Assignment 3: Costs of Production and the Organization of the Firm
Consider the following production function: Q K L . Explain the special characteristics of this production function. How is it different from a Linear
production function? How is it different from a Leontief production function? (8 marks)
b. Assuming that the firm hires 10 units of capital and 20 units of labour, use the production function given in part a to compute the average and marginal products of labour. (8 marks)
c. Explain how the firm would use the marginal product of labour to determine the profit maximizing quantity of labour which the firm would hire.
A firm produces the following units of output, Q, by hiring a fixed quantity of capital, K, and labour, L, as follows:
L: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Q: 16, 36, 65, 97, 137, 177, 209, 233, 249, 257
a. Determine the average and marginal products of labour. (6 marks)
b. Provide rough graphs of the total product, average product, and marginal product curves and explain why they behave in the way they do. Be sure to label your axes correctly. (4 marks)
c. Assuming that the cost of capital is $1,000 and labour costs $10.00 per hour, determine the total variable cost, average variable cost, and the marginal cost of the firm for the output levels given above. (6 marks)
d. Provide rough graphs of the TVC, AVC, and MC curves and compare their behaviour with the product curves in part b. Be sure to label your axes correctly. (4 marks)
Assume that a firm hires only labour and capital to produce bicycles.
a. Explain the cost minimization rule for this firm and why this rule is logical?(8 marks)
A private college adds a small café to its building to cater to the needs of its own students. The total cost of the facilities for the café is $100,000. After a year of operations the college determines that operating the café is interfering with its primary business of educating students. A group of enterprising business students offer to purchase the café facilities for $50,000. The college balks at the idea because it had paid $100,000 for the facilities. The college spends $10,000 advertising the café for sale hoping to get an outside buyer willing to pay much more than the students and operate the café on campus. When no outside offer was forthcoming the students increased their offer to $55,000. Should the college take the students’ offer? Why or why not?
Firms often pay managers a percent of profits to encourage them to work longer hours for the company. Managers are often conflicted by the desire for extra income and the reduction of leisure time for family and personal enjoyment. Consider the following example. When the manager is paid a salary of $100,000 without a share of profits, she spends the minimum required time at work and maximizes her leisure time. When the manager is paid $100,000 plus a small percent of profits she increases the time spent at work. Her average income increases to $120,000. Can you tell from this example whether the manager has shown a preference for the second compensation scheme? If so, has the company benefited from the second compensation scheme? (10 marks)
b. Suppose that the firm hires 100 units of capital and 500 units of labour and that the MPl is 20 while MPk is 25. If a unit of labour costs $4.00 and a unit of capital costs $5.00, is the firm minimizing costs? Explain. (4 marks)
c. If the price of capital falls to $4.00 what should the firm do to minimize cost? Explain why your answer is consistent with the cost minimization rule.
b. Explain why the short run ATC is U‐shaped? Explain why the long‐run ATC is also U‐shaped? How are the two curves different? (10 marks)
b. Explain the difference between economies of scope and cost complementarity. Provide one example of each. (10 marks)
Assignment 4: Market Structures
1. Having completed this course as part of your MBA program you have been hired by a medium‐sized company. You attend a meeting where the CEO explains that the goal of the company is to maximize profits, not total revenue. As such the firm must estimate both costs and revenues to determine the output where the difference between marginal revenue and marginal cost is the greatest. Will this output level maximize the firm’s profits? Explain why or why not. (20 marks)
2. You have been hired by a restaurant owner to advise whether or not to close the restaurant. You have determined that the restaurant’s only fixed cost is monthly rent of $5,000. The owner signed a 10‐year lease with the landlord four years ago when she opened the restaurant. In the last year her sales revenue has declined to $185,000. She trimmed her labour cost to $125,000, which includes the opportunity cost of her time managing the restaurant. Her cost of materials was reduced to $40,000. She does not foresee any change in revenues or costs over the next six years. Last year her loss was $40,000.00. Her friends advise her to close the restaurant to cut her losses. What would you advise the owner? Explain.
3. The market demand for woozles is given by:
Qd 2, 400 – 20p
There is only one available technology, and it is employed by all producers—
actual and potential. It implies the following average cost function: AC625q–1 0.25q
Currently, 20 firms serve the market.
a. Find the individual firm’s supply curve. (3 marks)
b. Find the industry supply curve. (3 marks)
c. Determine the short‐run competitive price and output. (3 marks)
d. How much profit is the typical firm making? (3 marks)
e. Determine the long‐run competitive market price and quantity and how many firms will operate. (8 marks)
4. A monopolist can produce at constant average and marginal costs of AC MC 9 . The firm faces a demand curve given by:
q 75 – p
a. Calculate the profit‐maximizing price quantity combination for the
monopolist. Also calculate the monopolist’s profits. (12 marks)
b. What output would be produced by this industry under perfect competition?
Showthat PMPCand QC2QM.(8marks)
5. Assume for a perfectly competitive firm that MC AVC at $12, MC ATC at $20, and MC MR at $16. On the basis of this information, the firm should not be in production. Do you agree? Explain fully. (20 marks)
Assignment 5: Game Theory and Pricing Strategies
After you finish Module 5, complete this assignment and submit it to your Open Learning Faculty Member for marking. The assignment has five questions worth 20 marks each, for a total of 100 marks, and counts for 12 per cent toward your final course grade.
1. a. Assume that a monopoly has a linear demand curve. If it is charging the profit maximizing price, will the demand for its product at that price be elastic or inelastic? Explain fully. (10 marks)
b. Bringing Up Baby has a monopoly in the production of step‐by‐step manuals for child rearing. Its total cost of producing manuals is given by TC 12.5Q , and the demand for manuals is given by the non‐linear demand,
Q 25,000P–2 .
Calculate the profit‐maximizing price and quantity of manuals.
2. You have been asked by your boss to report on the expected profits from a single price strategy compared with a two‐part pricing strategy. The estimated demand for the firm’s product is:
Qd 400 0.2P .
Per unit cost is estimated as constant at $1,000.00. Provide a report which explains the profits from a single price profit maximizing strategy with a two‐ part profit maximizing strategy involving a fixed fee plus a per unit fee. Assume that total fixed cost is $30,000. What is the optimal fixed fee? Why does the two‐ part pricing policy increase total profits? (20 marks)
3. Many service industries such as restaurants, night clubs, movie theatres, and hair dressers experience much higher demand during weekends compared to weekdays. Explain a pricing strategy which would increase profits compared to a single price profit maximizing strategy. Be sure to include a graph which explains your demand, marginal revenue, and marginal cost. (20 marks)
4. Explain why a monopolist can increase profits by practising price discrimination compared with using a single price to maximize profits? What are the different kinds of price discrimination? What are the necessary conditions required for a monopolist to be able to practice each kind? Provide one example of each of the different types of price discrimination. You may use graphs to illustrate.
5. You are the manager of a gas station in a small town in the United States, and your goal is to maximize profits. Based on your experience, the elasticity of demand of Texans for a car wash is –2, and that of non‐Texans is –1.5. Your marginal cost is $6.
a. Are the conditions necessary for price discrimination to be an effective means of enhancing profits being met? Explain fully.
b. What is the profit‐maximizing price to charge a Texan for a car wash? (5 marks)
c. What is the profit‐maximizing price to charge a Californian for a car wash? (5 marks)
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