Solutions to Even Numbered Problems

Solutions to Even Numbered Problems Chapter 2 Page 1 Chapter 2

Problem 2:

• S = 1.196. There are a number of ways to calculate S. The easiest is to use the formula

S = AC(q)/MC(q). Doing so, gives you S = 256/214 = 1.196. Similarly, using the elasticity formula from Application 2.6, you get (1/8)/(214/2048) = .125/.1045 = 1.196.

• The firm is experiencing economies of scale. The value of S is greater than one. Also,

the AC falls from 262 to 256 while q increases from 7 to 8.

• The value of S can be interpreted to read that for every one percentage increase in

costs, output will increase by 1.196 percent.

Problem 4:

• The production of shampoo exhibits economies of scale up until 2 units of output.

After that, the production of shampoo exhibits diseconomies of scale. There are two ways to see this. One way is to simply graph AC for different values of q. For example, qS AC

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• 4
• 5
• 8.5

You can see that at first, AC falls as q increases from 1 to 2, but then AC increases after that. Another way is more mathematical. If you set AC= 4/q s +qs equal to MC = 2qs, you will find that when AC=MC, q s=2. This implies, that AC is at a minimum when qs=2.(Also, finding the first derivative of AC and setting it equal to zero gives the same outcome.) b. Yes, it does exhibit economies of scale. For example, qT AC

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• 1.5

9 .778

16 .5

100 .14

As q increase, AC falls.

• Yes. No matter what combination, it will always be $1 less expensive to make the

products. Notice that C(q s,qT) is $1 less than C(qs,0) + C(0,qT). Note as the quantities become larger, this $1 difference, as a percentage of total costs, becomes somewhat trivial.(Industrial Organization Theory and Practice, 4e Don Waldman, Elizabeth Jensen) (Solution Manual all Chapters) 1 / 4

Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition Solutions to Even Numbered Problems Chapter 3 Page 2 Chapter 3

Problem 2:

• The firm sets P = MC. 50 = 2q+30; q=10. Because we only are given one of many

SRTC functions, we don’t know the LRTC function, and therefore, we cannot determine the LR equilibrium price. It’s probably not $50, but we can’t know for sure what it is from the information given in this question.

• The short-run supply function is simply the MC curve above minimum AVC. AVC =

q+30. This curve hits a minimum when q=0. Thus, the firm’s short-run supply function is

simply: P = 2q + 30.

Problem 4:

• Firm sets P = MC. 2q=60; q = 30 b. Profits = TR – TC = 60*30 – (30

2

+100) = 1800 – 1000 = 800

• Short-run supply is MC above minimum AVC. In this case, P = 2q

• The industry supply curve is calculated by summing each individual firm’s short-run

supply curve. q i = P/2. Q = 100 (P/2) = 50P. The formula for the industry supply curve

is: P = Q/50.

Problem 6:

• Set QD = QS. 100 – P = - 50 + 2P; 3P = 150; P e = 50; Qe = 50
• Consumer Surplus = ½ (100-50)*50 = 1250

Producer Surplus = ½ (50-25) * 50 = 625

Problem 8:

• MR = 55 – 4Q
• set MR = MC; 55 – 4Q = 2Q – 5; Q = 10; P = 55 – 2(10) = 35
• Profits = 35(10) – [10

2

– 5(10) + 100] = 350 – 150 = 200

• Consumer Surplus is shown graphically in Figure 3A.1 as triangle area ABC

Consumer Surplus = ½ (55- 35) (10) = 100

• P = MC; 55-2Q = 2Q – 5; Q = 15; P = 25
• Profits under perfect competition = 25(15) – [15

2

– 5(15) +100] = 375 – 250 = 125

Consumer Surplus under perfect competition is shown graphically in Figure 3A.1 as triangle area AEG. Consumer Surplus = ½ (55-25) *15 = 225 2 / 4

Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition Solutions to Even Numbered Problems Chapter 3 Page 3

• Deadweight Loss is shown graphically in Figure 3A.1 as the triangle BEF.

Deadweight Loss = ½ (35-15) * (15- 10) =50

FIGURE 3A.1

Problem 10:

As indicated in Figure Problem 3A.2, without trade the equilibrium price and quantity are: P=100- q

US=62.5

37.5=q yields q for solving

Supply=q+25=q-100=Demand USUS USUS

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Waldman/Jensen – Industrial Organization Theory and Practice, Fourth Edition Solutions to Even Numbered Problems Chapter 3 Page 4 Figure 3A.2

With trade the total supply curve is the sum of the US supply and the foreign

supply in the United States:

q 3 2 +25=P q+37.5=P 2 3

37.5-P

2 3

=12.5)-P

2 1 (+25) -(P=q+q=q

12.5-P

2 1 =q and 25 -P=q totaltotal fUStotal fUS

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