ANSWERS TO SELECTED EXERCISES • 723 gas were set at $3, the quantity supplied would be 21.06 Tcf and the quantity demanded would be 36.02 Tcf To calculate the deadweight loss, we measure the area of triangles B and C (see Figure 9.4) To find area B we must first determine the price on the demand curve when quantity equals 21.1 From the demand equation, 21.1 = 41.42 - 1.8PG Therefore, PG = $11.29 Area B equals (0.5)(25.3 - 21.1)(11.29 8.94) = $4.9 billion, and area C is (0.5)(25.3 - 21.1) (8.94 - 3) = $12.5 billion The deadweight loss is 4.9 + 12.5 = $17.4 billion b To find the price of oil that would yield a free market price of natural gas of $3, we set the quantity demanded equal to the quantity supplied, use PG = $3, and solve for PO Therefore, QS = 15.90 + 0.72(3) + 0.05PO = 0.02 - 1.8(3) + 0.69PO = QD, or 18.06 + 0.05PG = -5.38 + 0.69PO, so that 0.64PO = 23.44 and PO = $36.63 This yields a free market price of natural gas of $3 11 a To find the new domestic price, we set the quantity demanded minus the quantity supplied equal to 10 Therefore, QD - QS = (29.73 - 0.19P) - ( -7.95 + 0.66P) = 10 0.85P = 27.68, meaning that P = 32.56 cents If imports had been expanded to 10 billion pounds, the U.S price would have fallen by 3.44 cents b Substituting the new price of 32.56 cents into the supply and demand equations, we find that the U.S production of sugar would decrease to 13.54 billion pounds, while demand would increase to 23.54 billion pounds, with the additional 10 billion pounds supplied by imports In order to find the change in the consumer and producer surpluses, it might help to redraw the graph as Figure 9(a) The gain to producers is given by the area of trapezoid A: A = 12 * (32.56 - 24)(8.2)2 + (13.54 - 8.2) (32.56 - 24) = $930 million, which is $500 million less than the producer gain when imports were limited to 6.9 billion pounds To find the gain to consumers, we must find the change in the lost consumer surplus, given by the sum of trapezoid A, triangles B and C, and rectangle D We’ve already found the area of trapezoid A Triangle B = 12 (32.56 - 24)(13.54 - 8.2) = $228.52 million, triangle C = 12 (32.56 - 24)(25.4 - 23.54) = $79.47 m i l l i o n , a n d r e c t a n g l e D = (32.56 - 24) (23.54 - 13.54) = $856.34 million The sum of A, B, C, and D is $2.09 billion When imports were limited to 6.9 billion pounds, the loss in consumer surplus is $2.88 billion, meaning that consumers gain about $790 million when imports are raised to 10 billion pounds 50 45 40 Price (cents per pound) 35 PUS ϭ 32.56 30 A D B 25 C Pw ϭ 24 20 15 10 0 10 Qs ϭ 8.2 15 QЈs ϭ 13.54 20 25 30 QЈd ϭ 23.5 Qd ϭ 25.4 Quantity (billions of pounds) F IGURE 9(a) 35