Question

1. (20p) Suppose that, in a perfectly competitive industry, the technology for making the product (by any single firm) has the total cost function c(q) = 200 + 4q+ Barriers to entry and exit the market are low and an unlimited number of firms could enter this industry, all with the same total cost function. (a) Compute the long-run equilibrium price in this industry, as well as the amount of output each firm would produce at this price. Explain the significance of the conditions you use to derive the long-run equilibrium outcome. (b) If the demand for the product is given by D(P) = 100(30 - P), what is the total quantity demanded at the long-run equilibrium price? How many firms will be active in this market in the long-run? (c) Assume now that the government imposes a $4 unit tax on producers. What will be the short-run effect of the tax? How much will each firm produce after tax? How much profit would each firm make? What would you expect to happen with the price in the long-run and why?

Answer 1

Number of frems = q 600 - 130 firms Q Tax $4 C(q) = 200+ 4 q + q2 2 New C(q) 200 +49 +1 New C(q) 204 + 4q t qe Cla) 2 New AVC 2 New C(e) q = 1/204 +49 190 g New Ave 204 + 4 + q 204 408 +2 +4 22 Short Run Equilibrium : P = MC (Р New AUL = = (Ave News New New MC MC After Tax Nene New MC a cla) 2 dq of [ 204 + 49 ta ฝน 2 MC utq Since new С. MC Equilibrium price and in quanlity short run. remains the same Neus R = MC P = 4+9 P = 4420 P - $24 P- $24, q= 20 units Short Run Equilibrium Profits TR -TC where TR = P x 2 24 x 20 те $ 480 And TC C(q) = 204 it 42 + 2 2 204 +4(20) + (20) +203 204t got you No. 2 204 + sotzoo TL = $ 484 :. Progio = TR-TC $ (480 484) Profit $ -4 loss of $4 to each firm In the long run, AVE 408 + 9² 2q 4tq 408 tq 2 q=0 122 408tq? - 2q² =0 hos : 2 q 20. 199 P = 2 , Nueva MC 4+2 4+20.199 pNews $24.199 on the long pum cost the price has inchand due to the increax in the 멍 the firms ( because of tax) Moreover a few firms will exit the due to losses honce market supply will reduce this raising the long run equilibrium price. industry and