1. Firm L is the dominant firm with MC = 4. Industry demand is depicted by QD = 80 – 3P. The long-run MC = 5 + QF for the 3 "follower" firms.
To maximize profits set P = MC = 5 + QF. Therefore, QF = P – 5. To solve for the total supply curve set QS = 3(QF) = 3P – 15.
To solve set QL = QD – QS.
QL = (80 – 3P) – (3P – 15)
QL = 65 – 6P
To solve find the inverse demand equation.
6P = 65 – QL
P = 65/6 – 1/6QL
Set MR = MC
65/6 – 1/3QL = 4
Solve to get QL = 20.5.
Enter 20.5 into the inverse demand equation to get the price.
P = 65/6 – 1/6(20.5)
Solve to get PL = $7.42.
Plug $7.42 into the QS = 3P – 15 formula. Solve to get 7.26
2. Due in part to a set of Russian trade restrictions prohibiting imports, there is currently a monopoly operating in Russia under the following demand and cost equations:
P = 570 – 10Q and MC = 150 + 6Q
MR = MC
570 – 20Q = 150 + 6Q
420 = 26Q
16.15 = Q
P = 570 – 10(16.15) = $408.50
b. A national economics group wants to analyze the P and Q for this market given a competitive environment. Calculate the short-run P and Q under this condition assuming that the cartel's marginal cost function would represent the industry supply.
570 – 10Q = 150 + 6Q
420 = 16Q
26.25 = Q
P = 570 – 10(26.25) = $307.50
c. What would the welfare benefit be if the monopoly was dissolved and was forced into competition with other firms?
This is given by the triangular area defined by the two prices and quantities=
(408.50 – 307.50) x .5(26.25 – 16.15) =510.05
d. Given that TC = 100 + 150Q + 3Q2 for the cartel as a group, analyze costs, revenues, and profits with and without a monopoly in effect.
Costs: With monopoly
Q = 16.15: 100 + 150(16.15) + 3(16.15) 2 =
100 + 2422.5 + 782.46 = $3,304.96
With competiton
Q = 26.25: 100 + 150(26.25) + 3(26.25) 2 =
100 + 3937.5 + 2067.18 = $6,104.68
Revenues: With monopoly
Q = 16.15: 408.5 x 16.15 = $6,597.27
With competiton
Q = 26.25: 307.50 x 26.25 = $8,071.87
Profits: With monopoly
Q = 16.15: 6,597.27 – 3,304.96 = $3,292.30
With competiton
Q = 26.25: 8,071.87 – 6,104.68 = $1,967.19
Analysis: Under competition, revenues are 22% higher, therefore sales taxes awarded to government are greater. However, a firm would experience an 85% increase in costs, and profits would be reduced by 40%.
Furthermore, if entry is permitted, other firms will enter the industry over the long-run. This will further reduce price (to the minimum of LAC), raise quantity and eliminate economic profits.
e. The Russian government is in favor of breaking the monopoly. Discuss why. (hint: Russian government collects taxes based on firms’ sales because they are easier to monitor than profits.)
Citizens receive more products at lower prices.
Inhibits inflation due to lower more stable prices.
More in line with current free market philosophy.
Decreases corrupt business practices.
Increases Russian tax revenues.
f. What would be the most effective steps for the Russian government to take to end the monopoly?
Lift trade restrictions that have been protecting the monopoly.
Offer incentives to foreign firms to import lower, priced products to Russia.
3. Two railroads, the Chesapeake and Ohio and the Nickel Plate Road, provide transportation services between Buffalo and Chicago. Each railroad can ship one boxcar load at a cost of $1000.
Suppose that each railroad can charge either $1500 or $2000 to its customers for each carload. If both railroads charge $2000, 100,000 carloads will be shipped by each. On the other hand, if both charge $1500, they will each ship 150,000 carloads. If one railroad charges $2000 and the other $1500, the high priced railroad will ship 50,000 carloads and the low priced railroad will ship 250,000 carloads.
Provide an explanation of whether a prisoner’s dilemma is present and propose a method to overcome the dilemma.
Create a payoff table for the pricing strategies.
|
Profit, $million |
Nickel Plate Road |
||
|
$2000 |
$1500 |
||
|
Chesapeake & Ohio |
$2000 |
100, 100 |
50, 125 |
|
$1500 |
125, 50 |
75, 75 |
|
Yes, the prisoner’s dilemma does exist in this example. The railroads will maximize their profits when they both charge the higher carload price. However, individually, it is in each railroad’s best interest to charge a lower price than the other railroad.
In order to maximize the profit for the railroads collectively, they must cooperate in setting the rates. That kind of price collusion is illegal under US laws, but the railroads might be able to make arrangements in secret.
4. Acme Supply Company Inc. is a manufacturer of miscellaneous "pratfall props and sight gags" used by the cartoon industry. Acme is the dominant firm in this particular market, where industry demand is given by:
QD = 40 - 2P
Additionally, there are four follower firms competing in this market, each having a long-run marginal cost function of:
MC = 4 + QF
Acme’s long-run marginal cost is 4.
a. Assuming each follower acts as a price taker, what is the total supply curve (QS) of the followers?
Each follower maximizes its profits by setting P = MC = 4 + QF. Hence,
P = 4 + QF
QF = P - 4
With four follower firms, the total supply curve is:
QS = 4QF = 4P - 16
b. What is net demand curve facing Acme?
Acme’s net demand curve is:
Qd = QD - QS
Qd = (40 - 2P) - (4P - 16)
Qd = 56 - 6P
c. What is Acme’s optimal price and output?
Qd = 56 - 6P
6P = 56 - Qd
P = 9.33 - Qd/6
To maximize profits, set MR = MC.
MR = MC
9.33 - Qd/3 = 4
Qd/3 = 5.33
Qd = 15.99
With Qd = 15.99,
P = 9.33 - Qd/6
P = 9.33 - 15.99/6
P = 6.67
d. What is the combined total supply output of the four other follower firms?
QS = 4P - 16
With P = 6.67,
QS = 4(6.67) - 16
QS = 26.68 - 16
QS = 10.68
e.Are there other possible oligopoly solutions that might arise?
With 5 firms in the industry, there is always a possibility of cartelization. Note, however, that the followers have a higher MC (i.e., >4) than Acme. If Acme does not fear the antitrust laws, it may initiate a price war using its lower costs to drive out competitors, and then raise prices and lower output. Or it may simply buy them out to become a monopoly (and maintain its former rivals' plants as excess capacity to deter entry).
4. Carpenter Mining and Minerals (CMM) is a leading provider of metal and metal alloys. One of its products is an alloy that is a viable alternative to the Titanium components that are contained in most brands of golf clubs. There are three other major firms currently produce this product.
Answer: Tight Oligopoly
MCL = 3Q, where Q is the quantity of the product produced in tons.
The demand equation for the Market as a whole is:
Qd = 250 -10P, where P is the price in thousands of dollars per ton.
The supply equation for the three follower firms is:
Qf = 20 + P
P = Qf – 20 (Inverse supply equation)
1) What is the demand equation for CMM?
Answer: Qcmm = (Qd - Qf)
Qcmm= [(250 - 10P) – (20 + P)]
Qcmm = 230 - 11P
P=21-.09Qcmm (Inverse Demand Equation for CMM)
2) What is the optimum quantity and price for CMM?
Answer: Set MR = MC
21 - .18Qcmm = 3Qcmm
21= 3.18Qcmm
Qcmm= 6.6
Plug Q into the CMM inverse demand equation:
P= 21 - .09(6.6)
P= 21 - .59
P= $20.41
3) What quantity will the three following firms produce?
Answer: Plug the P found in part (b) into the supply equation for the followers:
Qf = 20 + P
Qf = 20+20.41
Qf = 40.41
Answer: TR = P * Q
TR = (40.41 + 6.6) * $20.41
TR = $ 959.47
c. CMM and the three other firms decided to form a Cartel. What would be their optimum price and quantity?
1) Answer: MCcmm=MCf=MR
MR = 25 - .2(Qcmm + Qf)
MR = 25-.2Qcmm - .2Qf
Set: MCf = MCcmm
Qf – 20 = 3Qcmm
Qf = 3Qcmm+ 20
Set: MR = MCf
25 - .2Qcmm - .2Qf = Qf - 20
45 - .2Qcmm = 1.2Qf
Qf = 37.5 - .1667Qcmm
Set the two results equal to each other:
37.5 - .1667Qcmm = 3Qcmm + 20
3.1667Qcmm = 17.5
Qcmm = 5.53
Qf = 37.5 - .1667 (5.53)
Qf = 36.59
Price: P = 25 - .10(36.59 + 5.53)
P = $20.78
Answer: TR = (Qcmm + Q2) * P
TR = (5.53 + 36.59) * $20.78
TR = $875.25
Answer: Price is in the elastic portion of demand. Any price increase will decrease TR (i.e., %change in Q>%change in P).
d. CMM is competing with one firm for the extraction and production of the more popular Titanium product that is more prevalent in the use of golf clubs. Very high mining costs create a significant barrier to entry into the market.
The market demand equation is:
Qd= 2500 - 10P
The marginal cost for both firms is constant at $100.
1) What is the inverse market demand equation for the two firms (Cournot Duopoly Theory)?
Answer: Qd = 2500-10P
10P= 2500 – (Qcmm + Q2)
P= 250 – .10(Qcmm + Q2)
2) What is the Total Revenue function for CMM?
Answer: TRcmm = Pcmm * Qcmm
TR = (250)Qcmm - .10 Q2cmm - .10Q2Qcmm
3) CMM believes that the competing firms production is constant, what is CMM’s demand equation?
Answer: MRcmm = MCcmm
dTRcmm/dQcmm = MRcmm = 250-.2Qcmm - .1Q2
250-.2Qcmm - .1Q2 = 100
.2Qcmm = 1.5 -.1Q2
Qcmm = 750 - .5Q2
4) What is the competing firms’ reaction demand equation?
Answer: P = 250- .1(Qcmm + Q2)
TR2= 250 (Q2) - .10QcmmQ2 - .1Q22
dTR2/dQ2 = MR2= 250 -.1Qcmm - .2Q2
MR2= MC2
250 - .10cmm- .2Q2 = 100
250 - .1Qcmm = 100 + .2Q2
150 - .1Qcmm = .2Q2
Q2= 750 - .5Qcmm
Answer: Qcmm = 750 -.5Q2
Qcmm = 750 - .5 (750 - .5Qcmm)
Qcmm = 750 – 375 + .25 Qcmm
Qcmm = 375 + .25 Qcmm
.75Qcmm= 375
Qcmm = 500
5) What is the output for Firm 2?
Answer: Q2 = 750- .5Qcmm
Q2 =750 –0.5(750-.5 Q2)
Q2 = 750 –375 +.25Q2
.75Q2= 375
Q2 = 500
6) What is the combined profit for the firms?
Answer: P = 250 - .1(Qcmm + Q2)
P = 250 - .1(500+500)
P = 250 – 100
P = 150
TC = Q * C
TC = 500 * 100
TC = 50000
TR = P * Q
TR = 150 * 500
TR = 75000
Profit = TR – TC
Profit = $ 75,000 - $ 50,000 = $25,000
Profit for both firms combined is $50,000.
e. Assume that CMM bought out the competitor which created a natural monopoly.
1) What is there optimum price and quantity?
Answer: Qd= 2500 – 10P
10P= 2500 – Q
P = 250 - .10Q
TR = 250Q - .1 Q2
MR= 250 -.2Q
Set MR = MC
250 - .2Qd = 100
.2 Qd = 150
Q= 750
P= 250 - .1(750)
P = 250 – 75
P = 175
Answer: Profit = TR – TC
TR = P * Q
TR= 175 * 750
TR = 131,250
TC = TC * Q
TC = 100 * 750
TC = $ 75,000
Profit = TR – TC
Profit = $ 131,250 – $ 75,000= $ 56,250
5. It has been one year since the introduction of the now wildly popular Bobby Beanies. In the rush to meet the needs for this fad item, three other companies have also started manufacturing their own bean bag animal toys. The current market share is as follows: Bobby Beanies (Firm A)= 63%, Firm B= 22%, Firm C= 10%, Firm D= 5%. The newest items on the market are high priced, limited edition beanies. Market demand is QD= 798 -2P and Bobby Beanie Co. is the dominant firm. The three follower firms have an MC= 4 + QF. Bobby Beanies long run MC= 3.
P= MC= 4 + QF
QF = P - 4
QS = 3(P-4)
QS = 3QF
QS = 3P-12
Qd = QD-QS
Qd = [798-2P]-[3P-12]
Qd = 810 - 5P
P=162-2Qd
Set MR=MC
R=PQ, MC=3
R=(162-2Qd)Q
R=162Q-.2Qd2
MR=162-.4Q
162-.4Q =3
Qd=397.5 beanies
P=162-.2(397.5)
P=$82.50
QS=3(P-4)
QS=3(82.50-4)
QS=235.5 beanies
HHI= s12 + s22 + s32 + s42
The current HHI index is: HHI=632+222+102+52=4578
If Firm B acquires Firm D, the HHI=632+272+102=4798
If Firm C acquires Firm D, the HHI=632+222+152=4678
According to government regulation, Firm B would be unable to acquire Firm D because the HHI index increased over 150 points with the acquisition. Firm C, however, would be able to acquire Firm D as the HHI index increased by only 100 points with the acquisition, thus staying below the 150 points cutoff.
QD = 40 - 2P
Additionally, there are four follower firms competing in this market, each having a long-run marginal cost function of:
MC = 4 + QF
Acme’s long-run marginal cost is 4.
a. Assuming each follower acts as a price taker, what is the total supply curve (QS) of the followers?
Each follower maximizes its profits by setting P = MC = 4 + QF. Hence,
P = 4 + QF
QF = P - 4
With four follower firms, the total supply curve is:
QS = 4QF = 4P - 16
b. What is net demand curve facing Acme?
Acme’s net demand curve is:
Qd = QD - QS
Qd = (40 - 2P) - (4P - 16)
Qd = 56 - 6P
c. What is Acme’s optimal price and output?
Qd = 56 - 6P
6P = 56 - Qd
P = 9.33 - Qd/6
To maximize profits, set MR = MC.
MR = MC
9.33 - Qd/3 = 4
Qd/3 = 5.33
Qd = 15.99
With Qd = 15.99,
P = 9.33 - Qd/6
P = 9.33 - 15.99/6
P = 6.67
d. What is the combined total supply output of the four other follower firms?
QS = 4P - 16
With P = 6.67,
QS = 4(6.67) - 16
QS = 26.68 - 16
QS = 10.68
Leaving aside antitrust concerns, collusion as described in problem 4 is possible. Note, however, that Acme 's has a lower MC=4 than the followers whose MC begins at 4 and is rising. Acme can drive them out by undercutting prices or simply by acquiring the competitors.
7. Little Lou works in a large auto parts plant in Flint, MI as a floor sweeper. As a floor sweeper, his job entails riding on a street cleaning machine down every aisle of the building for 4 hours. This gives him the opportunity to cover every square inch of the plant and to interact with all of his fellow employee’s. Little Lou sells cigarettes as a second job while riding on the street cleaning machine. Because the employee’s do not have the opportunity to leave the building during the work day his only competition is two other vending machines. One of the vending machine is in the salaried cafeteria and the other is in the hourly cafeteria and they are run by separate corperations. Therefore, This causes an Oligopoly inside the plant with three major players.
Key equations
Lou's marginal cost(mc)=2Q
Demand for the market(Qm)=100-2P
Supply for the competing firms(Qc)=50+P
a. What is the demand equation for Lou?
Q=Qm-Qc
Q=(100-2P)-(50+P)
Q=50-3P
b. How many packs of smokes should Lou sell.
MR=MC
16.67-.66Q=2Q
Q=6.27
c. What price should lou sell at?
P=16.67-.33(6.27)
P=$14.60
d. How many packs of cigarettes will the competition sell?
Qc=50+P
Qc=50+14.60
Qc=64.60
Lou often unplugs the vending machines or bribes the salesman to not put in as many cigarettes that are demanded.
(This is based on a true story)