Question

Kalamazoo Competition-Free Concrete (KCC) is a local monopolist of ready-mix concrete. Its annual demand function is Qd = 22,000 - 400P, where P is the price, in dollars, of a cubic yard of concrete and Q is the number of cubic yards sold per year. Its marginal cost is $20 per cubic yard, and it faces an avoidable fixed cost of $100,000 per year. Instructions: Round your quantity to the nearest whole number and all other answers to 2 decimal places.

a. What is its profit-maximizing sales quantity and price if the monopolist were to produce? Q = units. P = $ .

b. What is the deadweight loss from monopoly pricing? $

Answer 1

Given:

Monopoly marginal cost = $20 per cubic yard

Fixed cost = $100000 per year

Market demand: Qd = 22000-400P

Qd is the number of cubic yards sold per year.

a.) Profit maximization sales quantity and price for the monopolist.

The monopolist produces where the Marginal Cost (MC) is equal to the Marginal Revenue (MR) and charges the buyer's maximum willingness to pay for that quantity.

Finding the marginal revenue function from the demand function:

First of all, converting it into the inverse demand function.

Qd = 22000-400P

Therefore the Total Revenue (TR) is the price times the quantity sold.

Now Marginal Revenue (MR) is the derivative of the total revenue with respect to quantity sold.

Now to find the monopolist profit maximization quantity sold, setting marginal revenue and marginal cost equal.

Therefore the monopolist profit-maximizing quantity sold is 7000 cubic yards of concrete.

Putting this quantity into the demand function as monopolists charge the buyers maximum willingness to pay. Therefore,

Therefore the monopolist charges $37.5 per cubic yard.

Answer:

The monopolist profit-maximizing quantity sold is 7000 cubic yards.

Therefore the monopolist charges $37.5 per cubic yard.

b.) The deadweight loss is the loss to society because of the inefficiency created by the monopolist. As monopolist doesn't produce the competitive quantity and charges a higher price, therefore it creates inefficiency in the market.

So the deadweight loss is:

where P* and Q* are the competitive price and quantity sold. That is if monopolist would have acted as a competitive firm, what quantity and price it would charge.

If monopolist would have acted as perfect competition, it would charge the price equivalent to its marginal cost. And produces the quantity equivalent to that price.

Perfect comeptition price = Marginal cost

Competitive Price (P*) = $20 per cubic yard

Perfect competitive quantity sold:

Therefore the monopolists deadweight loss is:

Monopolist;

Price (P_M) = $37.5 per cubic yards

Quantity sold (Qd_M) = 7000 cubic yards

Competitive;

Price (P*) = $20 per cubic yards

Quantity sold (Qd*) = 14000 cubic yards

Therefore deadweight loss from monopoly pricing is $61250.