1. (6 points) 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 (q) and costs (C) and use econometrics to estimate the following cost function: C(q) = 2q~ +600q +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. 2. (6 points) 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 profit-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 profit-maximizer according the supply function from problem 1? 3. (6 points) In the short run, profit-maximizing firms shut down when market price falls below the minimum of average variable cost (AVC). Calculate average variable cost and determine the lowest value it can possibly take ( AVC ; ). This is the "shut down price."