Question

3. You produce two goods: Beer (B) and Whiskey (W). Further assume your total cost function is TC = 100B + 20Qw. The two demand curves you face are: PB = 100 - 2QB - 2Qw Pw = 200 - 2QB - 4Qw a) Find the profit maximizing output for each good assuming your total costs are set at $200. b) Find the profits for the QB and Qw you found in a). c) What happens to profits if total costs increase by SI?

Answer 1

Past (9) are set at ē suppose total costs where ē = 20 Profit (TT) = PB.QB+ Pw.gow -e = 100-293-20w) 8+ (200-290-299) Pw - ē = 1009 B-29,33-2989w + 2009 - 2989-40w- = 1 op QR+ 200 Qw - 2018 - 4962 - 49B Pw-200 * T = 1000*2009.-203 – 4042-4095-200 8 139 w set 1000 + 200w = 200 Lagrangian for this exa question is L=100 9Bt 200 9w 298496 - 496 9w- 200 + 2 (200 - 1096 - 209) OL = 0 = 100 - 49B-49w= lon - 0 a 200 - 80w-408 = 20 2 - 6 OL o = 200 = 10 ggt 200w - ③

part (b) At a B = 60, 9we lo π = 200x1o - 48102 - 200 T = 1400 Part (c) at the optimum we from envelope can write theorem that * indicates optimum Values) OT*_ * 6 = when $1, total cost ( e) increases by increases by $6 profit at the optimum,

Dividing eqn ☺ by ega 100-486- 496 2/100-490 296) ® 100-49B-49w = 100-40w - 293 29B=0 SB=0 O > π maximizing output of ß from egr ③ 200 - 200 = 10xo + 2o9w. Sw=10 1 π maximizing output of from egn 100- 480- 4x10=100 60 - 100 T7 = 6