Economic and Game Theory
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Thanks a lot,
1. Suppose we have two identical countries, denoted by i = 1, 2. Each country has a government that chooses a tariff rate, a monopoly that produces for both home consumption and export and consumers who buy on the home market from either the domestic monopoly or the foreign monopoly. The demand function in country i is Pi(Qi) = a - Qi. The firm in country i produces Hi for the home market and Ei for the export market. Thus Qi = Hi + Ei. The firms have a marginal cost c and no fixed costs. Total production costs are thus Ci(Hi, Ei,) = c*(Hi + Ei). The firms also incur tariff costs on exports: if firms i exports to country j when government j has set the tariff rate at Tj, then firm i must pay Tj*Ej to government j.
- Solve both firms' problme given that both governments have already chosen their tariff rates Ti and Tj. In other words, both firms first observe Ti and Tj and then simultaneously choose (Hi, Ei) and (Hj, Ej) to maximize their profits. Provide the conditions under which neither monopolies would produce for the export market.
- Without actually solving it, explain how you would go about solve the governments' problem of choosing a tariff rate.
2. Suppose a union is the sole supplier of labour to all the firms in a oligopoly, such as the United Auto Workers it to General Motors, Ford, Chrysler, etc. The timign of moves is the following: (1) the union makes a single wage demand, w, that applies to all the firms; (2) the firms observe and accept 2 and then simultaneously choose employment levels Li for firm i; (3) payoffs are (w-wa)L for the union where wa is the wage that union memebers can earn in alternative employment and L = L1 + L2 + ... + Ln is total employment in the unionized firms and profit P(w,Li) for firm i where the determinants of firm i's profits are described next.
All firms have the following production function, qi = L. The market clearing price is P(Q) = a - Q where Q = q1 + q2 + ... + qn. To keep things simple, assume that firms have no costs other than wages.
- What is the subgame-perfect outcome of this game?
- How (and why) does the numbers of firms affect the union's utility in the subgame-perfect outcome?