Question

20y25 Consider a product that has a cost function c(y) (А-р) Demand for this product is represented by the demand curve: y (NOTE: this the demand curve, not the inverse demand curve) 1) Write the profit maximization problem for a monopolist 2) Use the envelope theorem to determine whether the monopolist's profits will increase or decrease with b. C 3)What is the elasticity of demand (in terms of p)? What restriction must be on the elasticity of demand for a solution to the monopolist's problem to exist? What does this tell us about the relationship between the optimal price and A? 4) Assume that A=100, b-2. Find the monopolist's optimal price and quantity 5.) Now assume that instead of a monopolist that the market is competitive. What is the equilibrium price and quantity in the market (Hint: you can ignore the number of firms in the market)? 6.) What is the deadweight loss from a monopoly?

Answer 1

slassate Drusc dd A-by asta - LA-by) Ay by to wi.t Note b inclan of nveaoto Th mean Elactiaty o dlemand'1) dP dp A-P (A-P teguist becauolat For monepotists Raenue must be demand elahi denand MR0 > A -P A P A OY A

Page A = \0 and rutro demaud =b p'å (100-&y) TR = 60 NC dcly) dy egulikriw At 2a0) 100y0 )= 60 ptenal guandily opteaal prie in tansptli Haket HC=P 0P A -o At p 00-0 A= 100 and b= 2 eilihripuia sajallitbriom quataty