Ayudantía 8 Pauta

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2 Exercise: Vertical Product Differentiation (3.5pts)
(b) Consider the case in which both firms chooses sH . Find the prices the two
firms charge at equilibrium in stage 3 and the related profits of each firm.
Solution: Recall that cH1 > c
H
2 . We note that a consumer with preference for
quality x̂ is indifferent between buying the product and not bying the product
if: x̂sH − pi = 0, so pisH = x̂. In particular, the two firms would serve without at
least incurring a loss all consumer with a preference for quality higher than
x ≥ c
H
1
sH
and x ≥ c
H
2
sH
correspondingly for firms 1 and 2. We note that firm 1 would never charge
p1 < c
H
1 . (0.25pts). Suppose that firm 1 charges p1 > c
H
1 , then it can possibly
serve all customers who value quality more than p1sH . If firm 2 charges p2 > p1,
it will not get any customers, so its profits will be 0. If p2 = p1, it will get half
of the market and on each sale it will make a profit of p1 − cH2 > 0.In more
detail:
1
2
(
1 + θ − p1
sH
)
N
(
p1 − cH2
)
> 0
However, firm 2 may choose to undercut firm 1 by charging p2 = p1 − ε, where
ε is sufficiently small to both undercut firm 1 and make profits:(
1 + θ − p1 − ε
sH
)(
p1 − cH2 − ε
)
>
1
2
(
1 + θ − p1
sH
)(
p1 − cH2
)
Thus, we conclude that firm 1 would charge p1 = c
H
1 and firm 2 would charge
just a bit lower price than cH1 . (There are some technical math issues with this
statement, but the economic intuition is strong.) The profits are then
π1 = 0
π2 = N
(
1 + θ − c
H
1 − ε
sH
)(
cH1 − cH2 − ε
)
(c) Based on the previous parts of the exercise, describe in words a scenario
in which firm 2 chooses optimally to produce the low quality variety despite
being more efficient than firm 1 in the production of both the high and low
quality version of the product.
Solution: If the differences between the firms’ costs of production of each
quality type are not very large, then we may end up in a situation similar to what
we have already studied in class. Namely, firm 1 chooses to produce the high
quality verison of the product. Although it is more efficient at the production of
both quality types, firm 2 may choose optimally to go for the low quality type:
severe price competition if it chooses to produce the high quality type may drive
down its profits sufficiently to justify a decision to go for the low quality type.
(0.5pts for a complete answer and 0.25pts for a partial answer)
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