Download Econ 460: Industrial Organization

Econ 460: Industrial Organization
0101, Fall 2008
Due: Tuesday September 23, 11am
1. Consider the following two industries. For each industry, calculate the 4-firm
concentration ratio, HHI and draw the concentration curve. Which industry is more
concentrated? Can you tell?
Industry A
Firm:
Hereti-Corp
Morgan Industries
Rhesus
Enterprises
The Company
Regulus Systems
Revenue
87
94
Market
share
25.73964
27.81065
S^2
662.5293
773.4323
24.55621
5.029586
16.86391
603.0076
25.29673
284.3913
Market
share
13.74408
12.79621
54.50237
9.952607
9.004739
S^2
188.8996
163.743
2970.508
99.05438
81.08533
83
17
57
338
CR4
HHI
94.97041
2348.657
CR4
HHI
90.99526
3503.291
Industry B
Form:
Acme Inc
Barbatos
Cavalier
Derron
Excalibur
Revenue
29
27
115
21
19
211
Cumulative market share
Concentration curves
120
100
80
Industry A
60
Industry B
40
20
0
0
2
4
Firm Rank
6
2. Sirius and XM satellite radio want to merge. Suppose that you are a consumer of their
services and are worried about a merger increasing the price you pay. How might you
argue that their market should be defined, what types of firms should be included in this
market? Suppose that you work for one of the companies, and want the merger to go
ahead. How might you argue that their market should be defined, what types of firms
should be included in this market? Suppose that you are a Department of Justice
regulator deciding whether or not the merger should be allowed to go ahead. What
process might you use to try to define the market?
If I worked for Sirius or XM, I might argue that the relevant market was radio stations, of
which the two combined firms would have only a small market share. The market would
include all regular broadcast radio stations. If I was a customer who wanted to prevent
the merger, I would argue that the relevant market was satellite radio distribution, in
which the combined firm would have a monopoly. If I were the DOJ, I would try to
estimate how close substitutes these goods are; do increases in prices for satellite radio
increase the listening audience for broadcast radio? By how much?
Under no circumstances does it make sense to include companies that are providing
input goods for their product – these are clearly not the same market.
3. Suppose that we observe that an industry has high concentration. As policymakers,
should we require firms in the industry to separate? Why would we want to do this?
Why might we not want to do this?
We might want to require firms in the industry to separate in order to reduce market
power and the associated deadweight loss. We might not want to do this though because:
a) the industry might have large economies of scale, and increasing the number of firms
could increase average costs
b) high concentration leading to market power and positive profits might be necessary
for the industry to survive in the long-term because of large fixed costs or entry costs.
4. Suppose that a firm has technology such that f(x1,x2) = x12/3x21/3. Suppose that input
costs for goods (x1,x2) are (2,2). Solve the firm’s cost minimization problem for
producing 1 unit of output. What is the value of the cost function at 1 unit, ie what is
C(1)?
The firm solves:
Min 2x1 + 2x2 s.t. x12/3x21/3 = 1
Rearrange the constraint to get x1 = 1/x21/2
Substitute to get: Min 2/x21/2 +2x2
Foc: -1/x2-3/2 + 2 = 0
x23/2 = 1/2
x2 = (1/2)2/3 = 0.6300
x1 = 1/(1/2)1/3 = 1.260
C(1) = 2(1/(1/2)1/3) + 2(1/2)2/3 = 3.150
5. Consider the car manufacturing industry. Why might this industry demonstrate
economies of scale? Why might this industry demonstrate economies of scope?
Economies of scale:
There are many gains to be made from specialization; by organizing production lines
with specialist machines that perform a very specific function, and having specialist
workers who are experts in a few machines, average costs are much lower than they
would be if only a few people and machines tried to make an entire car.
There are large fixed costs to designing a new model of car, so average costs are much
lower if these are spread over a large number of cars.
Economies of scale are not something that result from a “change in technology”; they
are a property of the underlying technology and cost functions.
Economies of scope:
Different models of cars share many of the same inputs (metal, tires, computer
componentry, brand identity, etc), and use many similar machines and specialist workers.
Thus, there are economies of scope from producing different models of cars by the same
company.
Neither economies of scale or scope are about consumer demand; they are entirely
driven by cost considerations.
6. Suppose that demand for patented prescription drugs in the US and Canada are given
by:
PU = 32 – 2QU
PC = 4 – 2QC
Suppose that marginal costs are constant, c = 2. Suppose that importation of prescription
drugs from Canada into the US is forbidden by law.
a) Find the optimal linear pricing solution the drug manufacturer should adopt.
b) Suppose that the US repeals the law forbidding the importation of drugs, and
assume that the transport cost of drugs is zero. How will the drug company
respond – what will the new equilibrium be? Are US consumers better off?
Should Canada pass a law banning the export of drugs from Canada?
Market in US:
Profit maximization problem: MaxQU :QU(PU – 2)
Max: QU(32 – 2QU – 2) = QU(30 – 2QU)
FOC: 30 – 4QU = 0
QU = 30/4 = 7.5
PU = 32 – 2*7.5 = 17
Profit = 7.5*(15) = 112.5
Market in Canada:
Profit maximization problem: MaxQC :QC(PC – 2)
Max: QC(4 – 2QC – 2) = QC(2 – 2QU)
FOC: 2 – 4QC = 0
QC = 2/4 = 0.5
PC = 4 – 2*0.5 = 3
Profit = 0.5(1) = 0.5
Total profit = 113
Now, when importation is possible; firm can no longer price discriminate.
Find market demand curve, by inverting individual demand curves and adding.
Q = 16 – P/2
if 4 < P < 32
Q = 18 – P
if P < 4
Assuming we sell to both types (ie P <4), market demand is:
Q = 18 – P
Ie P = 18 – Q.
Here, Max: Q(18 – Q – 2)
FOC: 16 – 2Q = 0
Q=8
P = 10 > 4.
So selling to both types is not optimal (it would imply a price that violates our
restriction).
If we sell to just the US (ie P >4), market demand is:
Q = 16 – Q/2
This leads to a price of 17 and quantity of 7.5, and profit of 112.5.
So, if the US repeals the import ban, price and quantity in the US market remain
unchanged – US consumers are no better off. But Canadian consumers are no longer
sold to; they lose all their consumer surplus. So it would be in the interest of the
Canadian government to implement an export ban, to return to the price discrimination
solution.
7. Suppose a popular bar is considering setting its pricing pattern; it can either just set a
charge for drinks, or it can set a charge for drinks and set a cover charge that patrons
must pay to get inside (which they must pay in order to buy drinks).
Suppose that there are two types of customers; High Rollers (H) and Layabout Students
(L), who have different demands for drinks:
PH = 24 – QH
PL = 18 – QL
The bar can tell which type a consumer is at the door by checking IDs, but once inside
the bar cannot prevent arbitrage of drinks.
Suppose the marginal cost of supplying drinks is constant, c = 3.
a) If the bar sets just a charge for drinks, what price should it charge?
b) If the bar sets a cover charge and a price for drinks, what should these be? Should
the bar adopt a cover charge?
If the bar just sets a charge for drinks, it cannot price discriminate; it sets a uniform
price for all customers.
So, find the market demand curve:
Invert the inverse demand curves to find QH = 24 – PH , QL = 18 – PL.
Add these to find the market demand curve: Q = 24 – PH if P > 18. Q = 42 – 2P if P
≤18.
Suppose that we are selling to both types.
Re-invert the demand curve, gives: P = 21 – Q/2.
Solve the profit maximization problem:
Maxq Q(21 - Q/2 – 3)
Ie 18Q – Q2/2.
FOC: 18 – Q = 0.
Q = 18.
Substituting into the demand curve cives P = 21 – (18/2) = 12.
Check that this meets the constraint P ≤18. Yes, it does.
So, the optimal uniform price is P=$12 per drink, and the firm will sell 18 units (per pair
of types).
Suppose there are just one of each type, this gives us a profit of !8(12-3) = 162.
Now suppose that we can set a cover charge, and implement an optimal two-part tariff.
Recall the properties of an optimal two-part tariff; we set price = marginal cost = 3.
We set a cover charge for each type equal to their entire consumer surplus at a price of
3. High types will buy QH = 24 – 3 = 21 drinks. They get a consumer surplus of
21*21*1/2 = 220.5.
Low types will buy QL = 18 – 3 = 15 drinks. They get a consumer surplus of 15*15*1/2
= 112.5.
So, the optimal part-tariff charges $3 per drink, charges high types a cover charge of
$220.50, and charges low types a cover charge of $112.5.
If there are just one high type and one low type, we get a total profit of $333, which is
much higher than $162, so the club should definitely implement the cover charge.