Question

Consider a monopolist. If the demand it faces is Q=pɛ, what is the elasticity of demand? If marginal cost is $1 and the price elasticity of demand is -2, what is the profit-maximizing price?

Answer 1

Consider a monopolist. If the demand it faces is Q=pɛ, what is the elasticity of demand?

the elasticity of demand =(dQ/dP)*(P/Q)

dQ/dP=ɛ ............ first derivative of a demand function

Elasticity =(ɛ)*(P/Pɛ)=1

the elasticity of demand is 1 which we call unit elastic demand.

--------------------------------------------

If marginal cost is $1 and the price elasticity of demand is -2, what is the profit-maximizing price?

using the formula of markup

P=MC/(1+(1/e))

P=price

MC=marginal cost

e=elasticity

P=1/(1+(1/(-2))

=2

the price is $2