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According to the American Metal Markets Magazine, the spot market price of U.S. hot rolled steel recently reached per ton. Less than a year ago this same ton of steel was only . 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 when preparing 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 mini-mills. The mini-mill production process replaces raw iron ore as its primary raw input with scrap steel. Today, mini-mills account for approximately 52 percent of all U.S. steel production. However, the worldwide movement to the mini-mill production model has bid up the price of scrap steel. In December, the per-ton price of scrap was around , and it soared to just two months later. Suppose that, as a result of this increase in the price of scrap, the supply of raw steel changed from to . Assuming the market for raw steel is competitive and that the current worldwide demand for steel is , compute the equilibrium price and quantity when the per-ton price of scrap steel was , and the equilibrium price-quantity combination when the price of scrap steel reached per ton. Suppose the cost function of a representative mini-mill producer is . 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?