Suppose that lithium-ion batteries are produced by three firms, one each in Countries A, B, and C. The firms are called Firm A, Firm, B, and Firm C, respectively. Each firm produces with a marginal cost of $10 per battery, and the batteries they produce are identical. The firms compete as Cournot competitors. In each country, the demand for lithium-ion batteries is given by Q = 100- P, where Q indicates the number of batteries purchased and P is the price. Initially, each country charges an MFN tariff of $10 per battery imported from any source. Assume that no- one can move a shipment of batteries from one country to another except for the three firms that make them, so we can analyze the three markets separately.
(a) Compute the initial MFN equilibrium. With three Cournot competitors, in each country we have three quantities being chosen simultaneously and hence three unknowns, but we also have three equations, namely, the best-response equations for the three firms. However, under MFN, for each country the two foreign firms face an identical situation and will choose identical quantities. This allows one to write the problem as two equations (one domestic and one foreign) with two unknowns (the domestic quantity and the quantity sold by each foreign firm).
(b) Now, suppose that countries A and B sign a free-trade agreement, setting their mutual tariffs equal to zero, while all of the MFN tariffs are unchanged. How does this affect the equilibrium? Do firms A and B gain or lose from this free-trade agreement? How about firm C? Explain.