ECNS 251 Homework 6 Producer Theory

Transcription

1 ECNS 251 Homework 6 Producer Theory 1. Bob's Burgers faces the following demand and cost schedules for their hamburgers: Q (burgers/hour) P ($/burger) ($/hour) Total Revenue Marginal Revenue Marginal a. Complete the total revenue, marginal revenue, and marginal cost columns of the table. b. How many burgers should Bob's produce each hour in order to maximize profits? What price should they charge for burgers? What will be the profits at that output level? Bob's should produce 3 burgers per hour and charge $8 per burger. This is the point that equates marginal revenue and marginal cost. At that level of output, profits are TR - TC = = $12 per hour. Note that you could also have argued that he should produce 2 burgers per hour at $9 each since that level of production also earns Bob $12 in profits per hour. 1

2 2. Tori leases a farmer s field and grows pineapples. Tori hires students to pick and pack the pineapples. Her production function is shown in the table below. Labor (# of students per day) Output (# pineapples per day) Marginal Product of Labor Marginal /100 = /120 = /80 = /60 = /40 = /20 = 2.5 a. Fill in the marginal product of labor column in the table. b. Suppose that Tori pays each student $50 per day. She leases the field for $300. Given this information, complete the total cost and marginal cost columns in the table. c. If pineapples are priced at $2 each and Tori can sell all the pineapples that she wants to at that price level, how many students should Tori hire per day? What will be her profits at that level of employment and production? If pineapples are priced at $2 each, we can compare marginal revenue ($2) against marginal cost to determine the optimum amount of output to produce and the optimum number of students to hire. Hiring 5 students generates 400 units of output at a marginal cost of the 400 th pineapple of $1.25. This is the highest output/employment level where MR>MC, so this level maximizes Tori's profits. Total Revenue will be 400 pineapples * $2 each = $800 per day is $550 per day Profit is $250 per day 3. You are the chief financial officer for Tom s Brewery that sells beer (assume there is only one type of beer). Your firm has the following average total cost schedule: Quantity (number of kegs) Average ($/keg)

3 Your current level of production is 200 kegs, all of which have been sold. Theresa is having a Bastille Day party (assume it is Bastille Day) and has run out of kegs. She calls, desperate to buy a keg. She offers you $250 for it. Should you accept the offer? Why or why not? What if she offers you $300 for it? At an output level of 200 kegs, total cost is $20,000 (200 $100). The total cost of producing 201 kegs is $20,301 (201 x 101). Therefore, you should not accept the offer of $250, because the marginal cost of the 201st keg is $301 ($20,301-$20,000). For the same reason, you should not accept $300 for the keg. 4. The green conscience city government of Vienna is considering two tax proposals: A lump-sum tax of $300 on each producer of plastic bags. A tax of $1 per plastic bag, paid by producers of plastic bags. a. Which of the following curves average fixed cost, average variable cost, average total cost, and marginal cost would shift as a result of the lump-sum tax? Why? Show this in a graph. Label the graph as precisely as possible. The lump-sum tax causes an increase in fixed cost. Therefore, as the figure below shows, only average fixed cost and average total cost will be affected. b. Which of these same four curves would shift as a result of the per-plastic bag tax? Why? Show this in a new graph. Label the graph as precisely as possible. 3

4 Average variable cost, average total cost, and marginal cost will all be greater. Average fixed cost will be unaffected. 4

5 5. Sarah's Juice Bar has the following cost schedules: Quantity (vats of juice/period) Variable a. Calculate average variable cost, average total cost, and marginal cost for each quantity. Quantity (vats of juice/period) Variable Total Average Variable Average Marginal 0 $ 0 $ $5 $20 $

6 b. Graph all three curves (AVC, ATC, MC). What is the relationship between the marginal cost curve and the average total cost curve? What is the relationship between the marginal cost curve and the average variable cost curve? Explain. The figure below shows the three curves. The marginal cost curve is below the average total cost curve when output is less than four and average total cost is declining. The marginal cost curve is above the average total cost curve when output is above four and average total cost is rising. The marginal cost curve lies above the average variable cost curve. 25 s (AVC, MC, ATC) Blue=MC Yellow=ATC Red=AVC 6

7 6. Suppose that the price of labor (the wage rate) is $125 a day and that the rental price of capital is $30 a day. Currently the Jedie Weapons Corporation is using ten units of capital and five units of labor to produce 500 lightsabers a day. Each lightsaber sells for $2. At the current input use levels, the marginal product of capital is 40 lightsabers per day and the marginal product of labor is 80 lightsabers a day. a. Is the firm making an economic profit at its current levels of operation? Yes: Total revenue = P*Q = $2 *500 = $1000. Total cost = $125*5 + $30*10 = $925 The firm is making $75 profit b. Could the firm increase its profits at the current level of output by adjusting its use of labor and capital? If so, how should input use be adjusted? Yes MP L /MP K = 80/40=2, but P L /P K = $125/$30=$ These are not equal labor costs $4.166 more than capital, but at the current margin it is not times as productive. The firm could increase profits by replacing some L with some K. 7. Read, "Another Sign of the Improving Economy," (Marketplace.org post 12/08/2017) and answer the following. a. The caption under the photo in the story describes Target's plans to raise the wages for its employees. What are the tradeoffs associated with this plan? b. Why are the drop in part-time workers and people working multiple jobs a positive sign for the economy? c. What do the results from the National Federation of Independent Businesses survey indicating that small business owners were struggling to find qualified workers imply about the labor market? 7