Question

The Shiller Company is the only producer of DVD players on Music Island. The demand for DVD players is given by P=840−5Q, where Q is the number of products sold to the consumer, and P is the price. The Shiller Company has a cost function C(Q)=Q ² +120 so that the associated marginal cost function and average cost function are MC(Q)=2Q and AC(Q)=Q+ 120/Q, respectively.

(a) In equilibrium, how many units of output will the Shiller Company produce? What price will it charge? How much profit will it make?
(b) In a diagram, draw the demand curve, the marginal revenue curve, and the marginal cost curve. Then determine the consumer surplus, producer surplus, and the deadweight loss in equilibrium. Can you explain why there is a deadweight loss in equilibrium?
(c) Is the producer surplus larger than, equal to, or smaller than profit? Explain.

Answer 1

The Shiller Company will produce 60 units, charge $540 per unit, and make a profit of $28,680. A diagram would illustrate the demand curve, MR curve, and MC curve, showing consumer surplus, producer surplus, and the presence of deadweight loss due to monopoly pricing. Producer surplus is different from profit as it does not account for fixed costs.

Step-by-step explanation:

Determining Equilibrium Output, Price, and Profit

The Shiller Company, as a monopolist on Music Island, determines output where marginal revenue (MR) equals marginal cost (MC). To find this equilibrium output, we set the MR equal to MC. However, since this is a monopoly, MR is not the same as the price. MR can be derived from the demand function P = 840 - 5Q; thus, MR = 840 - 10Q. Setting MR equal to MC, we get 840 - 10Q = 2Q, resulting in Q = 60. To find the price, we substitute Q back into the demand equation, resulting in P = 840 - 5(60) = 840 - 300 = $540. The profit can be calculated as the total revenue (P x Q) minus total costs. The total revenue is 60*$540 = $32,400 and total costs from C(Q) = 60^2 + 120 = $3720, leading to a profit of $32,400 - $3720 = $28,680.

Diagram and Surplus Analysis

To analyze consumer surplus, producer surplus, and deadweight loss, we need to draw the demand curve, marginal revenue curve, and marginal cost curve. Consumer surplus is the area above the market price and below the demand curve. Producer surplus is the area above the MC curve and below the market price. Deadweight loss is present in a monopoly because the price is above MC, which results in underproduction from a societal perspective compared to a competitive market where P = MC. This inefficiency is represented by the area between the demand and MC curves from the monopolistic quantity to the competitive quantity.

Comparing Producer Surplus and Profit

Producer surplus may be different from profit as it is the area above the supply curve (MC in a monopoly) and below the price. It reflects the difference between what sellers are paid and the cost to produce the good. Profit, on the other hand, is total revenue minus total costs, including fixed and variable costs. Therefore, producer surplus is not always equal to profit as it does not account for fixed costs.