2.9. Consider two countries. At date 1, the countries both have
such high tariffs that there is no trade. Within each country, wages
and employment are determined as in the monopoly-union model
in Section 2.1.C. At date 2, all tariffs disappear. Now each union
sets the wage in its country but each firm produces for both mar-
kets.
Assume that in each country inverse demand is P(Q) = 2-Q,
where Q is the aggregate quantity on the market in that country.
Let the production function for each firm be q = L, so that wages
are the firm’s only cost, and let the union’s utility function be
U(w,L) = (w – wo)L, where wo is the workers’ alternative wage.
Solve for the backwards-induction outcome at date 1.
Now consider the following game at date 2. First, the two
unions simultaneously choose wages, wi and w2. Then the firms
observe the wages and choose production levels for the domestic
and foreign markets, denoted by h; and e; for the firm in country i.
All of firm i’s production occurs at home, so the total cost is withit
e;). Solve for the subgame-perfect outcome. Show that wages,
employment, and profit (and therefore also the union’s utility and
Huizinga (1989) for other examples along these lines.
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