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Solutions of Problem Set 1
2008/2009
Exercise I
1.
The “mark-up” can be expressed in the following way (assuming
Cournot market competition):
P  MgC si

P

si 
qi
Q
n
Q   qi
i 1
n
si2 H
P  MgC

s




i
P

i 1
i 1 
n
this equation shows that there is a positive relationship between equilibrium prices and
concentration level .
It is also important to notice that if there are less firms in the market it is easier to
sustain collusive strategies, avoiding price wars. Therefore prices will be higher if the
number of firms is lower.
2. a) Herfindahl Index1 = 0,27
Herfindahl Index2=0,33
We must assume that each of the “other brands” has very small market shares (less
than 1%) and that those market shares do not change after the merger.
b) In the case we define the relevant market as the soft drinks market. In this case,
Pepsi and 7-Up, together, hold relatively high market shares. If Pepsi argues that, in a
merger situation, the relevant market should not be just the soft drinks market, and, for
example, fruit juices and water ought to be consider, Pepsi’s market share drops
significantly.
Exercise II
1.
Topics for answer:
These three industries have some particular characteristics that must be taken
into account when analyzing market concentration.
 The relevant markets in cement industry are local markets because there
are high transportation costs
 Imports have a significant market share in the automobile industry
 Vertical differentiation in automobiles demands a more detailed analysis
by different segments
 Breakfast cereals are offered to consumers in a wide range of products
with different features (horizontal differentiation). Perhaps the different
types of products should be studied individually as they target different
consumer types.
2.
In some particular cases if an industry is more concentrated than other it does
not necessarily mean that in the first there is more market power than in the second. The
Bertrand oligopoly model is a very illustrative example of this fact. With only two firms
in the market we the price equilibrium is such that price equals marginal cost.
Contestable markets are another example of cases in which a very concentrated
market (i.e., a monopoly) reflects in low profits, as the monopolist can not increase
price because he will attract new firms into the market.
Exercise III
1.
Secret price cuts strategies predict that price wars start in periods of unexpected
low demand. This is consistent with the first observation above.
However, the effect of unexpected low demand is also consistent with a theory of price
wars caused by financial difficulty. The observation that prices fare wars take place
during periods of higher demand is consistent with demand fluctuation models: firms
have more incentives to get a higher market share in periods of high demand.
2.
The effect of standardization may correspond to the fact that it is easier to
monitor collusion with a standardized product (however, the effect of product
differentiation on collusion is a controversial issue). The effect of market share is
consistent with the theory that states that concentration facilitates collusion. The effect
of high market growth rate is also consistent with the theory.
Exercise IV
a)
The Nash Equilibrium is (M; M).
b)
Strategy: firm i chooses qi  L if the other firm produced q j  L in the previous
period. If the other firm does not cooperate and produces q j  L , then chose firm
i will set qi  M forever.
0,125
0,11
0, 015
0, 015
 c   nc  0,125 
 0,141 

 0, 016  i 

i
i
i
0, 016
 i  0,9375    0,5161
c)
The larger the efficiency asymmetry among firms, the stronger is the incentive to
deviate from the cooperative strategy. It is easier to maintain this type of agreement if
firms are very similar.
Exercise V
a)
Discounting can cheapen your brand image and identity, but may be worthwhile
if you still have relatively large margins and thus find it profitable to halt your slide in
market share.
Since the discounting is from other members of the Big Four, an aggressive
response on your part, perhaps followed by an exploratory price increase, might signal
that you will ought to avoid losing market share but are willing to accept today's shares
if your rivals raise prices somewhat.
b)
There is little you can do about this problem, since the fringe is hard to control
in any way, and entry of new fringe players is not likely to be very difficult. This is the
situation to emphasize your brand and to try to segment the market to retain your share
of those customers willing to pay a premium for a well-known brand (yours!).
c)
Generally, you can be more confident pushing prices up if rivals are at or near
capacity.
You will lose some sales, assuming that industry demand is not perfectly
inelastic, but you will lose little or no customers to your rivals in the short run (a year or
two) if they cannot expand production. Of course, if fringe firms are viewed as offering
close substitutes, and do not face capacity constraints, then the capacity limitations
faced by the other major players don't help you much at all.
d)
Such “detection lags" always make discounting look more attractive, simply
because any competitive responses will be delayed. Indeed, it seems that this is exactly
how you lost market share, to rivals who were discounting before you realized what was
going on.
e)
Now discounting is more attractive because marginal cost is low, so setting
marginal cost to the marginal revenue (associated with your residual demand curve)
involves a lower price.
Plus, even if you can engage in "cooperative pricing," the resulting price is lower,
the lower are marginal costs.
f)
In a declining market, the future is relatively less important commercially
relative to the present. In terms of our theories of “cooperative pricing”, declining
demand is much like a higher interest rate: the scale tips more towards maximizing
current profits and away from a “patient” approach of sacrificing short-run profits to
support or sustain long-run cooperation. So, discounting now to avoid a further loss of
market share (or to gain market share back) looks more attractive in a declining market,
even if this will trigger or inflame a price war.
Exercise VI
a)
Bundling strategies can increase profits when consumers differ with respect to
the amounts they are willing to pay for multiple products sold by the firm. So if
different people have different valuations of word processors and spreadsheets, it is
beneficial for software producers to sell these products jointly in order to enhance
profits.
b)
Ps
3
10
14
S
3
2
1
S
9
20
14
Pws
5
10
13
WS
 WS
3
2
1
15
20
13
If the products are sold separately XPTO should set Ps  10 and Pws  10 .
c)
Pb
16
19
20
Q

3
2
1
48
38
20
The optimal price for selling the two goods in a “pure bundling situation” is Pb  16 .
d)


Pb  16 all the groups will buy the bundle and individual prices should be such
that consumers always yield higher utility from buying the bundle ( Ps  14 and
Pws  13 ).  T  48
Pb  19 consumers A and B buy the bundle. If XPTO sells individual products at
the following prices: Pws  13 and Ps  14 , consumer C will buy the spreadsheet.
 T   b   s  38  13  51

Pb  20 only B chooses the bundle. If Ps  14 and Pws  13 , A will buy the
spreadsheet
and
C
will
buy
the
word
processor.
 T   b   s   wp  20  14  13  47
The optimal prices in a mixed bundling situation are Pb  19 , Pws  13 and Ps  14 .
Exercise VII
1)
Yes, these are cases of price discrimination. Consider the total price being paid
by each customer, P , as being composed of the price actually charged and the
transportation cost: P  pi  ti . Since locations are different, transportation costs are
different, thus, each consumer is charged a price pi that depends on his or her location.
This is a clear example of geographic price discrimination.
2)
This may be interpreted as a case of price discrimination. By offering coupons
(hence a lower price), supermarkets can serve the buyers with higher price elasticity at a
different price. In order for this strategy to improve revenues with respect to single price,
supermarkets should then set a higher regular price. Hence, empirical evidence is
consistent with the explanation that this is a form of price discrimination.