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PROBLEM SET 7 1. Keggs produces pantyhose for barmaids. Both the labor and product markets are perfectly competitive. Keggs’ production function for pantyhose is below. NUMBER OF WORKERS (L) 2 3 4 5 6 7 PAIRS OF PANTYHOSE PER HOUR (Q) 25 40 54 67 79 90 TOTAL REVENUE (TR) MARG. REV. PRODUCT (MRP) -- Suppose that each pair of pantyhose sells for $5. Suppose further that the average wage rate per worker is $60 a day. Keggs is currently employing four workers. Is this the optimal number of workers for Keggs to hire? Why or why not? (HINT: Find the TR and MRP schedules) 2. The following table shows the marginal physical product associated with different numbers of pizza chefs hired by “Crazy Jean’s Pizza Parlor. NUMBER OF PIZZA CHEFS (L) 0 1 2 3 4 5 6 a. b. c. d. e. MARGINAL PHYSICAL PRODUCT (MPPL) -35 30 25 20 15 10 MARG. REV. PRODUCT (MRP) P = $3 -- MARG. REV. PRODUCT (MRP) P = $4 -- Assuming a price per pizza of $3, find the marginal revenue product schedule. Draw Crazy Jean’s demand curve for pizza chefs. If the chefs are paid $45 a day, how many will Crazy Jean hire? How many would Crazy Jean hire if chefs’ wages rise to $60 per day? Suppose the price of a pizza rises from $3 to $4. What happens to the demand curve for chefs? How many chefs will Crazy Jean hire if chefs must be paid $60 a day (as in part d)? Does Crazy Jean hire more or fewer chefs than in part d? Does the change in the number of chefs hired make economic sense? 2 3. A widget producer has the following production function showing the quantity of widgets that can be produced for various amounts of labor hired. NUMBER OF WORKERS (L) 2 3 4 5 6 7 NUMBER OF WIDGETS (Q) 25 40 54 67 79 90 TOTAL REVENUE (TR) MARG. REV. PRODUCT (MRP) -- a. Calculate the widget producer’s Total Revenue and Marginal Revenue Schedules. b. Draw the widget producer’s demand schedule. c. If the wage rate the widget producer has to pay to each worker hired is $20, how many workers should the producer hire? d. If the wage rate increases to $40, how many workers should the producer hire? 3 4. Suppose that a single widget producer, operating in perfectly competitive product and labor markets has the following demand and supply curves for labor and therefore initially hires L1 workers. Wage rate $20 A SL DL = MRP L1 Number of workers (L) For each separate event below, show what will happen to the number of workers the firm will hire. Draw a separate diagram for each part. a. b. c. d. New equipment increases the marginal productivity of labor. A new technology reduces the marginal productivity of labor. The wage rate that must be paid to widget workers increases to $25. The price at which the producer can sell widgets increases. 4 SELECTED ANSWERS 1. PAIRS OF PANTYHOSE PER HOUR (Q) 25 40 54 67 79 90 NUMBER OF WORKERS (L) 2 3 4 5 6 7 TOTAL REVENUE (TR) 125 200 270 335 395 450 MARG. REV. PRODUCT (MRP) -75 70 65 60 55 Hiring four workers is not optimal because MRP > wage rate: by hiring more workers the firm can add more to its total revenue than to its total costs (NOTE: the 5th worker’s, MRP, the addition to total revenue, is $65 while the wage rate, the addition to total costs, is only $60). Thus, the firm should hire up to 6 workers where MRP = w. 2. a. MARGINAL PHYSICAL PRODUCT (MPPL) -35 30 25 20 15 10 NUMBER OF PIZZA CHEFS (L) 0 1 2 3 4 5 6 b. MARG. REV. PRODUCT (MRP) P = $3 -105 90 75 60 45 30 MARG. REV. PRODUCT (MRP) P = $4 -140 120 100 80 60 40 The demand curve for chefs is the MRP schedule: 105 90 DL = MRP 0 c. 1 2 3 4 5 5 chefs where MRP = w. 6 L 5 d. 4 chefs where MRP = w. e. The marginal revenue product of each additional chef hired increases. (See chart on previous page). Thus, the demand curve shifts to the right. Crazy Jean will hire 5 chefs, where MRP = w. Since the marginal revenue product of each additional worker hired has increased (workers contribute more to Crazy Jean’s total revenues), it is profitable to hire more workers than in part d. 3. a. NUMBER OF WORKERS (L) 2 3 4 5 6 7 b. c. NUMBER OF WIDGETS (Q) 25 40 54 67 79 90 6 workers where MRP = w. 4 workers where MRP = w. TOTAL REVENUE (TR) $60 110 150 180 200 210 MARG. REV. PRODUCT (MRP) -$50 40 30 20 10 6 4. a. b. A A $20 $20 c. d. $25 $20 $20 A A