8. The following table shows revenue, costs, and profits, where quantities are in thousands, and
total revenue, total cost, and profit are in millions of dollars:
Price
$100
90
80
70
60
50
40
30
20
10
0
Quantity
(1,000s)
0
100
200
300
400
500
600
700
800
900
1,000
Total
Revenue
$0
9
16
21
24
25
24
21
16
9
0
Marginal
Revenue
---$9
7
5
3
1
-1
-3
-5
-7
-9
Total
Cost
$2
3
4
5
6
7
8
9
10
11
12
Profit
$-2
6
12
16
18
18
16
12
6
-2
-12
a. A profit-maximizing publisher would choose a quantity of 400,000 at a price of $60 or a
quantity of 500,000 at a price of $50; both combinations would lead to profits of $18
million.
b. Marginal revenue is always less than price. Price falls when quantity rises because the
demand curve slopes downward, but marginal revenue falls even more than price
because the firm loses revenue on all the units of the good sold when it lowers the price.
c.
Figure 2 shows the marginal-revenue, marginal-cost, and demand curves. The marginalrevenue and marginal-cost curves cross between quantities of 400,000 and 500,000. This
signifies that the firm maximizes profits in that region.
Figure 2
d. The area of deadweight loss is marked “DWL” in the figure. Deadweight loss means that
the total surplus in the economy is less than it would be if the market were competitive,
because the monopolist produces less than the socially efficient level of output.
e. If the author were paid $3 million instead of $2 million, the publisher would not change
the price, because there would be no change in marginal cost or marginal revenue. The
only thing that would be affected would be the firm’s profit, which would fall.
f.
To maximize economic efficiency, the publisher would set the price at $10 per book,
because that is the marginal cost of the book. At that price, the publisher would have
negative profits equal to the amount paid to the author.
Figure 3
5. a. The table below shows total revenue and marginal revenue for the bridge. The profitmaximizing price would be where revenue is maximized, which will occur where marginal
revenue equals zero, because marginal cost equals zero. This occurs at a price of $4 and
quantity of 400. The efficient level of output is 800, because that is where price is equal
to marginal cost. The profit-maximizing quantity is lower than the efficient quantity
because the firm is a monopolist.
Price
$8
7
6
5
4
3
2
1
0
Quantity
0
100
200
300
400
500
600
700
800
Total Revenue
$0
700
1,200
1,500
1,600
1,500
1,200
700
0
Marginal Revenue
---$7
5
3
1
-1
-3
-5
-7
b. The company should not build the bridge because its profits are negative. The most
revenue it can earn is $1,600,000 and the cost is $2,000,000, so it would lose $400,000.
c.
If the government were to build the bridge, it should set price equal to marginal cost to
be efficient. Since marginal cost is zero, the government should not charge people to use
the bridge.
Figure 7
d. Yes, the government should build the bridge, because it would increase society's total
surplus. As shown in Figure 7, total surplus has area ½x 8 x 800,000 = $3,200,000,
which exceeds the cost of building the bridge.
Price Discrimination
13. a. Figure 11 shows the cost, demand, and marginal-revenue curves for the monopolist.
Without price discrimination, the monopolist would charge price PM and produce quantity
QM .
Figure 11
b. The monopolist's profit consists of the two areas labeled X, consumer surplus is the two
areas labeled Y, and the deadweight loss is the area labeled Z.
c.
If the monopolist can perfectly price discriminate, it produces quantity QC, and has profit
equal to X + Y + Z.
d. The monopolist's profit increases from X to X + Y + Z, an increase in the amount Y + Z.
The change in total surplus is area Z. The rise in the monopolist's profit is greater than
the change in total surplus, because the monopolist's profit increases both by the amount
of deadweight loss (Z) and by the transfer from consumers to the monopolist (Y).
e. A monopolist would pay the fixed cost that allows it to discriminate as long as Y + Z (the
increase in profits) exceeds C (the fixed cost).
f.
A benevolent social planner who cared about maximizing total surplus would want the
monopolist to price discriminate only if Z (the deadweight loss from monopoly) exceeded
C (the fixed cost) because total surplus rises by Z − C.
g. The monopolist has a greater incentive to price discriminate (it will do so if Y + Z > C)
than the social planner would allow (she would allow it only if Z > C). Thus if Z < C but Y
+ Z > C, the monopolist will price discriminate even though it is not in society's best
interest.
Monopolistic Competition
8. a. If there were many suppliers of diamonds, price would equal marginal cost ($1,000), so
the quantity would be 12,000.
b. With only one supplier of diamonds, quantity would be set where marginal cost equals
marginal revenue. The following table derives marginal revenue:
Price
(thousands of
dollars)
Quantity
(thousands)
Total Revenue
(millions of dollars)
8
7
6
5
4
3
2
1
5
6
7
8
9
10
11
12
40
42
42
40
36
30
22
12
Marginal
Revenue
(millions of
dollars)
---2
0
–2
–4
–6
–8
–10
With marginal cost of $1,000 per diamond, or $1 million per thousand diamonds, the
monopoly will maximize profits at a price of $7,000 and a quantity of 6,000. Additional
production beyond this point would lead to a situation where marginal revenue is lower
than marginal cost.
c.
If Russia and South Africa formed a cartel, they would set price and quantity like a
monopolist, so the price would be $7,000 and the quantity would be 6,000. If they split
the market evenly, they would share total revenue of $42 million and costs of $6 million,
for a total profit of $36 million. So each would produce 3,000 diamonds and get a profit
of $18 million. If Russia produced 3,000 diamonds and South Africa produced 4,000, the
price would decline to $6,000. South Africa’s revenue would rise to $24 million, costs
would be $4 million, so profits would be $20 million, which is an increase of $2 million.
d. Cartel agreements are often not successful because one party has a strong incentive to
cheat to make more profit. In this case, each could increase profit by $2 million by
producing an extra 1,000 diamonds. However, if both countries did this, profits would
decline for both of them.
5. a. Figure 4 illustrates the market for Sparkle toothpaste in long-run equilibrium. The profitmaximizing level of output is QM and the price is PM.
Figure 4
b. Sparkle's profit is zero, because at quantity QM, price equals average total cost.
c.
The consumer surplus from the purchase of Sparkle toothpaste is areas A + B. The
efficient level of output occurs where the demand curve intersects the marginal-cost
curve, at QC. The deadweight loss is area C, the area above marginal cost and below
demand, from QM to QC.
d. If the government forced Sparkle to produce the efficient level of output, the firm would
lose money because average total cost would exceed price, so the firm would shut down.
If that happened, Sparkle's customers would earn no consumer surplus.
8. a. Tap water is a perfectly competitive market because there are many taps and the
product does not differ across sellers.
b. Bottled water is a monopolistically competitive market. There are many sellers of bottled
water, but each firm tries to differentiate its own brand from the rest.
c.
The cola market is an oligopoly. There are only a few firms that control a large portion of
the market.
d. The beer market is an oligopoly. There are only a few firms that control a large portion of
the market.
6. Suppose that an industry is characterized as follows:
C  100  2Q2
MC  4Q
P  90  2Q
MR  90  4Q
a.
Firm total cost function
Firm marginal cost function
Industry demand curve
Industry marginal revenue curve
.
If there is only one firm in the industry, find the monopoly price, quantity, and
level of profit.
If there is only one firm in the industry, then the firm will act like a monopolist and
produce at the point where marginal revenue is equal to marginal cost:
MC=4Q=90-4Q=MR
Q=11.25.
For a quantity of 11.25, the firm will charge a price P=90-2*11.25=$67.50. The level
of profit is $67.50*11.25-100-2*11.25*11.25=$406.25.
b.
Find the price, quantity, and level of profit if the industry is competitive.
If the industry is competitive then price is equal to marginal cost, so that 90-2Q=4Q,
or Q=15. At a quantity of 15 price is equal to 60. The level of profit is therefore
60*15-100-2*15*15=$350.
c.
Graphically illustrate the demand curve, marginal revenue curve, marginal cost
curve, and average cost curve. Identify the difference between the profit level of
the monopoly and the profit level of the competitive industry in two different
ways. Verify that the two are numerically equivalent.
The graph below illustrates the demand curve, marginal revenue curve, and
marginal cost curve. The average cost curve hits the marginal cost curve at a
quantity of approximately 7, and is increasing thereafter (this is not shown in the
graph below). The profit that is lost by having the firm produce at the competitive
solution as compared to the monopoly solution is given by the difference of the two
profit levels as calculated in parts a and b above, or $406.25-$350=$56.25. On the
graph below, this difference is represented by the lost profit area, which is the
triangle below the marginal cost curve and above the marginal revenue curve,
between the quantities of 11.25 and 15. This is lost profit because for each of these
3.75 units extra revenue earned was less than extra cost incurred. This area can be
calculated as 0.5*(60-45)*3.75+0.5*(45-30)*3.75=$56.25. The second method of
graphically illustrating the difference in the two profit levels is to draw in the
average cost curve and identify the two profit boxes. The profit box is the difference
between the total revenue box (price times quantity) and the total cost box (average
cost times quantity). The monopolist will gain two areas and lose one area as
compared to the competitive firm, and these areas will sum to $56.25.
P
MC
lost profit
MR
Demand
Q
11.25 15
2. Consider two firms facing the demand curve P = 50 - 5Q, where Q = Q1 + Q2. The firms’
cost functions are C1(Q1) = 20 + 10Q1 and C2(Q2) = 10 + 12Q2.
a.
Suppose both firms have entered the industry. What is the joint profit-maximizing
level of output? How much will each firm produce? How would your answer change
if the firms have not yet entered the industry?
If both firms enter the market, and they collude, they will face a marginal revenue
curve with twice the slope of the demand curve:
MR = 50 - 10Q.
Setting marginal revenue equal to marginal cost (the marginal cost of Firm 1, since it
is lower than that of Firm 2) to determine the profit-maximizing quantity, Q:
50 - 10Q = 10, or Q = 4.
Substituting Q = 4 into the demand function to determine price:
P = 50 – 5*4 = $30.
The question now is how the firms will divide the total output of 4 among themselves.
Since the two firms have different cost functions, it will not be optimal for them to split
the output evenly between them. The profit maximizing solution is for firm 1 to
produce all of the output so that the profit for Firm 1 will be:
1 = (30)(4) - (20 + (10)(4)) = $60.
The profit for Firm 2 will be:
2 = (30)(0) - (10 + (12)(0)) = -$10.
Total industry profit will be:
T = 1 + 2 = 60 - 10 = $50.
If they split the output evenly between them then total profit would be $46 ($20 for
firm 1 and $26 for firm 2). If firm 2 preferred to earn a profit of $26 as opposed to $25
then firm 1 could give $1 to firm 2 and it would still have profit of $24, which is higher
than the $20 it would earn if they split output. Note that if firm 2 supplied all the
output then it would set marginal revenue equal to its marginal cost or 12 and earn a
profit of 62.2. In this case, firm 1 would earn a profit of –20, so that total industry
profit would be 42.2.
If Firm 1 were the only entrant, its profits would be $60 and Firm 2’s would be 0.
If Firm 2 were the only entrant, then it would equate marginal revenue with its
marginal cost to determine its profit-maximizing quantity:
50 - 10Q2 = 12, or Q2 = 3.8.
Substituting Q2 into the demand equation to determine price:
P = 50 – 5*3.8 = $31.
The profits for Firm 2 will be:
2 = (31)(3.8) - (10 + (12)(3.8)) = $62.20.
b.
What is each firm’s equilibrium output and profit if they behave noncooperatively?
Use the Cournot model. Draw the firms’ reaction curves and show the equilibrium.
In the Cournot model, Firm 1 takes Firm 2’s output as given and maximizes profits.
The profit function derived in 2.a becomes
1 = (50 - 5Q1 - 5Q2 )Q1 - (20 + 10Q1 ), or
  40Q1  5Q12  5Q1Q2  20.
Setting the derivative of the profit function with respect to Q1 to zero, we find Firm 1’s
reaction function:

Q 
= 40 10 Q1 - 5 Q2 = 0, or Q1 = 4 -  2 .
 Q1
2
Similarly, Firm 2’s reaction function is
Q 
Q2  3.8   1 .
2
To find the Cournot equilibrium, we substitute Firm 2’s reaction function into Firm 1’s
reaction function:
Q 
1 
Q1  4   3.8  1 , or Q1  2.8.
2
2
Substituting this value for Q1 into the reaction function for Firm 2, we find Q2 = 2.4.
Substituting the values for Q1 and Q2 into the demand function to determine the
equilibrium price:
P = 50 – 5(2.8+2.4) = $24.
The profits for Firms 1 and 2 are equal to
1 = (24)(2.8) - (20 + (10)(2.8)) = 19.20 and
2 = (24)(2.4) - (10 + (12)(2.4)) = 18.80.
c.
How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal
but the takeover is not?
In order to determine how much Firm 1 will be willing to pay to purchase Firm 2, we
must compare Firm 1’s profits in the monopoly situation versus those in an oligopoly.
The difference between the two will be what Firm 1 is willing to pay for Firm 2. From
part a, profit of firm 1 when it set marginal revenue equal to its marginal cost was
$60. This is what the firm would earn if it was a monopolist. From part b, profit was
$19.20 for firm 1. Firm 1 would therefore be willing to pay up to $40.80 for firm 2.