Question

consider a monopoly firm whose cost function is given as c(y)=y. if a monopolist faces a demand curve given by D(p)= 100-2p, what is its optimal level of output and price? calculate the deadweight loss associated with monopoly restriction of output. if the demand curve facing the monopolist has a constant elasticity of -2, what will be the monopolist's markup on marginal cost?

Answer 1

The total cost function is

c(y) = y.......(i)

and the demand function is

D(p) = q=100-2p

or, p= 50-q/2 .......(ii)

From (i), Marginal cost is d(c(y))/dy=1

From (ii), Marginal revenue is d(pq)/dq= 50-q

For optimal level of output and price of a monopolist,

                                        Marginal revenue=marginal cost

               or, 50-q=1 or, q=49 and p=50-q/2=50-24.5=25.5

Again under profit maximization rule of a monopolist,

                                  marginal revenue =0 or, 50-q=0 or q=50 and p=50-25=25

Therefore, the deadweight loss = 1/2(p₁-p₂)(q₂ -q₁) = 1/2*(25.5-25)*(50-49)=0.25

From the demand function, the elasticity of demand or e_d = dq/dp= -2

At this point, the monopolist markup = price-marginal cost = 25.5-1=24.5