D南=W，S D=W.S O* Quantity Figure 12.12.a.ii b.Calculate OPEC's optimal (profit-maximizing)price.(Hint:Because OPEC's cost is zero,just write the expression for OPEC revenue and find the price that maximizes it.) Since costs are zero,OPEC will choose a price that maximizes total revenue Max t=PQ=P(W-S) x=r160p-3p)=160p-3p To determine the profit-maximizing price,we find the change in the profi function with respect to a change in price and set it equal to zero: Solving for P. 5p80 rP=$16 pi c.Suppose the oil-consuming countries were to unite and form a"buyers'cartel to gain monopsony power.What can we say,and what can't we say, about the impact this would have on price? If the oil-consuming countries unite to form a buvers'carteL then we have a monopoly (OPEC)facing a monopsony (the buyers'carteD).As a result no well-defined demand or supply eurve.Wee will fall below the nopoly pric when n the becaus monopsony power offsets monopoly power. However.economic theory Price MR Quantity D = W - S S QW DW QNon-OPEC P* QOPEC S * P** MR* D* = W* - S* Q*Non-OPEC Q*D Figure 12.12.a.ii b. Calculate OPEC’s optimal (profit-maximizing) price. (Hint: Because OPEC’s cost is zero, just write the expression for OPEC revenue and find the price that maximizes it.) Since costs are zero, OPEC will choose a price that maximizes total revenue: Max  = PQ = P(W - S)  = P 160P −1/ 2 − 3 1 3 P  1/ 2    =160P 1/ 2 − 3 1 3 P 3/ 2 . To determine the profit-maximizing price, we find the change in the profit function with respect to a change in price and set it equal to zero:  P = 80P −1/ 2 − 3 1 3     3 2     P 1/ 2 = 80P −1/ 2 − 5P 1/ 2 = 0. Solving for P, 5P 1 2 = 80 P 1 2 , or P = $16. c. Suppose the oil-consuming countries were to unite and form a “buyers’ cartel” to gain monopsony power. What can we say, and what can’t we say, about the impact this would have on price? If the oil-consuming countries unite to form a buyers’ cartel, then we have a monopoly (OPEC) facing a monopsony (the buyers’ cartel). As a result, there is no well-defined demand or supply curve. We expect that the price will fall below the monopoly price when the buyers also collude, because monopsony power offsets monopoly power. However, economic theory