All problems of this homework concern a cow-calf operation in the Coast Range of Oregon that has been in operation for 20 years. This business has never paid any state income taxes because it has never produced a profit during its existence. The Oregon Department of Revenue (DOR) wants to classify the operation a"hobbyfarn1" instead of a for-profit business. As a hobby farm the operation would not be able to deduct expenses. This revised status would cause the operation to have to pay 20 years worth of back taxes. To avoid this, the cow-calf operation has hired a law firm to defend itself against this reclassification. a). The law firm hires you as an economist to determine whether or not the cow-calf operation is a for-profit concern. You collect 20 years of data on the firm's output (9) and costs (C) and use econometrics to estimate the following cost function: C(q) = 2q + SOOq +5,000. Suppose that the animals are sold into a competitive market where marginal revenue (MR) equals market price (MR = p). Derive the profit maximizing number of animals (q) that the operation should target. In particular, derive the supply function with q on left-hand side that is some function of price p on the right-hand side. b). The average price of calves sold by the cow-calf operation was p = $800. In reviewing the books of the cow-calf operation, you found that they typically sold 50 calves at this price. How many calves (@) would a profit-maximizing operation sell at that price? Calculate the optimal (1 using the supply function you found in problem 1. Did the amount that the cow-calf operation actually sold (50) make it a profit-maximizer according the