Answers to Even Problems for Waldman/Jensen

Answers to Even Problems for Waldman/Jensen 2nd Ed.

CHAPTER 2

2. a. SRMC = 2q + 30 = 50 =p

It is not a long-run equilibrium because:

b. Because the AVC=q+30, the short-run supply function is the SRMC curve above the AVC curve, which is identical to the SRMC.

The short-run supply function is: S=2q+30

4. a. MR=53-2Q

P=53-24=29

c. =TR-TC=Q(P-AC)

=24(29)-24(5)=24(29-5)

=576

e. Perfectly Competitive Q=48

P= 5

Monopoly Profits = 24(29-5)= 576

Consumer’s Surplus = 288

Dead Weight Loss = 288

Total = 1152

6. As indicated in Figure Problem 2.6, without trade the equilibrium price and quantity are:

P=100-qUS=62.5

With trade the total supply curve is the sum of the US supply and the foreign supply in the United States:

The equilibrium with trade:

With trade, q=45, P=55.

Welfare changes to the United States as a result of free

trade are identified below.

Consumer surplus without trade was:

Producer surplus without trade was:

Without trade, CS + PS = 703.125 + 703.125 = 1406.25

Consumer surplus with trade is:

The domestic firms' producer surplus with trade is:

With trade, CS + PS = 1012.5 + 450 = 1462.5

The net welfare gain to the United States from trade is:

1462.5 - 1406.25 = 56.25

CHAPTER 4

2.. a.. 4FCR=20+20+16+16=72

The numbers equivalent tells us something about the meaning of a particular HHI by informing us about how many equal size firms would “fit” in an industry with a given HHI. Smaller values of N suggest less competition.

The numbers equivalent does not convey any information about the distribution of market shares among firms.

6. DO NOT ASSIGN THIS PROBLEM UNLESS YOUR STUDENTS HAVE BEEN INTRODUCED TO THE COURNOT-NASH EQUILIBRIUM WITH N FIRMS IN A MICROECONOMICS COURSE. As we do on a number of occasions, we are introducing a concept before we go through the material in depth later in the text (chapter 7).

In this industry the perfectly competitive quantity is:

The Cournot-Nash equilibrium with linear demand, linear MC, and N=3 firms is:

If two firms merge the Cournot-Nash equilibrium would be:

In Figure Problem 4.2, as a result of the merger, consumer surplus declines more than profits increase, so economic welfare declines as a result of the merger.

The net change in consumer surplus plus profits is:

-1912.5+1125=-787.5

CHAPTER 6

2. The solution to the game is for Ben to “Enter” and Jerry to “Maintain Current Price.”

Perhaps Jerry could sign a contract with an independent lawyer stating that if Ben entered, the lawyer would play “Aggressive if Entry.” Such a public contract might deter entry.

CHAPTER 7

2. Note: Here we use the same concepts we introduced in chapter 4 problem number 6, but now the concept of a Cournot-Nash equilibrium has been analyzed in detail. With linear demand and linear marginal costs, the Cournot-Nash equilibrium is of the perfectly competitive quantity, that is:

For each firm, therefore, .

4. The Bertrand equilibrium is identical to the competitive equilibrium.

6. The Cournot-Nash equilibrium for the duopolists is obtained by finding the intersection of the two reaction functions. Because of symmetry each firm has the same reaction function. The American firm's reaction function is:

By symmetry the Japanese firm's reaction function is:

The Cournot-Nash equilibrium is:

By symmetry qJ=20 and total quantity q=40, and therefore, P=60.

a. With the tariff, the Japanese firm's reaction function changes to:

The American firm's Cournot-Nash output is then:

The Japanese firm's Cournot-Nash output is then:

b. Total output with the tariff is 23.33 + 13.33 = 36.66, and price P=63.34.

c. Before the tariff:

and CSUS + πUS = 800 + 150 = 950

After the tariff:

In addition, the government gains tax revenue equal to:

Tax Revenue = 10 x 13.33 = 133.33

CSUS + πUS + Tax Revenue = 671.98 + 317.85 + 133.33 = 1123.16

American welfare increases by 1123.16 - 950 = 173.16

CHAPTER 8

2. Neither Waldman or Jensen would ever defect.

4. It would be reasonably easy to maintain effective collusion in this case, because Firm A would always prefer a high price.

Firm A appears to be the dominant firm in this industry.

High price is Firm A’s dominant solution.

Firm B does not have a dominant solution. Firm B should play “High Price” if Firm A plays “High Price,” and Firm B should play “Low Price” if Firm A plays “Low Price.”

CHAPTER 10

2. If is “very small” (perhaps approaching zero), entry is virtually impossible and there is no need to limit price.

If is “very large,” limit pricing might be an attractive strategy if limit pricing results in profits that are greater than zero. However, limit pricing would not be attractive if profits equaled zero at the limit price.

Ceteris paribus, the higher the value of , the greater is the likelihood of limit pricing.

Of course even a high value of would not result in a high probability of limit pricing if there were very low profits to be earned at the limit price or if the firm had a very high discount rate.

4. The Nash equilibrium is not a subgame perfect Nash equilibrium because it requires that at the node DF1, the Dominant Firm would play limit price (L) if the potential entrant stays out. But playing L is not a Nash equilibrium for the subgame beginning at the node DF1.

6. To determine whether or not a pooling equilibrium exists, we must calculate the expected value of IBM’s profits as follows:

Because IBM’s expected profits are negative, a pooling equilibrium exists. Regardless of whether Xerox has high costs or low costs, Xerox would charge the price it prefers if it has low costs. Therefore, if Xerox has high costs, it would limit price in this case.

8. a. As we saw in problem 6 above, a pooling equilibrium exists because:

Therefore, a high-cost monopolist would limit price and charge P=55, the optimal price for a low-cost monopolist, in period 1.

b. A low-cost monopolist would charge its profit-maximizing price P=55 in period 1.

c. The high-cost monopolist limit prices in period 1 and charges its profit-maximizing price in period 2, therefore, total profits for a high-cost monopolist would be:

d. The low-cost monopolist charges its profit-maximizing price in period 1 and 2, therefore, total profits for a low-cost monopolist would be:

CHAPTER 11

2. The current solution is for the potential entrant to enter and the dominant firm to SR profit maximize.

The incumbent would have to spend an amount on advertising greater than 250 to prevent entry.

The new solution would be for the potential entrant to stay out and the dominant firm to maximize profits. The dominant firm would earn a profit of just under 2,250, which equals 2,500 minus the amount the dominant firm spends on advertising.

3. If the fixed costs of production of sickeningly sweet corn flakes were $225 instead of $75, Big G would not enter the sickeningly sweet corn flakes market when demand tripled because equation A1 would become:

Because profits are negative with the higher fixed costs, Big G would stay out of the market and there would be no need to use product proliferation to deter entry.

CHAPTER 12

2. Suppose there are three trucks, A, B, and C. Start with all three at the middle of the 10 mile stretch, i.e. at the 5-mile mark. Currently they each earn 33.3% of the profits.

If Truck A moves a “very small distance” to the right or left of the 5-mile mark it can capture 50% of the profits, leaving Trucks B and C to share the other 50%. Suppose Truck A moved to the right, then both Trucks B and C have an incentive to move a “very small distance” to the left of the 5-mile mark. Suppose Truck B moves ” to the left of center. We now have A slightly right of center, B slightly left of center, and C stuck earning almost nothing in the center.

Now Truck C has an incentive to move a “very small distance” to the right of A or the left of B. This shifting can go on indefinitely. Using such reasoning it is clear that at no time will all three trucks be doing the best they can given the choices of the other trucks. Therefore, there is no Nash equilibrium with 3 trucks.

4. a. The new introductory demand curve would be: P=(100-Q)(1-.75)=25-.

b. In Figure Problem 12.4, the new introductory demand curve would be the heavy kinked line CBAE.

c. For informed consumers, the maximum amount they would pay to try the second mover’s product is: P=(100-Q)(1-.75)=25--S. The line OA traces out the maximum amount each informed consumer would pay to try the second mover’s product. Note: The second mover would have to pay the first consume approximately 25 to try the product. Mathematically, the line OA is: P=-25+. Subtracting the line OA from the line AE, the demand curve for the second mover is:

P=12.5-=12.5-0.187q.

The highest price the second mover can charge to obtain any consumers is just under 12.5.

d. Yes. The increase in the risk-cost actor has substantially reduced the demand curve faced by the second mover, thus making it even more difficult to enter.

CHAPTER 13

2. Before the cost-saving invention the monopolist’s profits were:

Demand was: P=50-q; so MR=50-2q.

To maximize profits set MR=MC:

MR=50-2q=25; so q=12.5 and P=50-12.5=37.5

Profits then are:

With the introduction of the cost-saving device the monopolist’s profits would be calculated as follows:

MR=50-2q=20; so q=15 and P=50-15=35

Profits are then:

Profits for the monopolist increase by (225-156.75)=68.75 as a result of the introduction of the cost-saving device.

If the industry were perfectly competitive patent holder could license the devise for a royalty payment, R of 5 per unit. Price would remain at 25 and quantity sold would remain at 25, but the patent holder could earn a total royalty of:

Royalty=qR=25(5)=125.

The patent holder has a greater incentive to introduce the device because the patent holder can earn 125 compared to the monopolist’s increase in profits of only 68.75.5

CHAPTER 14

2. Note: We are ignoring the impact of fixed costs on profits in calculating the optimal pricing policy.

Without discrimination the optimal policy would be to charge $1,000 for an unrestricted ticket and sell one ticket. This yields a profit of

Compared to a profit with discrimination of:

The airline should discriminate and charge $1,000 for an unrestricted ticket and $250 for a ticket with a two-week minimum stay. This yields total surplus of:

CS + = $0 + $1,050= $1,050

Let’s make the same calculations with the new demand conditions.

Without discrimination the optimal policy would be to charge $650 for an unrestricted ticket and sell two tickets. This yields a profit of

Compared to a profit with discrimination of:

Now to maximize profits the airline should not discriminate, but charge all passengers $650 for an unrestricted ticket. This yields total surplus of:

CS + = $350 + $1,100= $1,450

In this case, welfare is greater without discrimination.

If discrimination is possible, the profit maximizing policy is to charge a price per unit price equal to marginal cost of 10 and charge a fixed fee of 4050 to consumer 1 and a fixed fee of 800 to consumer 2. Total profits would then be 4050+800=4850.

The situation is depicted in Figure Problem 14.6 above. In this case, the monopolist should charge a per copy fee equal to 20 and a fixed fee equal to 1600 to each consumer. The fixed fee equals the consumer surplus for the low demand Type B consumer if the per copy charge is 20. Profits then equal:

=2(fixed fee)+-2(fixed costs)

=2(1600)+20(80+40)-2(500)

=(3200)+(2400)-(1000)=4600

Using a two-part tariff still increases profits. In this case from 4500 to 4600 despite the dramatic reduction in the monthly rental fee from 5000 to 1600. The price ceiling, however, reduces profits for the monopolist from 4625 to 4600.

CHAPTER 15

In the figure above, with bilateral monopoly (a monopolist wholesaler and a monopolist retailer) the price to the consumer would be 80 and 20 units would be sold. Consumer surplus would equal the small triangle A, which equals . Producer surplus would be 20(80-20)=1200. Total surplus would equal 1400.

After a merger, the price would decline to 60 and quantity would increase to 40. Consumer surplus would increase to the sum of the three areas A+B+C, which equals . Producer surplus now equals 40(60-20)=1600. Total surplus is now 2400.

There is a gain of total surplus of 1000.

It does not matter whether the tax is placed on the monopolist manufacturer or the competitive retailers.

In the figure above, we’ve presented both ways of viewing the tax. If the tax is placed on the monopolist manufacturer, it increases marginal cost from MC to MCtax, where MCtax=MC+$1.00, but the demand curve and MR curves remain at D and MR. The result is that quantity declines to qtax and price increases from P to Ptax.

If the tax is placed on the competitive retailers, it does not affect MC for the monopolist, but reduces the demand curve to Dtax and the marginal revenue curve to MRtax. Note that Dtax lies everywhere exactly $1.00 below the original demand curve D. The new marginal revenue curve intersect the MC curve at qtax, so output is the same in both cases.

We can use algebra to prove the same result. Consider any linear demand curve P=a-Q and constant marginal cost curve, mc. A tax placed on the monopolist increases marginal cost to mc+ 1. With P=a-Q; MR=a-2Q, so MR=MC implies:

MR=a-2Q=mc+1

2Q = a-(mc+1)=a-1-mc

A tax on the retailers leaves marginal cost constant at mc, but changes demand to P=(a-1)-Q. Marginal revenue is then MR=(a-1)-2Q; so MR=MC implies: