Question

Given: Q = 50 - P and MC = 4+2Q. a) Determine the equilibrium price and quantity if this industry were purely competitive. b) Determine the equilibrium price and quantity if this industry were a profit tot maximizing monopolist.com broc) Determine the dollar value of the deadweight loss if this were a monopolized industry by completing the following table: Consumer Surplus Producer Surplus ! Total or Pure Competition g Y upeve n TOO THOD a 10 U Monopoly Monopoly til Difference adds to time agowo Deadweight Loss equals =

Answer 1

Q 50 P MC 4 20 a) For perfect competitive equilibrium P MC P 50 Q 50 Q 4 2Q 46 30 46 Q 3 46 P 50 104 P = 3 b) For Profit Maximising Firm (Monopolist) = MR dTR MC MR TR P Q TR 50Q Q dTR MR = = 50 20 dQ 50 2Q 4+2Q 46 40 23 Q2 23 P 50 2 77 P = 2

Consumer Surplus (CS) c) Let Po be the reservation price or price such that Q 0 Let P* be the equilibrium price and Q is the equilibrium Quantity 1 (Po-P)Q CS = 2 Po = 50 104 1 CS for Perfect Competition (CSpc) 46 (50-3 46 46 1058 = 117.56 1 CSPC 1 2116 9 77 1 23 CS for Monopolist (CSM)7" 50 2 23 23 2 529 1 CSM 66.13 8 Producer Surplus (PS) Let MC, be the MC for Q 0 1 - (P*- MCoe PS 2 MCO = 4 - 104 4) 2 3 1 46 PS for Perfect Competition (PSpc) 3

92 46 46 46 2116 PSpc 2 235.11 3 3 3 3 23 77 PS for Monopolist (PSM) 2 1587 1 69 23 PSM 2 198.38 8 Consumer Surplus Producer Surplus Total 235.11 352.67 198.38 264.51 Pure Competition 117.56 Monopolist 66.13 Difference 51.43 36.73 Deadweight Loss 88.16