Problem Set 6
Econ 613(01) Spring 2003
(Dr. Tin-Chun Lin)
1. Suppose there is a function of total cost:
a. What is total fixed cost (TFC) if total production (Q) is 2000 units? What is total fixed cost (TFC) if total production (Q) is 5000 units?
b. What is average fixed cost (AFC) if total production is 2000 units? What is AFC if total production is 5000 units?
c. What is average variable cost (AVC) if total production is 20 units?
d. What is marginal cost (MC) if total production is 20 units?
e. What is average total cost (ATC) if total production is 20 units?
f. What is the total production when marginal product of variable input starts diminishing?
g. What is the total production when average product of variable input starts diminishing?
h. What is the total production when the short-run production starts entering the second stage?
2. According to a statistical study, the following relationship exists between an electric light and power plant’s fuel costs (C) and its eight-hour output as a percent of capacity (Q): .
a. When Q increases from 50 to 51, what is the increase in the cost of fuel for this electric plant?
b. Of what use might the result in part (a) be to the plant’s managers?
c. Derive the marginal (fuel) cost curve for this plant, and indicate how it might be used by the plant’s manager.
3. A food company’s manager considers three different scales of plants. The followings are the information for these three different plants.
Plant A / Plant B / Plant CMaterial price per unit of product / $3.00 / $3.00 / $3.00
Labor price per unit of product / $0.40 / $0.70 / $1.15
The costs of machines / $75,000 / $60,000 / $25,000
The costs of equipments / $100,000 / $60,000 / $20,000
The maximum capacity per year / 500,000 units / 375,000 units / 125,000 units
If the manager decides to produce 300,000 units per year, in order to minimize average total cost (ATC), what plant size should the manager build?
4. A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $6 per hour and capital is rented at $12 per hour. If the marginal product of labor is 50 units of output per hour and the marginal product of capital is 75 units of output per hour, is the firm using the cost-minimizing combination of labor and capital? If not, should the firm increase or decrease the amount of capital used in its production process?
5. The Company B made and sold 10,000 metal tables last year. When output was between 5,000 and 10,000 tables, its average variable cost was $24. In this output range, each table contributed 60 percent of its revenue to fixed costs and profits.
a. What was the price per table?
b. If the Company B increases its price by 10 percent, how many tables will it have to sell next year to obtain the same profits as last year?
c. If the Company B increases its price by 10 percent, and if its average variable cost increases by 8 percent as a result of wage increases, how many tables will it have to sell next year to obtain the same profit as last year?