According to the American Metal Markets Magazine, the spot market price of U.S. hot rolled steel recently reached $580 per ton. Less than a year ago this same ton of steel was only $260. A number of factors are cited to explain the large price increase. The combination of China's increased demand for raw steel-due to expansion of its manufacturing base and infrastructure changes to prepare for the 2008 Beijing Olympics-and the weakening U.S. dollar against the euro and yuan partially explain the upward spiral in raw steel prices. Supply-side changes have also dramatically affected the price of raw steel. In the last 20 years there has been a rapid movement away from large integrated steel mills to minimills. The minimill production process replaces raw iron ore as its primary raw input with scrap steel. Today, minimills account for approximately 52 percent of all U.S. steel production. However, the worldwide movement to the minimill production model has bid up the price of scrap steel. In December, the per-ton price of scrap was around $156 and soared to $302 just two months later. Suppose that, as a result of this increase in the price of scrap, the supply of raw steel changed from Qs raw = 4,900 + 5P to Qs raw = 100 + 5P. Assuming the market for raw steel is competitive and that the current worldwide demand for steel is Qd raw = 8,800 - 10P, compute the equilibrium price and quantity when the per-ton price of scrap steel was $156, and the equilibrium price-quantity combination when the price of scrap steel reached $302 per ton. Suppose the cost function of a representative minimill producer is C(Q) = 1,000 + 10Q2. Compare the change in the quantity of raw steel exchanged at the market level with the change in raw steel produced by a representative firm. How do you explain this difference?