International Trade - Theory and Policy, 2010a

United States maintains its free trade position, then a partial equilibrium welfare analysis suggests the
following:
1. Brazilian welfare will rise (we’ll assume from 100 to 120 units).
2. U.S. welfare will fall (we’ll assume from 100 to 70 units).
3. World welfare will fall (thus the sum of the U.S. and Brazilian welfare initially is 200 units but falls to 120 + 70 =
190 afterward).
Similarly, if the United States imposes optimal tariffs on all of its imports while Brazil maintains free
trade, then the countries will realize the payoffs in the upper right-hand box. The United States would get
120 units of welfare, while Brazil would get 70. To keep the example simple, we are assuming that the
effects of tariffs are symmetric. In other words, the effect of U.S. optimal tariffs on the two countries is of
the same magnitude as the effects of Brazilian tariffs.
Finally, if both countries set optimal tariffs against each other, then we can simply sum up the total
effects. Since each country’s actions raise its own welfare by 20 units and lower its trade partner’s welfare
by 30 units, when both countries impose tariffs, national welfare falls to 90 units in each country.
To determine which strategy the two governments would choose in this game, we need to identify the
objectives of the players and the degree of cooperation. Initially, we will assume that each government is
interested in maximizing its own national welfare and that the governments do not cooperate with each
other. Afterward, we will consider the outcome when the governments do cooperate.
The Noncooperative Solution (Nash Equilibrium)
A noncooperative solution is a set of strategies such that each country maximizes its own national welfare
subject to the strategy chosen by the other country. Thus, in general, if the U.S. strategy (r) maximizes
U.S. welfare, when Brazil chooses its strategy (s) and if Brazil’s strategy (s) maximizes Brazil’s welfare
when the United States chooses strategy (r), then the strategy set (r,s) is a noncooperative solution to the
game. A noncooperative solution is also commonly known as a Nash equilibrium.
How to Find a Nash Equilibrium
One can determine a Nash equilibrium in a simple two-player, two-strategy game by choosing a strategy
for one of the players and answering the following series of questions:
1. Given the policy choice of the first player, what is the optimal policy of the second player?
2. Given the policy choice of the second player (from step one), what is the first player’s optimal policy choice?
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