Ps CS PS TS Begin 0 Q Pd 0 Consumer and Producer Surplus Row of Last Question 42 Increment 100 132 126 43.5 300 325 8625 192 100 200 120 45 1200 1530 16500 Linear Demand and Supply Inverse Functions 300 114 46.5 2700 20925 23625 132 Consumer Surplus is defined as the area under the demand curve minus P*Q (total revenue) Pd Intercept alpha 4800 25200 30000 400 108 Pd Slope beta 0.06 48 500 102 19.5 7500 28125 35625 PadQ, - P.Q. = I(a + Bo.)do -P.Q. -(a + 20 -BO. Ps Intercept lambda 42 0.015 600 96 51 10800 29700 40500 Ps Slope delta 44625 Producer Surplus is defined as P*Q (total revenue) minus the area under the supply curve 700 90 52.5 14700 29925 800 84 54 19200 28800 48000 P. Qx - JP.do, = P.Q. -I(2+80.)do, -P.Q. = P.Q. -(re + so 4275582 900 78 55.5 24300 26325 50625 Qe 72 57 30000 22500 52500 1000 Total Surplus = Consumer Surplus + Producer Surplus: Note Pr 2, drops out. Max TS 110 66 58.5 36300 17325 53625 1200 60 60 43200 10800 54000 1300 54 61.5 50700 2925 53625 6300 52500 140 48 63 58800 dTS =(a + BQ.) -(2 +80.) =0- 9, = 1-a , this is equilibrium Q. 1500 42 64.5 67500 -16875 50625 *8 - B 48000 1600 36 66 76800 -28800 d'TS d'TS = B-8 and B 0, B-8 BQ. -80, = In(2) -In (a)-> delta 0.000789 600 700 (B -8)2, = In(2) -In(a) - 9. = In (2) - In (a) 800 Qe 900 (B -8) 1000 Max TS 1100 Pe = a exp BQ: ] or Pe = 2 exp [80;] 1200 1300 1400 Note: The Integral of an Exponential Function is a little peculiar. 1500 1600 Box