Question

PART TWO. Answer the following problems in the space provided. Please show your work in an organized way with clearly labeled graphs should if you choose to use any. Total 80 Points. 5. Suppose that the market for a certain good has a demand of P 80 -Q. The aggregate private marginal cost for the firms that produce the good faces is MC = 3Q + 20. However, production of the good also creates pollution with a marginal external cost of MEC = 2Q. (40) a. If this is a perfectly competitive market with no regulation, what is the equilibrium price and quantity produced? b. Determine the socially efficient price and quantity for the good. c. What is the deadweight loss in the competitive market with no tax. d. Calculate the socially optimal per-unit tax to levy on the competitive firm to make them produce at the socially efficient level. Page 3 of 5

Answer 1

7o units- ;, Equilibrium is ginen by: Poptinum Bophinum * 1ounits. me. hane conidered the C) In Hue folowing diagrang, Market for the good 'in quertion. Price [This Diagram is nt be šcaled]. SMC (MC + MEC) ме 70 65 50 Demand 10 15 In Mhe above dingram, me hane the deimand wme indicated Demand', marginal cost wrue (private) by MC and the so cial marginal ost wrue as sme. Correspondling prices and quantities to Hhe are also ginen. when & =0, a P=, 80 -8 = 80 yuertical intercept of Denand Cume. MC = 38 +20 SMC = 58+20 =20 → uertical intercopt of Further, at 8 = dptimona = 10, = 20 → uertical intercept of Me wnue. SMC wrne. 34 +20 = (3x10)+ 20 -) MC = 50 units = MC' ме -50

Mere, the deadweight loss is ginen by the triangle ABe. Heme , the area of ABC will be : Area of (ABC) = x (15-10) × (70 -50). - 50 Deadweight loss in the competitine market with no thx is 50 units. d) For the productioon of socially efficient lenel, iie, Soptimum = 10 unite,

Pophimum = 70 unik and MC' Heme, the per- unit tax nuust be : = 50 unite = 50 unite . Poptimum - Me' = 20 unite. = 70-50 = Thus, 20 unik per-unit tax must be levied on the conpehtive firm to make 'them produce the soially efficient leuel of production oulput (and'heme generake of deadutight the deniresd lenel loss, ¡ie," 50 Units.)