1. Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is L = cH0.8N0.2.
a. Beginning with a health input of $400 per year (H = 4) and a nutrition input of $4900 per year (N = 49), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing.
b. Does this production function exhibit increasing, decreasing, or constant returns to scale?
c. Suppose that in a country suffering from famine, N is fixed at 2 and that c = 20. Plot the production function for life expectancy as a function of health expenditures, with L on the vertical axis and H on the horizontal axis.
d. Now suppose another nation provides food aid to the country suffering from famine so that N increases to 4. Plot the new production function
2. Suppose the process of producing lightweight parkas by Uluru’s Parkas is described by the function
q = 10K0.8(L − 40)0.2
where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor. In addition to capital and labor, $10 worth of raw materials is used in the production of each parka.
a. By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output (q), wage rates (w), and rental rates on machines (r). Use these results to derive the total cost function: that is, costs as a function of q, r, w, and the constant $10 per unit materials cost.
b. This process requires skilled workers, who earn $32 per hour. The rental rate on the machines used in the process is $64 per hour. At these factor prices, what are total costs as a function of q? Does this technology exhibit decreasing, constant, or increasing returns to scale?
c. Uluru’s Parkas plans to produce 2000 parkas per week. At the factor prices given above, how many workers should the firm hire (at 40 hours per week) and how many machines should it rent (at 40 machine-hours per week)? What are the marginal and average costs at this level of production?
[25 Marks] School of Business Semester 1, 2015 Faculty of Law, Education, Business & Arts ECO201 Assignment 2 7 of 7
3. Doug’s Doorstops, Inc. (DD) is a monopolist in the doorstop industry. Its cost is C = 100 - 5Q + Q2, and demand is P = 55 - 2Q.
a. What price should DD set to maximize profit? What output does the firm produce? How much profit and consumer surplus does DD generate?
b. What would output be if DD acted like a perfect competitor and set MC = P? What profit and consumer surplus would then be generated?
c. What is the deadweight loss from monopoly power in part a?
d. Suppose the government, concerned about the high price of doorstops, sets a maximum price at $27. How does this affect price, quantity, consumer surplus, and DD’s profit? What is the resulting deadweight loss?
e. Now suppose the government sets the maximum price at $23. How does this decision affect price, quantity, consumer surplus, DD’s profit, and deadweight loss?
4. Northern Airlines (NA) flies only one route: Darwin-Adelaide. The demand for each flight is Q = 500 - P. NA’s cost of running each flight is $30,000 plus $100 per passenger.
a. What is the profit-maximizing price that NA will charge? How many people will be on each flight? What is NA’s profit for each flight?
b. NA learns that the fixed costs per flight are in fact $41,000 instead of $30,000. Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that NA faces, NA’s average cost curve when fixed costs are $30,000, and NA’s average cost curve when fixed costs are $41,000.
c. Wait! NA finds out that two different types of people fly to Adelaide. Type A consists of business people with a demand of QA = 260 - 0.4P. Type B consists of students whose total demand is QB = 240 - 0.6P. Because the students are easy to spot, NA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does NA charge the students? What price does it charge other customers? How many of each type are on each flight?
d. What would NA’s profit be for each flight? Would the airline stay in business? Calculate the consumer surplus of each consumer group. What is the total consumer surplus?
e. Before NA started price discriminating, how much consumer surplus was the Type A demand getting from air travel to Adelaide? Type B? Why did total consumer surplus decline with price discrimination, even though total quantity sold remained unchanged?