# HW 9 solutions

```Chapter 10: Market Power: Monopoly and Monopsony ID:
Name:
HW #9: Due Monday, 4th July
REVIEW QUESTIONS
1. A monopol i s t i s produci ng at a poi nt at whi ch marginal cos t exceeds marginal revenue.
How s hould i t adjust i ts output to i ncreas e profit?
When marginal cost is greater than marginal revenue, the incremental cost of the last unit
produced is greater than incremental revenue. The firm would increase its profit by not
producing the last unit. It should continue to reduce production, thereby decreasing marginal
cost and increasing marginal revenue, until marginal cost is equal to marginal revenue.
2. We wri te the percentage markup of pri ces over marginal cos t as (P - MC)/ P. For a
profit-maxi mi zing monopol i s t, how does thi s markup depend on the el as ti ci ty of demand?
Why can thi s markup be vi ewed as a meas ure of monopol y power?
We can show that this measure of market power is equal to the negative inverse of the price
elasticity of demand.
P − MC
1
=−
P
ED
The equation implies that, as the elasticity increases (demand becomes more elastic), the inverse
of elasticity decreases and the measure of market power decreases. Therefore, as elasticity
increases (decreases), the firm has less (more) power to increase price above marginal cost.
3.
Why i s there no market s upply curve under conditi ons of monopol y?
The monopolist’s output decision depends not only on marginal cost, but also on the demand
curve. Shifts in demand do not trace out a series of prices and quantities that we can identify as
the supply curve for the firm. Instead, shifts in demand lead to changes in price, output, or both.
Thus, there is no one-to-one correspondence between the price and the seller’s quantity; therefore,
a monopolized market lacks a supply curve.
4. Why mi ght a fi rm have monopo l y power even i f i t i s not the onl y producer i n the
market?
The degree of monopoly (or market) power enjoyed by a firm depends on the elasticity of the
demand curve that it faces. As the elasticity of demand increases, i.e., as the demand curve
becomes flatter, the inverse of the elasticity approaches zero and the monopoly power of the firm
decreases. Thus, if the firm’s demand curve has any elasticity less than infinity, the firm has
some monopoly power. It is only the competitive firm that faces a horizontal demand curve
who has no market power.
EXERCISES
5. The fol l owi ng tabl e s hows the demand curve faci ng a monopol i s t who produces at a
cons tant marginal cos t of \$10.
a.
Pri ce
Quanti ty
18
16
14
12
10
8
6
4
2
0
0
4
8
12
16
20
24
28
32
36
Cal cul ate the fi rm’s marginal revenue curve.
138
Chapter 10: Market Power: Monopoly and Monopsony ID:
Name:
To find the marginal revenue curve, we first derive the inverse demand curve. The intercept of
the inverse demand curve on the price axis is 18. The slope of the inverse demand curve is the
change in price divided by the change in quantity. For example, a decrease in price from 18 to
16 yields an increase in quantity from 0 to 4. Therefore, the slope is
is
−
1
and the demand curve
2
P = 18 − 0.5Q.
The marginal revenue curve corresponding to a linear demand curve is a line with the same
intercept as the inverse demand curve and a slope that is twice as steep. Therefore, the marginal
revenue curve is
MR = 18 - Q.
b.
What are the fi rm’s profit-maxi mi zing output and pri ce?
What i s i ts profit?
The monopolist’s maximizing output occurs where marginal revenue equals marginal cost.
Marginal cost is a constant \$10. Setting MR equal to MC to determine the profit-maximizing
quantity:
18 - Q = 10, or Q = 8.
To find the profit-maximizing price, substitute this quantity into the demand equation:
P = 18 − (0.5)(8) = \$14.
Total revenue is price times quantity:
TR = (14 )(8) = \$112.
The profit of the firm is total revenue minus total cost, and total cost is equal to average cost
times the level of output produced. Since marginal cost is constant, average variable cost is
equal to marginal cost. Ignoring any fixed costs, total cost is 10Q or 80, and profit is
112 − 80 = \$32.
c.
What woul d the equi li bri um pri ce and quanti ty be i n a competi ti ve i ndustry?
For a competitive industry, price would equal marginal cost at equilibrium.
expression for price equal to a marginal cost of 10:
Setting the
18 − 0.5Q = 10 ⇒ Q = 16 ⇒ P = 10.
Note the increase in the equilibrium quantity compared to the monopoly solution.
d.
What woul d the s oci al gai n be i f thi s monopol i s t were forced to produce and pri ce at
the competi ti ve equi li bri um? Who woul d gai n and l os e as a res ult?
The social gain arises from the elimination of deadweight loss. Deadweight loss in this case is
equal to the triangle above the constant marginal cost curve, below the demand curve, and
between the quantities 8 and 16, or numerically
(14-10)(16-8)(.5)=\$16.
Consumers gain this deadweight loss plus the monopolist’s profit of \$32. The monopolist’s
profits are reduced to zero, and the consumer surplus increases by \$48.
6.
Suppose that an industry is characterized as f o l l o w s :
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 i s onl y one fi rm i n the i ndus try, fi nd the monopol y pri ce, quanti ty, 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
139
Chapter 10: Market Power: Monopoly and Monopsony ID:
Name:
Q=11.25.
For a quantity of 11.25, the firm will charge a price P=90-2*11.25=\$67.50.
profit is \$67.50*11.25-100-2*11.25*11.25=\$406.25.
b.
The level of
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*15-1002*15*15=\$350.
c.
Graphi cal l y i l l us trate the demand curve, margi nal revenue curve, margi nal co s t
curve, and average cos t curve. Identi fy the di fference between the profi t l evel of
the monopol y and the profi t l evel of the competi ti ve i ndus try i n two di fferent ways .
Verify that the two are numerically equivalent.
The graph below illustrates the demand curve (P=90 – 2Q), marginal revenue curve (MR=90 –
4Q), and marginal cost curve (MC=4Q). The average cost curve (AC=100/Q + 2Q) 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, we draw 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) or (P –
AC)*Q. The monopolist will gain two areas and lose one area as compared to the
competitive firm, and these areas will sum to \$56.25.
Alternatively this difference is represented by the lost profit area, which is the triangle below the
marginal cost curve and above the marginal revenue curve (shaded in dark grey), between the
quantities of 11.25 and 15. T his is lost profit because for each of these 3.75 units extra revenue
earned was less than extra cost incurred.
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Chapter 10: Market Power: Monopoly and Monopsony ID:
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MR
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