Question

Model the profit maximizing decision of a monopolistic landlord and the effect of price control regulation. Assume that the market demand for the rental properties supplied by the monopolist is given by the equation below. QD = 40 - 3P The monopolist's marginal cost = Q. Upload your supply and demand diagram showing the following:

The monopolist's profit maximizing price and quantity?

The deadweight loss?

The price cap?

Answer 1

Given, Qd = 40 - 3P and MC = Q

Inverse demand function is given as: P = 40/3 - Q/3

In a monopoly, equilibrium is attained at a point where MR = MC

Thus, MR = dTR/DQ = d( 40/3 - Q^2/3) = 40/3 - 2Q/3

in equilibrium, 40/3 - 2Q/3= Q

which gives Q = 8

Ans. Profit maximizing price = $ 32/3 and equilibrium quantity = 8 unts

The deadweight loss is depicted by the shaded area and calculated as:

1/2. (10-8)(32/3 - 10) = 2/3 units

Ans. Deadweight loss = 2/3 unis

In order to regulate the monopoly, the government should set a price cap of P =MC = 10