管理经济学 原书第六版 课后答案8

Chapter 8: Answers to Questions and Problems

1.

a.7 units.

b.$28.

c.$224, since $32 x 7 = $224.

d.$98, since $14 x 7 = $98.

e.$126 (the difference between total cost and variable cost).

f.It is earning a loss of $28, since ($28 -$32) x 7 = - $28.

g.- $126, since its loss will equal its fixed costs.

h.Shut down.

2.

a.Set P = MC to get $80 = 8 + 4Q. Solve for Q to get Q = 18 units.

b.$80.

c.Revenues are R = ($80)(18) = $1440, costs are C = 40 + 8(18) + 2(18)2 = $832, so

profits are $608.

d.Entry will occur, the market price will fall, and the firm should plan to reduce its

output. In the long-run, economic profits will shrink to zero.

3.

a.7 units.

b.$130.

c.$140, since ($130 – 110) x 7 = $140.

d.This firm’s demand will decrease over time as new firms enter the market. In the

long-run, economic profits will shrink to zero.

4.

a.MR = 200 – 4Q and MC = 6Q. Setting MR = MC yields 200 – 4Q = 6Q. Solving

yields Q = 20 units. The profit-maximizing price is obtained by plugging this into

the demand equation to get P = 200 - 2(20) = $160.

b.Revenues are R = ($160)(20) = $3200 and costs are C = 2000 + 3(20)2 = $3200,

so the firm’s profits are zero.

c.Elastic.

d.TR is maximized when MR = 0. Setting MR = 0 yields 200 – 4Q = 0. Solving for

Q yields Q = 50 units. The price at this output is P = 200 – 2(50) = $100.

ing the results from part d, the firm’s maximum revenues are R = ($100)(50) =

$5,000.

f.Unit elastic.

5.

a. A perfectly competitive firm’s supply curve is its marginal cost curve above the

minimum of its AVC curve. Here, 25083i i i MC q q =−+ and

23

2504504i i i i i i i q q q AVC q q q −+==−+. Since MC and AVC are equal at the

minimum point of AVC, set MC i = AVC i to get 225083504i i i i q q q q −+=−+, or 2i q =. Thus, AVC is minimized at an output of 2 units, and the corresponding

AVC is ()()2

5042246i AVC =−+= . Thus the firm’s supply curve is described by the equation 23850i i q q MC +−= if $46P ≥; otherwise, the firm produces zero units.

b. A monopolist produces where MR = MC and thus does not have a supply curve.

c. A monopolistically competitive firm produces where MR = MC and thus does not

have a supply curve. 6.

a. Q = 3 units; P = $70.

b. Q = 4 units; P = $60.

c. ()()1

$70$401$15.2

DWL =−=

7.

a. The inverse linear demand function is P = 10 – .5Q.

b. MR = 10 – Q and MC = –14 + 2Q. Setting MR = MC yields 10 – Q = –14 + 2Q. Solving for Q yields Q = 8 units. The optimal price is P = 10 – .5(8) = $6.

c. Revenues are R = ($6)(8) = $48. Costs are C = 104 – 14(8) + (8)2 = $56. Thus the firm earns a loss of $8. However, the firm should continue operating since it is covering variable costs.

d. In the long run exit will occur and the demand for this firm’s product will increase until it earns zero economic profits. Otherwise, the firm should exit the business in the long run.

8.

a. The optimal advertising to sales ratio is given by ,,0.10.052

Q A Q P E A R E ===−. b.

()(),,0.1.05$50,000$2,500$50,0002

Q A Q P E A A A R E =⇒=⇒==−.

9.

Chastise the manager. Profit maximization requires producing where MR = MC.