ECO2011: Homework 8
Due on April 15, 5 pm
1. You are thinking about opening a hardware store. You estimate that it would cost $500,000 per year to rent the location and buy the stock. However, if, instead, you worked as an accountant, you could have earned $50,000 per year.
a) What are your opportunity costs of opening a hardware store? What are the explicit costs? What are the implicit costs? (5pt)
b) If you think you can sell $540,000 worth of merchandise in a year, should you open the store? Explain. (5pt)
2. A juice bar has the following (short-run) cost schedules:
a) What is the fixed cost? (3pt)
b) Calculate average variable cost, average fixed cost, average total cost, and marginal cost for each quantity. (12pt)
c) Graph all four curves in b).(8pt)
d) What is the quantity that minimizes the average total cost? Explain it using the relationship between the marginal-cost curve and the average-total-cost curve.(7pt)
3. Consider the (short-run) production function q = F(L, K) = , where = 1. The total cost C = wL + r, where w = 5, r = 10.
a) Derive the short-run cost function. Show your work. (5pt)
b) Derive average variable cost, average fixed cost, average total cost, and marginal cost. (8pt)
c) Graph all four curves in b). (4pt)
d) What is the quantity that minimizes the average total cost? (3pt)
4. Consider the (long-run) production function q = F(L, K) = . The total cost C = wL + rK, where w = 5, r = 10.
a) Is there a fixed cost? If yes, calculate it. If no, explain. (5pt)
b) Derive the long-run cost function. Show your work. (15pt)
c) What is the relationship between the long-run cost function and the short-run cost function (you derived in question 3)? Explain. (5pt)
d) Is there a quantity of output in which the long-run cost coincides with the short-run cost (you derived in question 3)? Explain. (5pt)