1. Please answer True or False, and explain your answer. A consumer purchases a book by driving across town to a bookstore, standing in line for five minutes to pay thecashier, and then pays $5. The same book is purchased by another consumer who spends two minutes placing the order over the Internet for $10. The book necessarily cost the first consumer less.
2. Evan wants to go into the donut business. For $500 per month he can rent a bakery complete with all the equipment he needs to make a dozen different kinds of donuts (K = 1, r = 500). He must pay unionized donut bakers a monthly salary of $400 each. He projects his monthly production function to be Q = 5KL, where Q is tons of donuts.
a.With the current level of capital, what is the marginal product of labor? Is the marginal product diminishing? Explain.
b.If Evan wishes to make 25 tons of donuts, how many bakers are required given the current level of capital? How much will it cost to produce this (total cost)?
c.Derive Evan's short-run cost function with K = 1.
d.Derive the marginal cost curve from your answer to (c) and show the relationship between the marginal cost and marginal product of labor.
3. A firm produces output according to the following function:
q = f (L, K) = L1/2 K1/3. The cost of labor is $9 per hour and the rental cost of capital is $4 per hour.
a. With the given prices, use the Lagrangian method to compute the optimal (cost- minimizing) capital to labor ratio (K/L) for the firm.
b. Suppose the firm wishes to produce 72 units of output. How much capital and how much labor does the firm employ?
c. What is the total cost of producing 72 units of output?
d. Suppose that the firm suddenly decides to double the quantity of output but only has a day to complete the order. In that timeframe, the amount of capital is fixed but labor hours are not. How much will it cost to produce 144 units of output? How much would it cost if the firm could also vary capital? Provide a graph (isocost/isoquant) illustrating the optimal bundles.
4. Firms in a competitive sandbox industry have the following long-run cost curve: C(q) = F + 6q +5q2, where F is a positive constant. The sandbox industry has a market demand of p = 90 - 2Q.
a.Suppose F = 20. Find the competitive equilibrium price, quantity and number of firms.
b.Suppose F is actually an accreditation fee established by the sandbox sellers association. A firm that avoids this fee will not be able to operate in the industry, and is therefore mandatory. How does the equilibrium price and number of firms vary with F? You do not have to use calculus, but explain whether each increases or decreases with F. How does the profit of each firm vary with F?
5. Suppose that there are 80 firms in a market, each with the following costfunction:
C(q) = 100 + 4q2.
a. Derive the short-run market supply curve.
b. Suppose the market demand is QD = 1280 - 30p. Find the equilibrium market quantity and price.
c. How much output will each firm produce? How much profit is each firm making?