Chapter 6 Sellers and Incentives

Active Learning Exercises for Chapter 6: Sellers and Incentives 1. (Marginal produce of labor; Diminishing marginal returns) Heather owns a vegetable farm and hires workers to pick tomatoes. Using the table below calculate the marginal product per worker and fill in the Marginal Product column. At which worker does the marginal product begin to diminish? Bushels Per Day # Employed Marginal Product 0 0 - 80 1 200 2 260 3 310 4 350 5 380 6 400 7 410 8 405 9 Solution: The marginal product per worker is the change in the total output associated with using one more unit of input. In this case, the inputs are workers and the output is the number of bushels picked in a day. The values of the marginal product are shown in the table below. The marginal product declines with the third worker. Bushels Per Day # Employed Marginal Product 0 0 - 80 1 80 200 2 120 260 3 60 310 4 50 350 5 40 380 6 30 400 7 20 410 8 10 405 9 -5 2. (Marginal product; Cost curves) John owns a nail salon and they produce manicures. John has provided you with the following information on the output per day based on the number of employees as well as the total cost. Fill in the remaining columns of the table. Output Per Day # Employed Marginal Product Variable Cost (VC) Fixed Cost (FC) Total Cost (TC) Average Total Cost (ATC) Average Fixed Cost (AFC) Average Variable Cost (AVC) Marginal Cost (MC) per unit of output per day 0 0 400 10 1 500 30 2 600 60 3 700 75 4 800 80 5 900 Solution: See table below. Marginal product is calculated as the change in (1). FC equals TC (6) when output is 0 or $400. VC equals TC minus FC. Each of the average cost columns are the respective cost divided by (1). And marginal cost is the change in (6) divided by the change in (1). (1) Output Per Day (2) # Employed (3) Marginal Product (4) Variable Cost (VC) (5) Fixed Cost (FC) (6) Total Cost (TC) (7) Average Total Cost (ATC) (8) Average Fixed Cost (AFC) (9) Average Variable Cost (AVC) (10) Marginal Cost (MC) per unit of output per day 0 0 $0 $400 $400 x 10 1 10 $100 $400 $500 $50 $40 $10 $10 30 2 20 $200 $400 $600 $20 $13.33 $6.67 $5 60 3 30 $300 $400 $700 $11.67 $6.67 $5 $3.33 75 4 15 $400 $400 $800 $10.67 $5.33 $5.33 $6.67 80 5 5 $500 $400 $900 $11.25 $5 $6.25 $20 3. (Cost curves) Deidra is an accountant who completes income tax returns for small businesses. The table below represents her costs of production. Complete the table. Hint: To get started, what is the fixed cost when output per day is one unit? Output Per Day Variable Cost (VC) Fixed Cost (FC) Total Cost (TC) Average Total Cost (ATC) Average Fixed Cost (AFC) Average Variable Cost (AVC) Marginal Cost (MC) 0 --------- ---------- -------- -------- 1 $600 $500 2 $200 3 $700 4 $800 Solution: Output Per Day Variable Cost (VC) Fixed Cost (FC) Total Cost (TC) Average Total Cost (ATC) Average Fixed Cost (AFC) Average Variable Cost (AVC) Marginal Cost (MC) 0 $0 $500 $500 --------- ---------- -------- -------- 1 $100 $500 $600 $600 $500 $100 $100 2 $300 $500 $800 $350 $250 $150 $200 3 $700 $500 $1,200 $400 $166.67 $233.33 $400 4 $1,500 $500 $2,000 $500 $125 $375 $800 4. (Firm profit maximization; Profits; From the firm to the market; Marginal revenue) Assume that Isaac’s Bagel Shop operates in a perfectly competitive market. The market price for bagels is $1.50 per bagel. Isaac’s Bagel Shop sells 1,000 bagels per day at this price and their average total cost of 1,000 bagels is $1.25. A. Is Isaac’s Bagel Shop making a profit or loss? B. Represent this situation in two graphs. First, draw a graph with the market demand and supply curves. Second, draw a graph for Isaac’s Bagel Shop. Be sure to label the curves and the area that presents the firm’s profit or loss. C. Calculate the firm’s profit or loss per day. Solution: A. Isaac’s Bagel Shop is making a profit as the average revenue per bagel, $1.50, is higher than the average total cost per bagel, $1.25. B. See graph below. C. The firm’s profit is (P – ATC) X Q. ($1.50 - $1.25) X 1,000 = $250 per day. 5. (From the firm to the market; Comparative statics) Assume the market for eggs is perfectly competitive. Several reports in 2014 highlighted the health benefits of eating eggs. Assume the reports caused a rightward shift in the market demand curve for eggs. In a graph with the market demand and market supply curve show the impact of the shift in the market demand curve on the market price and label the producer surplus before and after the change in market demand. Solution: The reports suggested health benefits from eating eggs and therefore could cause an increase in demand (market demand curve shifts to the right). The shift in the demand curve would increase the market price as shown in the graph as the movement from P1 to P2. The area representing the producer surplus would increase from area A to area ABC. 6. (From the firm to the market; Comparative statics; Long-Run competitive equilibrium) The previous question discussed a shift in the market demand curve for eggs caused by reports that extoled the health benefits of eating eggs. Assume that before the report was issued the egg market was in long-run equilibrium and assume firms are identical. In a graph of the egg market, again show the shift of the market demand curve and label this D2. How will the market adjust to a new long-run equilibrium? Explain and show the adjustment in your graph. Solution: The report caused the market demand curve to shift to the right. If the market was initially in long-run equilibrium, then we know that P1 is the price where firms make zero profits. At P2, the higher price associated with demand curve D2, we know that firms are making profits. This means that over time firms would be attracted to the egg market. As firms enter the market supply curve will shift rightward, shown as S2, and firms will keep entering until the market price falls back to P1. Note that overall market quantity has increased to Q3. See graph below. 7. (From the firm to the market; Comparative statics; Long-Run competitive equilibrium) The previous two questions have examined the effects of an increase in demand caused by reports of health benefits from egg consumption on the market for eggs and assumed that firms are identical. Assume Xavier’s Eggs was in business before the shift in demand. Show the firm graph and label the price and quantity produced by Xavier’s Eggs in: the initial situation, after the shift in demand, and finally after the market adjusts to a new long-run equilibrium. How does Xavier’s Eggs quantity produced in the initial situation compare to the new long-run equilibrium? Solution: In the initial situation, Xavier’s Eggs produce Q1 when price is P1. After the increase in price to P2, caused by the rightward shift in demand, output increases to Q2. Finally, as first enter and drive the price back down to P1, Xavier’s Eggs return to producing Q1. Note that despite Xavier’s Eggs producing the same number of eggs in the new long-run equilibrium as in the initial situation more eggs are produced in the overall market in the new long-run equilibrium because there are more firms in the market. See graph below.