Assume a profit maximizing monopolist with marginal cost equ

Assume a profit maximizing monopolist with marginal cost equal to $2 faces demand MWTP(Q) = 12 - 2Q. Assuming it must charge the same price for each unit it sells, what is elasticity of demand at the price it chooses? (Remember, for some elasticities keep the negative sign if negative, for others, we do not.)

Solution

The monopolist will maximize profit by equating Marginal revenue (MR) with Marginal cost (MC).

MWTP: P = 12 - 2Q

Total revenue (TR) = P x Q = 12Q - 2Q²

MR = dTR/dQ = 12 - 4Q

Equating with MR,

12 - 4Q = 2

4Q = 10

Q = 2.5

P = 12 - (2 x 2.5) = 12 - 5 = $7

Since P = 12 - 2Q,

2Q = 12 - P

Q = 6 - 0.5P

Elasticity of demand = (dQ/dP) x (P/Q) = - 0.5 x (7/2.5) = -1.40