U3 Business Calculus Practice FRQs 1. Bob’s lawn mowing service is a profit-maximizing competitive firm. Bob mows lawns for $27 each. His total cost each day is $280, of which $30 is a fixed cost. He mows 10 lawns a day. What can you say about Bob’s short-run decision regarding shut down and his long-run decision regarding exit? 2. Consider total cost and total revenue given the following table: Quantity 0 1 2 3 4 5 6 7 Total Cost $8 9 10 11 13 19 27 37 Total Revenue $0 8 16 24 32 40 48 56 a. How many units should this firm produce? b. Is this firm a perfectly competitive firm? How do you know? c. Is the industry in long-run equilibrium? d. Using the table above, determine the long-run equilibrium price. 3. Callahan’s Orchard grows apples and operates in a constant-cost, perfectly competitive apple industry. Callahan’s Orchard is currently in long-run equilibrium. a. Draw correctly labeled side-by-side graphs for the apple market and Callahan’s Orchard, and show each of the following. i. Market output and price, labeled as “QM” and “PM”, respectively ii. Callahan’s output and price, labeled as “QF” and “PF”, respectively b. Now assume that the government provides farm support to apple growers by granting an annual lump-sum subsidy (hint: there’s a difference between a lump-sum subsidy and a per-unit subsidy and this will affect your answer) to all apple growers. Indicate the effect the subsidy would have on each of the following in the short run. i. Callahan’s quantity of output. Explain. ii. Callahan’s profit iii. The number of firms in the industry c. Indicate how each of the following will change in the long run as a result of the lump-sum subsidy. i. The number of firms in the industry. Explain. ii. Price iii. Industry output 4. Assume that corn is produced in a perfectly competitive market. Farmer Roy is a typical producer of corn. a. Assume that Farmer Roy is making zero economic profit in the short run. Draw a correctly labeled side-by-side graph for the corn market and for Farmer Roy and show each of the following. i. The equilibrium price and quantity for the corn market, labeled as PM1 and QM1, respectively ii. The equilibrium quantity for Farmer Roy, labeled as QF1 b. For Farmer Roy’s corn, is the demand perfectly elastic, perfectly inelastic, relatively elastic, relatively inelastic, or unit elastic? Explain. c. Corn can be used as an input in the production of ethanol. The demand for ethanol has significantly increased. i. Show on your graph in part (a) the effect of the increase in demand for ethanol on the market price and quantity of corn in the short run, labeling the new equilibrium price and quantity as PM2 and QM2, respectively. ii. Show on your graph in part (a) the effect of the increase in demand for ethanol on Farmer Roy’s quantity of corn in the short run, labeling the quantity as QF2. iii. How does the average total cost for Farmer Roy at QF2 compare with PM2? d. Corn is also used as an input in the production of cereal. What is the effect of the increased demand for ethanol on the equilibrium price and quantity in the cereal market in the short run? Explain. 5. Suppose that roses are produced in a perfectly competitive, increasing-cost industry in long-run equilibrium with identical firms. a. Draw correctly labeled side-by-side graphs for the rose industry and a typical firm and show each of the following. i. Industry equilibrium price and quantity, labeled Pm and Qm, respectively ii. The firm’s equilibrium price and quantity, labeled Pf and Qf , respectively b. Is P m larger than, smaller than, or equal to P f ? c. Assume that there is an increase in the demand for roses. On your graphs in part (a), show each of the following. i. The new short-run industry equilibrium price and quantity, labeled Pm2 and Q m2, respectively ii. The new short-run profit-maximizing price and quantity for the typical firm, labeled P f2 and Qf2, respectively d. As the industry adjusts to a new long-run equilibrium, i. what will happen to the number of firms in the industry? Explain. ii. will the firm’s average total cost curve shift upward, shift downward, or remain unchanged? e. In the long run, compare the firm’s profit-maximizing price in each of the following. i. Pf in part (a)(ii) ii. Pf2 in part (c)(ii) 6. Tori is a producer of palm trees in a perfectly competitive market that is currently in long-term equilibrium at the price of $50. At equilibrium quantity of 100 trees, Tori’s average variable cost per tree is $35. a. Draw a graph for both the industry and Tony’s firm (include MR, MC, ATC, and AVC). (4 points) i. Label the area of Tony’s Total Revenue (1 point) ii. Label the area of Total Cost (1 point) iii. Label the shutdown point. (1 point) b. Describe Tony’s firm in terms of the following: i. Productive efficiency (1 Point) ii. Allocative efficiency (1 point) c. With side-by-side graphs, show the results of an increase in demand for palm trees and identify what happens to the following in the short-run. (2 points) i. Price for Tony’s firm. (1 point) ii. Quantity for Tony’s firm. (1 point) 7. Assume that apples are an inferior good. Draw a perfectly competitive market for apples and a firm selling apples in long-run equilibrium where price is $10 and the firm’s equilibrium quantity is 50. Explain the following situations graphically and in words (draw and label side-by-side graphs for each). (4 points) a. GRAPH and EXPLAIN what happens in the short-run if incomes increase by 15%. (2 points) b. GRAPH and EXPLAIN the process by which markets return to the long-run equilibrium. (2 points) 8. La Lecheria, a typical profit-maximizing dairy firm, is operating in a constant-cost, perfectly competitive industry in long-run equilibrium. a. Draw correctly labeled side-by-side graphs for the dairy market and for La Lecheria and show each of the following: i. Price and output for the industry (2 points) ii. Price and output for Bestmilk (2 points) b. Assume that milk is a normal good and that consumer income falls. Assume that La Lecheria continues to produce. On your graphs in part (a), show the effect of the decrease in income on each of the following in the short run. i. Price and output for the industry ii. Price and output for Bestmilk iii. Area of profit or loss for Bestmilk c. Following the decrease in consumer income, what must be true for La Lecheria to continue to produce in the short run? d. Assume that the industry adjusts to a new long-run equilibrium. Compare the following between the initial and the new long-run equilibrium. i. Price in the industry ii. Output of a typical firm iii. The number of firms in the dairy industry 9. Below is information regarding Cory’s Surfboard Inc. Complete the table and do the following: a. On a large graph, plot the MC, AFC, AVC, and ATC curves from this data. b. EXPLAIN what would happen to each of Cory’s per unit cost curves if the price of Styrofoam blanks (a variable input) increases. How would the cost curves change if there were an increase in his rent (a fixed input)? Explain why the results are different. c. If the market for surfboards was perfectly competitive and the market price was $150, how many surfboards should Cory make and how much profit will he make for EACH surfboard? Draw the firm’s demand on your graph in (a) Explain how you got your answer. d. Label Productive efficiency and Allocative efficiency Total Product 0 1 2 3 4 5 6 7 Variable Costs (TVC) $0 60 90 130 180 250 340 490 Total Cost (TC) $100 Average Fixed Cost (AFC) Average Variable Cost (AVC) Average Total Cost (ATC) Marginal Cost (MC) 8 680 10. A commercial fisherman notices the following relationship between hours spent fishing and the quantity of fish caught. Hours Fish (lbs.) TP MP AP FC VC TC 0 1 2 3 4 5 a. What is the MP of each hour spent fishing? b. Graph: Total Product (TP), Marginal Product (MP), Average Product (AP) c. The fisherman has a fixed cost of $10 (his pole). His opportunity cost is $5/hr. Complete the table and graph his FC, TC, and VC curves.