where the subscript e denotes Europe and the subscript U denotes the United States.Assume that BMW can restrict U.S.sales to authorized BMW dealers only a.What quantity of BMWs should the firm sell in each market,and what will the price be in each market?What will the total profit be? With separate markets,BMW chooses the appropriate levels of and Q to maximize profits,where profits are: π=TR-TC=(gP+QP)-g+Q20,000+10,000,000,000} Solve for Pa and P using the demand equations,and substitute the expressions into the profitequation: x=g(400m-8+e(0om-9-{g,+)20m+100,0m,0o. 100 20Y Differentiating and setting each derivative to zero to determine the profit-maximizing quantities: 0.0r10,0.cm and 10 Substituting and into their respective demand equations we may determine the price ofcars in each market: 1,000,000=4,000,000-100P。orPe=s30,000and 300,000=1,000.000.20PorP=$35.000. Substituting the values for Q.Q.Pe and P into the profit equation,we have x=《1.000,000(S30,000)+(300,000(35,000y·《1,300,000)20,000)+10.000.000,000.or 元=$4.5 billion. b.If BMW were forced to charge the same price in each market,what would be the qu antity sold in each market,the equi riu price,and the company profit? If BMW charged the same price in both markets,we substitute Q=+into the demand equation and write the new demand curve as 120 -120 Since the marginal revenue curve has twice the slope of the demand curve MR5000000_g 120where the subscript E denotes Europe and the subscript U denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only. a. What quantity of BMWs should the firm sell in each market, and what will the price be in each market? What will the total profit be? With separate markets, BMW chooses the appropriate levels of QE and QU to maximize profits, where profits are:   = TR− TC= QEPE + QUPU ( )− QE + QU ( )20,000 +10,000,000,000. Solve for PE and PU using the demand equations, and substitute the expressions into the profit equation:   = QE 4 0, 000 − QE 100     + QU 5 0, 000 − QU 2 0     − QE + QU ( )2 0, 000 + 1 0,000,000,000. Differentiating and setting each derivative to zero to determine the profit-maximizing quantities:    QE = 4 0,000 − QE 5 0 − 2 0, 000 = 0, or QE = 1,000,000 cars and    QU = 5 0, 000 − QU 1 0 − 2 0, 000 = 0, o r QU = 300, 000 cars. Substituting QE and QU into their respective demand equations, we may determine the price of cars in each market: 1,000,000 = 4,000,000 - 100PE , or PE = $30,000 and 300,000 = 1,000,000 - 20PU, or PU = $35,000. Substituting the values for QE , QU, PE , and PU into the profit equation, we have  = {(1,000,000)($30,000) + (300,000)($35,000)} - {(1,300,000)(20,000)) + 10,000,000,000}, or  = $4.5 billion. b. If BMW were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company’s profit? If BMW charged the same price in both markets, we substitute Q = QE + QU into the demand equation and write the new demand curve as Q = 5,000,000 - 120P, or in inverse for as  P = 5,000,000 120 − Q 120 . Since the marginal revenue curve has twice the slope of the demand curve:  MR = 5,000,000 120 − Q 60