A.(Autarky) Firm A in the US is the only seller of wine there. Let QAUS be Firm As sales in the US where demand isAgiven by 11 (1/4)QAUS. Firm As costs are 1 per unit. pA(QAUS) = (11 (1/4)QAUS).QAUS QAUS What value of QAUSmaximizes profit? What is the sum of consumer surplus and firm profit? B.(Free Trade) Now trade is opened between the US and France. Firm A is still the only producer in the US, while firm B is the onlyUSproducer in France. Both can sell in either country: QAUSis As sales in the US; QAFris As sales in France; QBUSis Bs sales in the US; QBFris Bs sales in France. If a firm sells in the other country, their costs include not only their production costs but also a transportation cost of 1 per unit. Demand in the US is 11 (1/4)(QAUS + QBUS) while demand in France is 11 (1/4)(QAFr + QBFr). There is an important separability here; e.g., pA(QAUS, QAFr, QBUS, QBFr) = PUS(QAUS + QBUS).QAUS + PFr(QAFr + QBFr).QAFr (QAUS + QAFr) QAFr = [11 (1/4)(QAUS + QBUS)].QAUS + [11 (1/4)(QAFr + QBFr)].QAFr QAUS 2QAFr = {[11 (1/4)(QAUS + QBUS)].QAUS QAUS} + {[11 (1/4)(QAFr + QBFr)].QAFr 2QAFr} =pA1(QAUS, QBUS) +pA2(QAFr, QBFr) Assume A and B act as Cournot duopolists in each of the US and French markets. What are the Nash equilibrium values of QAUS, QAFr, QBUSand QBFr? What is the value of the sum (US consumer surplus + Firm As profit)?
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