1. (35 points) A single seller is facing the demand curve:q=b2ap, where b>0;a>0. Themarginalcostisc>0andthereisno fixedcost. Itisassumed that0 < c b? 2ac) If the monopolist chooses

1. (35 points) A single seller is facing the demand curve:q=b2ap, where

b>0;a>0. Themarginalcostisc>0andthereisno fixedcost. Itisassumed

that0< c

a) Derive the monopoly price, quantity, and profits. (Suppose the monopolist chooses quantity)

b) Draw average revenue curve AR(q), the marginal revenue curve MR(q), and the marginal cost curve MC(q) in a diagram. What would happen ifc >b?

2ac) If the monopolist chooses price instead of quantity, will the the monopoly

price, quantity and prots be dierent?

d) Computate the price elasticity of demandEdand explain why a monop-

olist will never produce on the inelastic portion of the demandEd>1?

e) Show graphically that the price elasticity of demandEd<1at the

monopoly price.

e) Calculate Lerner index under the monopoly equilibrium.

f) Calculate the deadweight loss of monopoly. Will the deadweight loss

monopoly increase or decrease when parameterarises?