Question

Take a monopolist facing the inverse demand function p(y) = 100 – y. Suppose his total cost function is C(y) = 20 + y^2. Compute the monopoly equilibrium and the deadweight losses.

Answer 1

the monopolist inverse demand function is P(y) = 100 - y

so its Total Revenue (TR) = P*y = 100y - y²

Marginal Revenue (MR) = 100 - 2y

cost function given as C(y) = 20 + y²

so marginal cost (MC) is 2y

for equilibrium out put (y) of monopoly MC = MR

or, 2y = 100 - 2y

4y = 100

y = 100/4 = 25

so the equilibrium price of monopoly is P = 100 - y

   = 100 - 25

= 75

and the monopoly deadweight loss will be calculated by the equation P= MC

100 - y = 2y

   y = 100 / 3 = 33.33

and competitive price will be P = 100 - 33.33 = 66.67

so the change in price due to monopoly is 75 - 66.67 = 8.33

and the change in quantity production due to monopoly is 25 - 33.33 = - 8.33

so the deadweight loss is change in price multiplied by change in quantity due to monopoly

= 8.33 * -8.33 = - 69.38

Thus the deadweight loss is equal to 69.38