Unit 6 Homework Key

Ch. 7

2. Let q equal the number of offices cleaned per hour. Then C = 2q (15 minutes of labor is required per office). Variable cost is also 2q because there are no fixed costs. Average variable cost and marginal cost are $2. See Figure 7.4.

Figure 7.4

4. Solution in text

24. C = q, MC = AVC = AC = 1 for q less than or equal to 80 per day. C = 80 + 1.5 (q - 80) = 1.5q - 40, MC = 1.5, AVC = AC = 1.5 - 40/q for all q greater than 80 per day. See Figure 7.11a and 7.11b.

Figure 7.11

Ch. 8

1. The shutdown rule states that a firm should shut down when it can avoid additional losses by doing so. This occurs when losses would exceed fixed costs. If the firm can cover any portion of fixed costs by continuing production, it should do so.

2. Solution in text.

3. Solution in text.

10. See Figure 8.7. The lower of average minimum variable cost will extend firm’s supply curve downward. As a result, the market supply curve shifts rightward.

Figure 8.7

32. Marginal cost is computed by taking the derivative dC/dq. Profits are maximized by setting
MC = MR = p. For the function given, MC = 10 - 2q + q². Thus profits are maximized when
p = 10 - 2q + q². The supply curve is p = 10 - 2q + q² for P > 9.25.

34. In the long run price equals marginal cost, and profits are zero. Thus given that industry output
Q = nq, the following will be true in long-run equilibrium, p = 24 - nq. Therefore,

24 - nq = 2q

(24 - nq)q = 16 + q².

Solving these equations for q, n, Q, and p yields

q = 4

n = 4

Q = 16

p = 8.