THE GEORGE WASHINGTON UNIVERSITY
Department of Economics
Fifth Problem Set Answers in Econ 11
1. Steel can either be produced from iron ore at traditional mills or from scrap at mini-mills.
that the marginal cost per ton of steel produced at traditional mills is MC
= 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
= 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.
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
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
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
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).