1. Joe quits his computer programming job, where he was earning a salary of $50,000 per year, to start his own computer software business in a building that he owns and was previously renting out for $24,000 per year. In his first year of business he has the following expenses: salary paid to himself, $40,000; rent, $0; other expenses, $25,000. Find the accounting cost and the economic cost associated with Joe’s computer software business.
2. A firm has a fixed production cost of $5000 and a constant marginal cost of production of $500 per unit produced.
a. What is the firm’s total cost function? Average cost?
b. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.
3. Suppose the economy takes a downturn, and that labor costs fall by 50% and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path.
4. You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q 5 KL, where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r $10,000 per week, and each team costs w $5000 per week. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design.
a. What is the cost function for your plant—namely, how much would it cost to produce q engines? What are average and marginal costs for producing q engines? How do average costs vary with output?
b. How many teams are required to produce 250 engines? What is the average cost per engine?
c. You are asked to make recommendations for the design of a new production facility. What capital/labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q?
5. The short-run cost function of a company is given by the equation TC 200 55q, where TC is the total cost and q is the total quantity of output, both measured in thousands.
a. What is the company’s fixed cost?
b. If the company produced 100,000 units of goods, what would be its average variable cost?
c. What would be its marginal cost of production?
d. What would be its average fixed cost?
e. Suppose the company borrows money and expands its factory. Its fixed cost rises by $50,000, but its variable cost falls to $45,000 per 1000 units. The cost of interest (i) also enters into the equation. Each 1-point increase in the interest rate raises costs by $3000. Write the new cost equation.
6. Suppose that a firm’s production function is
. The cost of a unit of labor is $20 and the cost of a unit of capital is $80.a. The firm is currently producing 100 units of output and has determined that the cost-minimizing quantities of labor and capital are 20 and 5, respectively. Graphically illustrate this using isoquants and isocost lines.
b. The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm require? Illustrate this graphically and find the firm’s new total cost.
c. Graphically identify the cost-minimizing level of capital and labor in the long run if the firm wants to produce 140 units.
d. If the marginal rate of technical substitution is
, find the optimal level of capital and labor required to produce the 140 units of output.Pindyck and Rubinfeld, Chapter 7 Appendix
1. The production function for a product is given by q 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output?
2. Suppose a production function is given by F(K, L) KL2; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output?