Example - Imperfect Information
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Again we consider the situation where B is a monopolist country and
A is a potential new entrant. However, in this case, we assume that A
does not know B's marginal cost, so that when A enters, B's response is
not clear:
If the marginal cost is high, B will not fight, as B can't
lower its price much.
If the marginal cost is low, B will fight by producing more
and decreasing the price. Then A will experience a loss and the
entry is not successful.
In this case, we analyse two game trees - one to represent each
possibility.
With a high marginal cost, we can assume that if A enters the market,
B can choose to fight or not,
and finds that not fighting is better
(B's payoff from fighting is 3, compared with 4 for not fighting),
in which case A receives 4.
If A chooses not to enter, B clearly gains.
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On the other hand, if B has a low marginal cost, then
if A enters the market,
B can choose to fight or not,
and finds that it is better to fight
(since B's payoff from fighting is 6, compared with 5 for not
fighting),
in which case A receives -3.
As before, if A chooses not to enter, B clearly gains.
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Expected Returns
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Suppose A estimates that the probability of B's marginal cost being
high is p, so the probability of it being low is (1 - p).
What is A's expected profit by entering? This is:
4p + (-3)(1 - p)
= 7p - 3
So A's expected profit is positive if 7p - 3 > 0. Thus A enters the market if
p > 3/7. B, on the other hand, attempts to make it appear that
p < 3/7 to dissuade A from entering the market.
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Other Implications
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In reality, the situation is not so simple. There are other
strategies that B might use to maintain its monopoly:
B knows that by fighting A, even if this is not B's optimum
strategy, A will always lose. Even if B's marginal cost is high,
and it is expensive to fight A, B might choose to do so anyway, so
that it can eliminate A from the market and then revert to its
monopolistic prices.
B can also signal to other potential entrants that it will
adopt this strategy (fighting) if someone enters the market.
Even if there is a high probability of B's marginal cost
being high, B might attempt to make it appear that the opposite is
true.
If there actually is a high probability that B's
marginal cost is low, B might demonstrate this, signalling to A
that it is not worth attempting to enter the market.
If there is a threat from A, B's government might choose to
subsidise B.
If A's government promises the entrant that it will subsidise
the entrant (to make its payoff 0 rather than -4) if B's MC is
low, then A's expected profit by entering is:
4p + (0)(1 - p)
= 4p
Now A's expected profit will be positive for any value of
p > 0. So A will always enter the market in these circumstances.
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Strategic Trade Policies - More Advanced Students
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Can government intervention raise national welfare by shifting oligopoly rents from foreign to domestic firms?
This topic was mainly researched by Brander and Spencer (1983, 1985). In principle, government policies such as export subsidies can serve the strategic purpose of altering the subsequent incentives of firms, acting as a deterrent to foreign competitors. This seems to offer possible rationales for trade poicies. The topic became especially 'hot' as the US experienced so called competitivenessd problems in the 1980s.
Critiques
- The dependence of trade policy recomendations on the nature of competition between firms (Eaton and Grossman, 1986).
- The general equilibrium issue that industries must compete for resources within a country (Dixit and Grossman, 1984).
- The question of entry (Hortman and Mqarksen, 1986; Dixit, 1989).
- The question of who is behaving strategically with respect to whom (Dixit and Kyle, 1985).
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[1] A simplified version of the Brander-Spencer Analysis
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Two firms, each in one country
Neither country has any domestic demand for the industry's product.
No distortion other than the presence of monlpoly power (for each country national welfare can be identified with the profits earned by its firm)
Two firms compete in Cournot fasion (quantity)
Profit functions:
In a simplified Cournot model where c1=c2=c, P=a-bX=a-bX1-bX2 country 1’s reaction is maximization of  with respect to X1 given X2 which gives
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 ,
this is the reaction curve for country (company) 1.
Country 2’s reaction is maximization of  with respect to X2 given X1 which gives
 ,
this is the reaction curve for country (company) 2.
The only possible equilibrium is in the point where country(company) 1 produces X1* and country(company) 2 produces X2*.
Let us now suppose that country 1 subsidizes its domestic firm (Firm 1),
where s is the amount of subsidy per unit produced. Accordingly, the reaction curve of X1 changes to
 .
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thus the output of company (country) 1 will increase and the output of company (country) 2 will decrease.
A government policy can serve the purpose of making a commitment credible.
Country 1's firm, with subsidy, behaves as a Stackelberg leader.
As the subsidy has the deterrent effect of reducing country 2's production, the profits of the contry 1's firm will rise more than the amount of subsidy.
Country 1's national income rises.
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[2] The Nature of Competition
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The particular policy recommendation depends critically on details of the model. The B-S case for export subsidies depends on the assumption of Cournot competition.
For example, Bertrand competition results in a different conclusion.
A simplified version of Bertrand competition
Assumptions:
Two firms compete using price, not quantity.
Other assumptions are the same as before (the Cournot case).
Profit functions:
Reaction functions:
Suppose  , where b, d > 0.
First order condition:
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Therefore, the reaction function for Firm 1 is
i.e. the reaction curve is upward sloped. The reaction curve for the Firm 2 will be:
Country(company) 1 can increase its profits by persuading country(company) 2 to charge a higher price than at the Nash equilibrium.
For this, country 1 should commit to a higher price.
Government should impose an export tax! (not export subsidy).
What if government 1 chooses export subsidy? In this case, Firm 1’s profit function is
and the reaction curve function is
i.e. the reaction curve shifts down.
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Eaton and Grossman (1986) embedded both Cournot and Bertrand in a general conjectural variations formulation. They found that, if the conjectures are rational, free trade turns out to be the optimal policy.
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