Test 2 8 November 2006

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1 Eco 301 Name Test 2 8 November points. Please write all answers in ink. You may use pencil and a straight edge to draw graphs. Allocate your time efficiently. 1. A fast-food restaurant currently pays $5 per hour for servers and $50 per hour for rental machinery. The restaurant uses seven hours of server time per unit of machinery time. Determine whether the restaurant is minimizing its cost of production when the ratio of marginal products (capital to labor) is 12. If not, what adjustments are called for to improve the efficiency in resource use? 2. Suppose there is an increase in the demand for shoes, which are provided by a competitive constant-cost industry. a. Does the industry-wide quantity change by more in the short run or in the long run? Illustrate your answer. b. Does the quantity provided by each individual shoemaker change by more in the short run or in the long run? Justify (illustrate) your answer. c. Do the profits of shoemakers change by more in the short run or in the long run? Justify (illustrate) your answer 3. Every firm in the widget industry has fixed costs of $6 and faces the following marginal cost curve: Quantity Marginal Cost ($) a. Suppose the price of widgets is $10. How many widgets does each firm produce? How much profit does each firm earn? Is the industry in long-run equilibrium? How do you know? b. In the long run, will there be entry or exit from this industry? What will be the price of widgets in the long run? How many widgets will each firm produce? 4. A retail liquor license in Montana was recently sold for over $110,000. The seller was the person who initially got the license from the state of Montana at a price of $2, 225. a. Can the buyer of the license expect to make a rate of return that is greater than the normal rate of return, thereby earning economic profits? Can the buyer expect to make an accounting profit? Explain. b. Is it likely that the seller of the license made more than the normal rate of return during the time he was selling liquor? Explain.

2 1. If the firm is minimizing its costs of production, then the MRTS will equal a ratio of prices of inputs. Pk r 50 The ratio of prices -- = -- = -- = 10 and the MRTS of capital for labor PL w 5 MPK = 12. MPL Since these two ratios are not equal, the firm should change the mix of inputs. To increase efficiency in the use of inputs, the firm should use more capital and use less labor to make the ratios equal. Another way of thinking about this is that capital is 12 times as productive but only ten times more costly. 2. a) Quantity changes more in the long run.. b) More in the short run; does not change in the long run c) Firms earn profits in the short run, but not in the long run.

3 Eco 301 Name Test 2 8 November points. Please write all answers in ink. You may use pencil and a straight edge to draw graphs. Allocate your time efficiently. 1. a. If firms are identical and in a competitive market, where on their average cost curve do they produce (and why)? b. How does a change in the competitive market equilibrium affect an individual firm s supply and demand curves? How does an individual firm s decision affect the market demand and supply curves? 2. A competitive firm sells its product at a price of $0.10 per unit. Its total and marginal cost functions are: TC = Q Q2 MC = Q where C is total cost ($) and Q is output rate (units per time period). a. Determine the output rate that maximizes profit or minimizes losses in the short-term. b. If input prices increase and cause the cost functions to become TC' = Q Q2 MC' = Q what will the new equilibrium output rate be? Explain what happened to the profit maximizing output rate when input prices were increased. 3. Suppose the price of labor is $1 per unit, and the price of capital is $1 per unit. Consider the short run case when capital is fixed at 2 units. a. Complete the following table. Quantity of Total Labor Output Variable Cost AVC Total Cost Marginal Cost

4 b. Suppose it is a competitive market where the price of output is $0.50. How much will it sell and what are profits? 4. In a USA Today article, Lack of liquor license dries up sales at restaurants, (24 October 2006), Rick Hampson reports that [Boston] famed for its thirst for spirits and suds has run out of restaurant alcohol licenses. As a result some Bostonians are being forced to down corned beef without beer, penne sans pinot noir. In Boston, the only way to get a liquor license is to buy another establishment's, and prices have shot up. A liquor license can cost more than $275,000; a beer and wine license goes for $50,000 to $100,000. That's more than many smaller places can afford. "In a state where you can't legally scalp a Red Sox ticket, you can sell a license granted by the city of Boston for a hundred times face value," fumes Chris Spaguolo, Sullivan's partner. a. Does the cap on the number of liquor licenses guarantee that those who currently own licenses earn economic profits? Explain why or why not. b. If the state legislature issues new licenses, will current license holders suffer economic losses? Explain why or why not.

5 1. 2. a. TR = R(Q) = PQ = 0.10Q MR = 0.10 TC = Q Q2 MC = Q = 0.10 = MR Q = 75 b. MC' = Q = 0.10 = MR Q = 50.0 c. As a result of the increase in input costs, the firm's marginal cost increased. This caused the intersection of MC to occur at the lower production rate, 50 vs. 75. This also reduced the firm's level of profit.

6 Eco 301 Name Test 2 8 November points. Please write all answers in ink. You may use pencil and a straight edge to draw graphs. Allocate your time efficiently. 1. A retail liquor license in Montana was recently sold for over $110,000. The seller was the person who initially got the license from the state of Montana at a price of $2, 225. a. Can the buyer of the license expect to make a rate of return that is greater than the normal rate of return, thereby earning economic profits? Can the buyer expect to make an accounting profit? Explain. b. Is it likely that the seller of the license made more than the normal rate of return during the time he was selling liquor? Explain. 2. Michelle s business produces ceramic cups using labor, clay, and a kiln. She can manufacture 25 cups a day with one worker and 35 with two workers. Does her production process illustrate diminishing returns to scale or diminishing marginal returns? What is the likely explanation for why output doesn t increase proportionately with the number of workers? 3. Conigan Box Company produces cardboard boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for $100 per thousand. Conigan's total and marginal cost curves are: TC = 3,000, Q2 MC = 0.002Q where Q is measured in thousand box bundles per year. a. Calculate Conigan's profit maximizing quantity. Is the firm earning a profit? b. Analyze Conigan's position in terms of the shutdown condition. Should Conigan operate or shut down in the short-run? 4. A firm's total cost function is given by the equation: TC = Q + 10Q2. (1) Write an expression for each of the following cost concepts: a. Total Fixed Cost b. Average Fixed Cost c. Total Variable Cost d. Average Variable Cost e. Average Total Cost f. Marginal Cost (2) Determine the quantity that minimizes average total cost. Demonstrate that the predicted relationship between marginal cost and average cost holds.

7 3. a. Given the competitive nature of the industry, Conigan should equate P to MC. 100 = 0.002Q Q = 50,000 To determine profit: π = TR - TC TR = PQ TR = $100 ú 50,000 TR = 5,000,000 TC = 3,000, (50,000)2 TC = 3,000, ,500,000 TC = 5,500,000 π = 5,000,000-5,500,000 π = -500,000 Conigan is losing 500,000 per year. b. To determine if the firm should operate or shutdown, we must compare P to AVC. AVC = TVC/ Q TVC = TC - TFC TVC = 5,500,000-3,000,000 TVC = 2,500,000 AVC = 2,500,000/50,000 = $50 AVC = 50; P = $100 The firm should operate since P > AVC 4. PART (1) a. TFC = 4000

8 b AFC = QS c. TVC = TC - TFC TVC = 5Q + 10Q2 d. TVC 5Q + 10Q2 AVC = = Q Q e. TC Q + 10Q2 AVC = = Q Q f. MC = Q PART (2) ATC is minimized where MC is equal to ATC. Equating MC to ATC Q + 10Q = Q Q Q = 5Q + 20Q = 10Q2 Q2 = 400 Q = 20 ATC is minimized at 20 units of output. Up to 20, ATC falls, while beyond 20 ATC rises. MC should be less than ATC for any quantity less than 20. For example, let Q = 10: MC = (10) = (10) + 10(10)2 ATC = =

9 MC is indeed less than ATC for quantities smaller than 20. MC should exceed ATC for any quantity greater than 20. For example, let Q = 25: MC = (25) = (25) + 10(25)2 ATC = = MC is indeed greater than ATC for quantities greater than 20.

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