Questions 48 through 54 are related.

48. The annual harvest of feed corn occurs in October but demand is spread evenly throughout the year. Suppose monthly demand for feed corn has been estimated to be Q_Dt= 90 - 3.1 P_twhere Q_Dtis the demand in month t and P_tis the price in month t. Monthly storage costs, which include a profit to cover the opportunity cost of tying up funds while storing, are estimated to be $0.10 per bushel per month. The price must rise every month to compensate for storage costs. So if the price is P in October, it must be P+$0.10 in November and then P+$0.20 in December and so on through the following September. Plugging the monthly prices into the monthly demand curves and then summing the monthly demand curves determine the annual demand. The Price in October, P, will be the only variable in the Demand function. Assuming corn is not stored beyond one year [or that the quantity of corn stored beyond one year is held constant] and imports and exports are not permitted, the annual demand must equal the annual supply. If the annual supply of feed corn from the October harvest is forecast to be 900 bushels, what will be the price of feed corn when the harvest is completed in early October? Write the answer in dollars and round off to one cent.

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49. With reference to question 48, what price is forecast for March? Write the price in dollars and round-off to one cent, for example write $3.45 or $4.42.

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50. With reference to question 48, what price is forecast for July?

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51. With reference to the previous questions, what is the forecast for the quantity demanded for the month of December? Write the quantity and round-off to two decimal places, for example write34.76 or 52.17.

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52. With reference to the previous questions, what is the forecast for the quantity demanded for the month of August? Write the quantity and round-off to two decimal places, for example write34.76 or 52.17.