Western Illinois University - Your potential. Our purpose.
Additional Chapter 12 problems and solutions
2. Price/Output Determination. Tallahassee Cars Unlimited, Inc., a rapidly expanding new entrant to this metropolitan area, is considering two proposals for the provision of its cosmetic detailing of cars (washing, waxing, polishing, engine cleaning, etc.). First, a large janitorial agency with some experience in the detailing of cars has offered to purchase the business detailing equipment in return for an exclusive franchise. A second proposal would allow several small contractors to enter the business without any exclusive franchise agreement or competitive restrictions. Under this plan, individuals would bid for the right to provide service on groups of cars as they were delivered to the lot, presumably based on how busy they were at the time. The car lot would then allocate business to the lowest bidder.
TCU has conducted a study of its past sales records and the amount of detailing spent on each car, and the premium over book value recouped in the sale to estimate the amount they would be willing to pay for various amounts of detailing. The car lot has also estimated the total cost of service per car. Service costs are expected to be the same whether or not an exclusive franchise is granted. To instigate bidding, TCU guarantees the winner of any bid a minimum per car, whether or not the service is used.
|A. |Use the indicated price and cost data to complete the following table. |
| | |
| |Hours of |Price | | | | |
| |Detailing |per |Total |Marginal |Total |Marginal |
| |per Car |Hour |Revenue |Revenue |Cost |Cost |
| |0 |$24.00 | | |$ 0.00 | |
| |1 |23.40 | | |18.00 | |
| |2 |22.80 | | |36.00 | |
| |3 |22.20 | | |54.00 | |
| |4 |21.60 | | |72.00 | |
| |5 |21.00 | | |90.00 | |
| |6 |20.40 | | |108.00 | |
| |7 |19.80 | | |126.00 | |
| |8 |19.20 | | |144.00 | |
| |9 |18.60 | | |162.00 | |
| |10 |18.00 | | |180.00 | |
| | |
|B. |Determine price and the level of service if competitive bidding results in a perfectly competitive price/output |
| |combination. |
| | |
|C. |Determine price and the level of service if the car lot grants a monopoly franchise. |
ANS:
|A. | |
| |Hours of |Price | | | | |
| |Detailing |per |Total |Marginal |Total |Marginal |
| |per Car |Hour |Revenue |Revenue |Cost |Cost |
| |0 |$24.00 |$ 0.00 |-- |$ 0.00 |-- |
| |1 |23.40 |23.40 |$23.40 |18.00 |$18.00 |
| |2 |22.80 |45.60 |22.20 |36.00 |18.00 |
| |3 |22.20 |66.60 |21.00 |54.00 |18.00 |
| |4 |21.60 |86.40 |19.80 |72.00 |18.00 |
| |5 |21.00 |105.00 |18.60 |90.00 |18.00 |
| |6 |20.40 |122.40 |17.40 |108.00 |18.00 |
| |7 |19.80 |138.60 |16.20 |126.00 |18.00 |
| |8 |19.20 |153.60 |15.00 |144.00 |18.00 |
| |9 |18.60 |167.40 |13.80 |162.00 |18.00 |
| |10 |18.00 |180.00 |12.60 |180.00 |18.00 |
| | |
|B. |In a perfectly competitive industry, P = MR so the optimal activity level occurs where P = MC. Here, P = MC = $18 at Q = |
| |10 hours of detailing per car, and profits equal zero. |
| | |
|C. |A monopoly will maximize profits by setting MR = MC. Here, MR = MC = $18.60 > $18 at Q = 5 hours of detailing per car and|
| |P = $21 per hour. Note that MR < MC when Q > 5. |
15. Costs of Regulation. Glove-Box, Inc., produces glove boxes designed to allow workers to safely handle hazardous materials used in a wide variety of products. Market demand and marginal revenue relations for the Glove-Box units are:
P = $500,000 - $250Q
MR = ∂TR/∂Q = $500,000 - $500Q
Assume the Occupational Health and Safety Administration (OSHA) has recently ruled that Glove-Box must install expensive new shielding equipment to further guard against worker injuries. This will increase the $200,000 marginal cost of manufacturing by $250,000 per unit. Glove-Box's fixed expenses of $50 million per year, which include a required return on investment, will be unaffected.
|A. |Calculate Glove-Box's profit-maximizing price/output combination and economic profit level before installation of the |
| |OSHA-mandated shielding equipment. |
| | |
|B. |Calculate the profit-maximizing price/output combination and economic profit level after Glove-Box has met OSHA |
| |guidelines. |
| | |
|C. |Compare your answers to parts A and B. Who pays the economic burden of meeting OSHA guidelines? |
ANS:
|A. |Glove-Box will maximize profits by setting MR = MC. Before the OSHA-mandated increase in costs, MC = $200,000. Therefore,|
| | |
| |MR = MC |
| |$500,000 - $500Q = $200,000 |
| |500Q = 300,000 |
| |Q = 600 |
| | |
| |P = $500,000 - $250(600) |
| | = $350,000 |
| | |
| |Total Economic Profits = PQ - TC |
| | = $350,000(600) - $200,000(600) - $50,000,000 |
| | = $40,000,000 |
|B. |After the OSHA-mandated increase in costs, MC = $250,000. Therefore, Glove-Box's optimal activity level changes as |
| |follows: |
| | |
| |MR = MC + $50,000 |
| |$500,000 - $500Q = $250,000 |
| |500Q = 250,000 |
| |Q = 500 |
| | |
| |P = $500,000 - $250(500) |
| | = $375,000 |
| | |
| |Total Economic Profits = PQ - TC |
| | = $375,000(500) - $250,000(500) - $50,000,000 |
| | = $12,500,000 |
|C. |In this instance, Glove-Box and its customers share the costs of meeting OSHA guidelines. The number of units sold falls |
| |by 16.7% from 600 to 500 in response to the $25,000 price increase from $350,000 to $375,000. Therefore, customers bear |
| |some of the regulatory burden due to higher prices and fewer units of output being available. The rest of the burden of |
| |this regulation has fallen on Glove-Box stockholders in terms of lost economic profits, and Glove-Box employees in terms |
| |of lost employment opportunities due to reduced levels of production. |
20. Monopoly Regulation. The Woebegone Telephone Company, a utility serving rural customers in Minnesota, is currently engaged in a rate case with the regulatory commission under whose jurisdiction it operates. At issue is the monthly rate the company will charge for basic hookup service. The demand curve for monthly service is P = $50 - $0.005Q. This implies annual demand and marginal revenue curves of:
P = $600 - $0.06Q
MR = ∂TR/∂Q = $600 - $0.12Q
where P is service price in dollars and Q is the number of customers served. Total and marginal costs per year (before investment return) are described by the function:
TC = $100,000 + $100Q + $0.04Q2
MC = ∂TC/∂Q = $100 + $0.08Q
The company has assets of $4 million and the utility commission has authorized a 12.5% return on investment.
|A. |Calculate Woebegone's profit-maximizing price (monthly and annually), output, and rate-of-return levels. |
| | |
|B. |What monthly price should the commission grant to limit Woebegone to a 12.5% rate of return? |
ANS:
|A. |To find the profit-maximizing level of output, set MR = MC where: |
| | |
| |MR = MC |
| |$600 - $0.12Q = $100 + $0.08Q |
| |0.2Q = 500 |
| |Q = 2,500 |
| | |
| |P = $50 - $0.005(2,500) | |
| | = $37.50 |(Monthly price) |
| | | |
| |P = $600 - $0.06(2,500) | |
| | = $450 |(Annual price) |
| | |
| |π = TR - TC |
| | = $450(2,500) - $100,000 - $100(2,500) - $0.04(2,5002) |
| | = $525,000 |
| | |
| |If the company has $4 million invested in plant and equipment, its optimal rate of return on investment is: |
| | |
| |Return on investment = [pic] |
| | = 0.13125 or 13.125% |
| | |
| |(Note: Profit is falling Q > 2,500.) |
| |With a 12.5% return on total assets, Woebegone would earn profits of: |
|B. | |
| | |
| |π = Allowed return × Total assets |
| | = 0.125($4,000,000) |
| | = $500,000 |
| | |
| |To determine the level of output that would be consistent with this level of total profits, consider the profit relation:|
| | |
| |π = TR - TC |
| |$500,000 = $600Q - $0.06Q2 - $100,000 - $100Q - $0.04Q2 |
| |500,000 = -0.1Q2 + 500Q - 100,000 |
| |0 = -0.1Q2 + 500Q - 600,000 |
| | |
| |which is a function of the form aQ2 + bQ + c = 0 where a = -0.1, b = 500 and c = -600,000, and can be solved using the |
| |quadratic equation. |
| | |
| |Q = [pic] |
| | = [pic] |
| | = [pic] |
| | = 2,000 or 3,000 customers |
| | |
| |Because public utility commissions generally want utilities to provide service to the greatest possible number of |
| |customers at the lowest possible price, the "upper" Q = 3,000 is the appropriate output level. This output level will |
| |result in a monthly service price of: |
| | |
| |P = $50 - $0.005(3,000) |
| | = $35 |
| | |
| |This $35 per month price will provide Woebegone with a fair rate of return on total investment, while ensuring service to|
| |a broad customer base. |
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