ton is put on steel but that demand is as in (1c).
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This note was uploaded on 04/18/2008 for the course ECON 011 taught by Professor Yezer during the Fall '07 term at GWU.

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- A Yezer THE GEORGE WASHINGTON UNIVERSITY Department of Economics Fifth Problem Set Answers in Econ 11 Fall 2007 1 Steel can either be produced

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