Download Industrial Organization Answer Key to Assignment # 1

Trinity College Dublin
Department of Economics
Instructor: Martin Paredes
Michaelmas Term 2006
Industrial Organization
Answer Key to Assignment # 1
1. What are the economic costs of operating the restaurant during the first year? In other
words, what level of revenues will you need to achieve in the first year to make the first
year profitable in an economic sense?
There are three opportunity costs:
1. The salary you could earn if you do not quit: $46,000.
2. The interest income your savings could earn if you do not cash in:
$200k0. 06  $12,000.
3. The rent your building could earn if you do not use it for your restaurant:
$2, 500 12 months  $30,000.
There are four direct costs:
1. Maintaining the equipment: $4,000.
2. Food: $50,000.
3. Hiring extra help: $40,000.
4. Utilities and supplies: $14,000.
Note that the $200,000 cost of the equipment is not an economic cost because it is
essentially reversible. That is, you can always sell the equipment for its current market
value as long as you maintain it. Only the interest you would have earned on the
money tied up in the equipment and the cost to maintain it are economic costs. Adding
up opportunity and direct costs yields $196,000. This is the break-even revenue for
first year of operations.
2. Las-O-Vision is the sole producer of holographic TVs, 3DTVs. The daily demand for
q2
3DTVs is Dp  10200  100p. The cost of producing q 3DTVs per day is 2 (note
this implies that MC  q).
a. What is Las-O-Vision’s total revenue schedule?
Total Revenue is given by pq  q, that is, the revenue that Las-O-Vision receives
when it sells q units. To get pq, we invert the demand function
q
q  10, 200  100p by solving for p in terms of q, or pq  102  100 .
Substituting this into our total revenue equation, we obtain
q
q2
TRq  102  100   q  102q  100 .
b. What is Las-O-Vision’s marginal revenue schedule?
Since our demand equation is linear in q, we can obtain the marginal revenue
q
using the "twice-as-steep" rule, so MRq  102  50 . Alternatively, we can
obtain it by realling that marginal revenue is the derivative of Total Revenue with
respect to q.
c. What is the profit-maximizing number of 3DTVs for Las-O-Vision to produce each
day? What price does Las-O-Vision charge per 3DTV? What is its daily profit?
The profit maximizing quantity, q  is that quantity at which marginal cost and
marginal revenue are equal. Setting MRq  MC, we have
q
 q
50
q   100
The profit maximizing price is that which generates q   100 in sales or,
substituting into the inverse demand function calculated in a,
p100  102  100  101
100
When selling 100 units, Las-O-Vision generates Total revenues equal to
2
TR100  102100  100  $10, 100
100
100 2
Its total cost is TC  2  5, 000. Therefore its total profit when it sells 100
units is 10, 100  5, 000  $5, 100.
102 
3. Engineers have determined that the cost function of pens (q 1 ) and pencils (q 2 ), in
millions of units per year, is:
6  q 1  3q 2  q 1 q 2
Cq 1 , q 2  
. if q 1  0 and q 2  0
4  3q 2
if q 1  0 and q 2  0
3  q1
if q 1  0 and q 2  0
a. Are there scope economies? Explain how you came to this conclusion
Scope economies exist when
Cq 1 , q 2   Cq 1 , 0  C0, q 2 
Then, we have scope economies when
6  q 1  3q 2  q 1 q 2  4  3q 2  3  q 1
 q 1 q 2  1.
b. Are there multi-product increasing or decreasing returns to scale? Explain your
answer.
We measure multi-product returns to scale by:
Cq 1 , q 2 
S
q 1  MC 1  q 2  MC 2
If S  1, then we have multi-product increasing returns to scale. If S  1, then we
have multi-product decreasing returns to scale. In this case:
6  q 1  3q 2  q 1 q 2
S
q 1  1  q 2   q 2  3  q 1 
6  q 1  3q 2  q 1 q 2

q 1  3q 2  2q 1 q 2
Thus, S  1 if and only if 6  q 1 q 2 , and S  1 if and only if 6  q 1 q 2 .
c. Derive an expression for the Ray Average Cost function when pens constitute 67 of
the firm’s total production. (Hint: MCq 1   1  q 2 and MCq 2   1  q 1 ).
The values of the   s are  1  67 and  2  17 . Then, the ray average cost function
would be:
RACq 
C 67 q,
q
1
7
q
q  3 17 q   67 q 17 q
q
6  97 q  496 q 2
9
6

 6
q
q  7  49 q
d. Does it make sense to produce pens and pencils together or separately? Support
your answer with the results from a, b and c.
If q 1 q 2 is sufficiently small enough, say q 1 q 2  1, then it makes sense to produce
them jointly. We would have scope economies and multi-product increasing
returns to scale. If not, then it makes sense to produce both goods separately.

6
6
7
4. "The degree of monopoly power is limited by the elasticity of demand." Comment.
Optimal monopoly pricing leads to the following relation between the price-cost
margin and demand elasticity:
p  MC
 1
p
where p is price, MC marginal cost, and  demand elasticity. It follows that the greater
the value of , the lower the value of p  MC and the lower monopoly profits. A
monopolist facing a very elastic demand curve makes profits at the level of a
competitive firm.
5. The technology of book publishing is characterized by a high fixed cost (typesetting the
book) and a very low marginal cost (printing). Prices are set at much higher levels
than marginal cost. However, book publishing yields a normal rate of return. Are these
facts consistent with profit maximizing behavior by publishers? Which model do you
think describes this industry best?
The model of monopolistic competition is probably the best approximation to
describing this industry. The model of monopolistic competition shows that
price-making, profit-maximizing behavior is consistent with a zero-profit long-run
equilibrium. The strong scale economies in book publishing imply that the gap
between price and marginal cost is particularly high.
6. Suppose the marginal cost of producing pizzas for the typical firm in a local town is
MC  2  4Q
a. Describe the competitive supply behavior of the typical pizza firm.
The competitive supply behavior of the typical pizza firm is described by:
q  P4  12 .
We set price equal to marginal cost for any one of the firms to obtain:
MC  4q  2  P
4q  P  2
q  P2  P  1.
4
2
4
b. Suppose there are 100 firms in the industry, each acting as perfect competitor.
Find the market supply curve.
Q
The market supply curve is given by: P  2  25 .
Because there are 100 identical firms, we can simply multiply the supply curve in
part (a) by 100 as follows to obtain the supply equation:
Q  100q  100 P  1  25P  50
2
4
We then solve this equation for P as a function of Q to get inverse supply:
Q  25P  50
Q  50  25P
Q
2  P
25
7. Suppose the market for widgets is QP  1000  50P. Widgets can be produced at a
constant average and marginal cost of $10 per unit.
a. Calculate the market output and price under perfect competition.
First find the inverse demand function by solving the demand equation for P as a
function of Q:
Q  1, 000  50P
50P  1, 000  Q
Q
P  20 
50
Then set this equal to marginal cost to find the competitive solution. This will give
Q
P  20 
 10  MC
50
Q
 10
50
Q  500
Q
 20  500  10
P  20 
50
50
Notice that, in this case, we cannot determine the number of firms, but only the
aggregate market output.
b. Calculate the market output and price under monopoly.
Under monopoly we set marginal revenue equal to marginal cost. We can find
marginal revenue by applying the "twice-as-steep" rule to the inverse demand:
Q
P  20 
50
Q
Q
MR  20  2
 20 
50
25
Seting this equal to marginal cost we obtain:
MR  20 
Q
 10  MC
25
Q
 10
25
Q  250
P  20 
Q
 20  250  15
50
50
8. There is a domestic monopolist in the American zonker market. The U.S. demand for
zonkers is P  100  Q and the monopolist’s marginal cost is $20 per unit. There is an
import ban on zonkers into the U.S. right now. If trade were allowed, a group of small
international firms would enter the U.S. market, and the American monopolist would
act as a dominant firm leader. The supply of the international fringe firms in the U.S.
would be P  20  q f .
a. Calculate the market output and price right now (i.e., without trade)
Right now, there is a monopoly in the American zonker market. The American
monopolist will produce all the market output at the level where MR  MC. By
the "twice-as-steep" rule, MR  100  2Q. Solving:
MR  MC
100  2Q  20
Q  40
and
P  100  40  60
b. Calculate the market output and price if trade were allowed
If trade were allowed, the American monopolist will behave as a dominant firm,
so first we need to determine the residual demand for the firm. Since total demand
is Q  100  P and the fringe supply is q f  P  20, then:
qd  Q  qf
q d  100  P  P  20
q d  120  2P
We can re-write the residual demand as P  60 
rule, MR d  60  q d . Solving:
MR d  MC
1
2
q d . By the "twice-as-steep"
60  q d  20
q d  40
and
P  60  1 40  40
2
Moreover, the international fringe firms will supply
q f  40  20  20
c. What would be the net welfare effect on the United States of allowing trade?
Would American consumers benefit? Would the American monopolist benefit?
The American producer will still provide the same 40 units than before, but he is
forced to set a lower price, so his profits are reduced by $800. Consumers are able
to buy 20 more zonkers than before, so consumer surplus increases by $200.