Question

Consider a situation where a monopolist faces the following inverse market demand curve p= 100 – 4 and the following cost function TC = 4q+72 a) Derive the marginal revenue and marginal cost functions. b) What are the equilibrium price and quantity if this market behaved as if it were perfectly competitive? c) Calculate the Consumer Surplus, Producer Surplus and Welfare levels under perfect com- petition. d) What are the equilibrium price and quantity when the monopolist produces as a monop- olist?

Answer 1

P=100 - Q TH=PQ = 100Q - Q² MR = 100 - 20 TC = 4q tq² mai 4 + 2q In perfect competition , P=mc. 4+2 = 100-q 39 = 96 q=32 P 100-32= 68 Consumer Producer Welfare suoples = suophus = levels are 0.5 (100-68) 32= 512 0.5(684) 32= 1024 maximum under perfect competition Under monopoly , MR=mc. 10o-20 = 4+2Q 96=40 Q = 24 P= 100-24= 76