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 prot during its existence. The Oregon Department of Revenue (DOR) wants to classify the operation a \"hobby farm\" instead of a for-prot 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 rm to defend itself against this reclassication. l. (6 points) The law rm hires you as an economist to determine whether or not the cow-calf operation is a for-prot concern. You collect 20 years of data on the rm's output (q) and costs (C) and use econometrics to estimate the following cost function: C(q) = 2:;2 + 60091 + 5, 000. Suppose that the animals are sold into a competitive market where marginal revenue (MR) equals market price (MR = p). Derive the prot maximizing number of animals (q) that the operation should target. In particular, derive the supply function with q on le-hand side that is some function of price p on the right- hand side. 2. (61001311129) 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 40 calves at this price. How many calves (q) would a prot-maximizing operation sell at that price? Calculate the optimal q using the supply function you found in problem 1. Did the amount that the cow-calf operation actually sold (40) make it a prot-maximizer according the supply function from problem 1? 3. ( 6 points) In the short run, prot-maximizing rms shut down when market price falls below the minimum of average variable cost (A VC). Calculate average variable cost and determine the lowest value it can possibly take (A VCmin ). This is the \"shut down price.\" 4. ( 6 points) If there are 100 identical cow-calf operations in Oregon, what is the short-run market supply function? (Hint: start with your result from problem 1.) 5. ( 6 points) In the long run, only rms that produce at minimum average cost (AC) will survive. Since marginal cost (MC) always intersects average cost at its lowest point, you can nd this point by calculating MC and AC and equating them. The q that equates them can then be plugged back into either MC or AC to nd the price (p). Report the long-run equilibrium q and p of calves. 6. (5 points) Suppose that the market demand for calves is Q = 5700 p. Given what you found for p and q in problem 5, how many cow-calf operations will survive in a competitive long-run equilibrium? 7. (51001311129) The law rm invites you to Salem for questioning by DOR researchers. What will you tell them? Do you have evidence that the cow-calf operation under investigation is a prot-seeking operation? Did you get different result for the long run versus short run