8 Oligopoly - Luiscabral.net

Figure 8.10
Cournot equilibrium after exchange rate devaluation
q 1
45 ◦
q 2
q ∗ 2(q 1 )
̂q 1
̂q 2
• N ′
N
•
q ∗ 1(q 2 )
... .... .... .... .... ... ... ... .... .
............
. .
statics might help to answer is: What is the impact on market shares of a 50% devaluation
of the Yen?
Since the market is in $US, a shift in the exchange rate will change the Japanese firm’s
marginal cost in dollars, while keeping the U.S. firm’s marginal cost constant. Specifically,
suppose that both firms start with marginal cost c. Then the Japanese firms marginal cost
will change to c/e as a result of the devaluation, where e is the exchange rate in Yen/$.
For example, suppose marginal cost was initially $12 for the U.S. firm and Y1200 for
the Japanese firm; and that the initial exchange rate was 100 Y/$. This implies that the
Japanese firm’s marginal cost in US$ was 1200/100 = $12. A 50% devaluation of the
Yen means that $1 is now worth Y150. The Japanese firm’s marginal cost in US$ is now
1200/150 = $8. We thus have to compute the new equilibrium where one of the firm’s
marginal cost is lower.
In the previous application, we saw that an increase in marginal cost implies a downward
shift in the best response. By analogy, we now deduce that the Japanese firm’s best response
will shift upwards as a result of the reduction in its marginal cost (in US$). Since only the
Japanese firm’s best response has changed, we are now ready to determine the equilibrium
shifts resulting from a Yen devaluation. This is done in Figure 8.10, where the Japanese
firm’s output is measured in the vertical axis and the American firm’s on the horizontal
one. As can be seen, the new equilibrium point N ′ is above the 45 ◦ line, that is, the
Japanese firm’s output is now greater than the American firm’s. This is not surprising, as
the Japanese firm has decreased its cost (in US$), whereas the U.S. firm’s cost remained
unchanged.
Algebraic computation. The graphical analysis has the limitation that it is difficult to
determine the precise value of market shares. The best strategy is then to solve the model
algebraically, which we do now. The first thing we must do is to determine the Cournot
equilibrium for the asymmetric case. From Section 8.2, we know that a firm’s best response
is given by
q1(q ∗ 2 ) = a − c − q 2
2 b 2