NAME_______________________________________________________________
FE461 Professor Schmitt
First Problem Set
Due 31 January 2012
1. (20 points) Suppose Tyco International has complete control over the plastic hangar
market. Suppose the inverse demand for hangars is given by: P(Q)  3 
Q
.
16,000
Suppose that the total costs is given by: C (Q)  100  Q
a) What is the equilibrium price and quantity of hangars in the market if the market is
competitive?
To find the competitive quantity we set price equal to marginal cost and solve for Q:
P  3
Q
Q
 1  MC 
 2  Q  32,000
16,000
16,000
We obtain price by substituting the competitive quantity in the inverse demand function.
P  3
32,000
Q
 P  3
 3 2 1
16,000
16,000
Or we could simply note that with P = MC, price must be equal to 1, and then substitute this
in the inverse demand equation and solve for Q.
b) What is the equilibrium price and quantity of hangars if the market is monopolized?
With an inverse demand of P  3 
Q
Q
, marginal revenue is given by MR  3 
16,000
8,000
(same intercept, twice as steeply sloped  recall this comes from the demand being linear
and TR = P*Q = (3 
dTR
Q
Q
 3 2*(
).
)Q and MR 
dQ
16,000
16,000
Setting this equal to marginal cost will yield the monopoly value of Q.
Q
Q
=1=MC  2 
 Q = 16,000. Solving for price we
8,000
8,000
16,000
obtain P  3 
 3 1  2 .
16,000
MR  3 
c) What is the deadweight or welfare loss of the monopoly in this market?
The competitive industry has no profits and so producer surplus is zero. Consumer surplus
is given by the triangle that starts at 1, proceeds over to C, and then angles up to . The base
is 32,000, the height is 2, and the area is ½(32,000)(2) = 32,000.
With a monopoly, consumer surplus is given by the triangle that starts at 2, proceeds over
to A, and then angles up to 3. The base is 6,000, the height is 1, and the area is ½(16,000)(1)
= 8,000. Profits or producer surplus for the monopolist are given by the rectangle beginning
at 1, proceeding over to B, up to A and then back over to 2. This rectangle has dimensions
16,000x1 = 16,000. So total surplus with monopoly is 24,000. The loss from monopoly is
then 32,000 - 24,000 or 8,000. One can also compute the area of the deadweight loss triangle
ABC = ½ b*h = 8,000
The following diagram will be useful for this problem.
Price
3
Pmon = 2
A
PPC
B
=1
C
16,000
32,000
MR=3-Q/8,000
D = 3 – Q/16,000
48,000 Q
2. (20 points) Use the following tables to answer questions about market concentration and
market power:
Firm
Daimler Chrysler
Mazda
Mitsubishi
Subaru
BMW
Hundai
Mercedes
Volkswagen
Suzuki
General Motors
Ford Motor Company
Toyota
Honda
Nissan
Other (Fringe Firms)
Market Share
0.087
0.019
0.026
0.013
0.018
0.026
0.017
0.049
0.002
0.281
0.228
0.101
0.071
0.041
0.021
Firm
Disney
Dreamworks
Fox
MGM/UA
Miramax
New Line
Paramount
Sony
Universal
Warner
Other (Fringe Firms)
Market Share
0.147
0.103
0.097
0.013
0.063
0.052
0.105
0.088
0.145
0.119
0.068
a) Use the information above to calculate the concentration of the top 4 firms in each
industry. Which is more concentrated based on your analysis?
auto
C4 = .281 + .228 + .101 + .087 = 0.697
C4movie = .147 + .145 + .119 +.105 = 0.516
Automobile – higher C4
b) Using the alternative measure of market concentration, the Herfindahl-Hirshman Index
which industry is more concentrated? (For Fringe firms you can IGNORE these in your
calculation, this does not mean 1 firms has 2.1% and 6.8% market share but that MANY
firms together have 2.1% and 6.8% market share.
HHIauto = .2812 + .2282 + .1012 + .0712 + …+ .0182 + .0172 + .0132 = .1603
(note other omitted because these “fringe” firms are small and have a very small
percentage of the market)
1,603
HHImovie = .1472 + .1452 + .1192 +.1052 + … + .0632 + .0522 + .0132 = .1024
1,024
3. (20 points) We defined the Lerner index LI 
1


1

, where     the absolute
value of the price elasticity of demand. We also showed (through profit maximization of
a monopolist) that LI 
P  MC
. Use these relationships to show that the LI can never
P
exceed 1. What does this imply is the minimum demand elasticity we should observe for
a monopolist?
We can write the Lerner index as follows
First note that prices and marginal costs are always positive. Then note that a profit
maximizing firm will only operate at a point where P  MC . This means that the ratio
MC/P is always less than one which means than L is always less than one and greater
than zero.
Given that L is  1 it is clear than   1 for a monopolist. In particular,
4. (20 points) The Q & H Company produces a number of products including shampoo, qS,
and toothpaste qT. Suppose the cost functions for these products are given by
C (q S ,0)  4  q S2
C (0, qT )  4  qT
C (q S , qT )  7  q s2  qT
a) Does the production of shampoo exhibit economies of scale? Explain your
reasoning.
4  q s2
qs
AC
2 1
S

 2   1?
MC
2q s
qs 2
2 1

q s2 2
4  q s2
The production of shampoo exhibits economies of scale up until 2 units of output. After
that, the production of shampoo exhibits diseconomies of scale.
b) Does the production of toothpaste exhibit economies of scale? Explain your
reasoning.
4  qT
S
AC

MC
qT
1

8
qT
 2  1?
2 qT
Yes, it does exhibit economies of scale.
c) Are there economies of scope associated with producing shampoo and
toothpaste? Explain your reasoning.
Yes. No matter what combination, it will always be $1 less expensive to make the products.
Notice that C(qs,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.
5. (20 points) Let a firm’s total cost function be TC  800  8q  8q 2 . Find the range of
production characterized by economies of scale (that is, for q < #).
To find the output where MES sets in, we can look for the level of q where AC = MC. 800/q
+ 8 + 8q = 8 + 16q ; 8q = 800/q; q=10
Alternatively, you can take the first derivative of the AC function and set it equal to zero to
see where it reaches a minimum. The result will yield the same answer: q=10. Economies of
scale occur from q = 0 to q = 10. After q = 10, the firm experiences diseconomies of scale.