Problem 1: Explain the difference between the short-run and the long-run with regard to firm behavior. What are fixed and variable factors of production, and how does this distinction relate to the short-run, long-run distinction? How does the concept of sunk costs relate to fixed and variable costs?
Problem 2: Carefully explain why the short-run supply curve for a competitive firm is the portion of its short-run margin cost curve above its average variable cost. Why would a firm be willing to operate at a loss in the short-run, but not in the long-run? Carefully explain the distinction between the short-run and the long-run in your answer.
Problem 3: Suppose a firm's short-run total cost function is described by the following quadratic cost function:
C(q) = 100 + 6q + q2.
Solve for the equations for the firm's MC, AVC, and ATC curves. Construct a graph showing the firm's MC, AVC, and ATC curves.
Problem 4: Consider the table below which gives two total cost schedules for two different scales of operation for a firm. TC1 is for a fixed cost of $25, while TC2 is for a fixed cost of $30. Assume the firm is a price taker.
|
Output per month
|
TC1
|
TC2
|
|
0
|
$25
|
$30
|
|
1
|
45
|
45
|
|
2
|
57
|
63
|
|
3
|
70
|
76
|
|
4
|
84
|
91
|
|
5
|
102
|
107
|
|
6
|
123
|
125
|
|
7
|
147
|
145
|
|
8
|
175
|
167
|
|
9
|
209
|
191
|
|
10
|
249
|
223
|
a. If the market price is $25, at what output, rate will the firm maximize profits in the long run? Does it matter whether the firm believes that a price of $25 will persists as the equilibrium price? Carefully explain.
b. Suppose the price falls to $19 from $25. How would the firm react in the short run if it expected the $19 price to be temporary, remaining to $25? What would the firm do if it expected the new $19 price to be permanent?
Problem 5: A firm produces units of output (q) by applying the production function q = L.5 .K.5, where L and K refer to labor and capital, respectively. The firm faces fixed per-unit prices for L and K (PL = 10 and PK = 40) and chooses a long-run output rate of q = 50. First, solve for the long-run optimal (cost-minimizing) input combination of L and K for q = 50. Second, given the firm has chosen the optimal K for q = 50, derive the firm's short-run total cost function. Third, derive the function for short-run ATC, AVC, and MC. Finally, if the firm is competitive and faces an output price P = 40, what is the firm's short-run profit-maximizing output and total profit?