Question

1. Consider a monopolist having market demand given by p = 50 - Q, and TC = 60Q - 3/2 x Q^2 which gives MC = 60 - 3Q.

(b) Find the elasticity of demand at the optimal output

Answer 1

Answer(b) Price elasticity of demand at the optimal output is -4

Explanation

Given,

P = 50 –Q

Where,

P is price and Q is quantity sold

&

MC = 60 - 3Q

Where,

MC is marginal cost and Q is quantity sold

We know that

Total Revenue (TR) = Price(P)*Quantity(Q)

TR = 50Q – Q²

Marginal Revenue (MR) is the addition to the total revenue (TR) when one more unit of output is sold or

MR = dTR/dQ

MR= 50 -2Q

At equilibrium, MR is equal to MC

50 – 2Q = 60 – 3Q

Q = 10

At equilibrium 10 units will be sold

Now,

Demand equation is given as

P = 50 –Q

Q= 50-P

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

dQ/dP = -1

(P/Q) = P/Q= (50 –Q)/Q

When q =10

P/Q = (50-10)/10 = 4

Price elasticity of demand = -1*4 = -4