1. Songs \"R\" Us writes songs and then sells them to musicians. Here is the relationship between the number of song writers and Songs \"R\" Us's output during a given day: Number of Marginal Total Average Marginal Writers Output Produ et Cost Total Cost Cost 0 0 1 20 2 50 3 90 4 120 5 140 6 150 7 155 a. Fill in the column of marginal products. What pattern do you see? How might you explain it? b. A song writer costs $100 a day, and the rm has xed costs of S200. Use this information to ll in the column for total costs. c. Fill in in the column for average total cost. (Recall that ATC = TC/Q) What pattern do you see? (1. Now ll in the column for marginal cost. What pattern do you see? Recall that MC _ Change in Total. Cost Change in output e. Compare the column for marginal product with the column for marginal cost. Explain this relationship. 2. Bob's lawnmowing service is a protmaximizing, competitive rm. Bob mows lawns for $27 each. His total cost each day is $280, of which $30 is a xed cost. He mews 10 lawns a day. What can you say about Bob's short-run decision regarding shutdown and his long-run decision regarding exit? (hint: rstnd Bob 'sA VC, ATC, and MC) 3. A prot-maximizing rm in a competitive market is currently producing 100 units of output. It has average revenue of $10, average total cost of $8, and xed cost of $200. a. What is its prot? b. What is its marginal cost? 0. What is its average variable cost? 4. The residents of the city of Rochester all love being outside, and the mayor proposes building a park. The park has a xed cost of $24,000 and no variable costs. There are 1,000 city residents, and each has the same demand for park visits: Q\" = 10 + P, where P is the price of admission. a. b. Graph the park's average-total-cost curve and its marginal-cost curve. What kind of market would describe the park? The mayor proposes nancing the park with a lump-sum tax of $24 and then opening the park to the public for free. How many times would each person visit? Calculate the benet each person would get from the park, measured as consumer surplus minus the new tax. The mayor's anti-tax opponent says the park should nance itself by charging an admission fee. What is the lowest price the park can charge without incurring losses? (Hint: Find the number of visits and park prots for prices of $2, $3, $4, and $5.) [optional] For the break-even price you found in part (c), calculate each resident's consumer surplus. Compared with the mayor's plan, who is better off with this admission fee, and who is worse off? Explain