Question

A monopolist can produce at constant average and marginal costs of \(A C=M C=5 .\) The firm faces a market demand curve given by \(Q=53-P\). a. Calculate the profit-maximizing price-quantity combination for the monopolist. Also calculate the monopolist's profits. b. What output level would be produced by this industry under perfect competition (where price \(=\) marginal cost)? c. Calculate the consumer surplus obtained by consumers in case (b). Show that this exceeds the sum of the monopolist's profits and the consumer surplus received in case (a). What is the value of the "deadweight loss" from monopolization?

Short answer

Answer: The deadweight loss resulting from monopolization in this scenario is 288.

Step-by-step solution

Identify the Profit-maximizing Quantity

To maximize profits, monopolists set MR=MC. First, we need to find the inverse demand curve, P = 53 - Q. Next, we compute the total revenue function, TR = P * Q = (53-Q) * Q. Finally, we find the marginal revenue function, MR, by taking the derivative of the total revenue function with respect to Q. MR = d(TR)/dQ = d[(53-Q)*Q]/dQ Now we can find the profit-maximizing quantity by setting MR = MC = 5.

Solve for the Profit-maximizing Quantity

We have the marginal revenue function: MR = d[(53-Q)*Q]/dQ Calculate the derivative: MR = d(53Q - Q^2)/dQ = 53 - 2Q Set MR = MC: 53 - 2Q = 5 Rearrange and solve for Q: 2Q = 48 Q = 24 The profit-maximizing quantity for the monopolist is Q = 24.

Find the Profit-maximizing Price

Now that we have the profit-maximizing quantity, we can find the profit-maximizing price by plugging the quantity into the inverse demand curve: P = 53 - Q P = 53 - 24 P = 29 The profit-maximizing price is P = 29.

Calculate the Monopolist's Profits

Profits can be calculated by the following formula: Profit = (P - MC) * Q Plug in the values for P, MC, and Q: Profit = (29 - 5) * 24 Profit = 24 * 24 Profit = 576 The monopolist's profits are 576.

Output level under Perfect Competition

Under perfect competition, price is equal to marginal cost, so: P = MC P = 5 Now, plug P into the inverse demand curve and solve for Q: 5 = 53 - Q Q = 53 - 5 Q = 48 Under perfect competition, the output level would be Q = 48.

Calculate Consumer Surplus in case (b)

Consumer surplus can be calculated as: Consumer Surplus = 0.5 * (P_max - P) * Q Where P_max is the price when quantity is zero (demand curve intercept), P is the equilibrium price under perfect competition (already found to be 5), and Q is the quantity produced under perfect competition (already found to be 48). In our case, P_max = 53. Consumer Surplus = 0.5 * (53 - 5) * 48 Consumer Surplus = 0.5 * 48 * 48 Consumer Surplus = 1152

Calculate Deadweight Loss

First, calculate the consumer surplus in case (a) (monopoly): Consumer Surplus_a = 0.5 * (53 - 29) * 24 Consumer Surplus_a = 0.5 * 24 * 24 Consumer Surplus_a = 288 Now, we can calculate the deadweight loss, which is the difference between the sum of monopolist's profits and consumer surplus in case (a) and the consumer surplus in case (b): Deadweight Loss = Consumer Surplus_b - (Consumer Surplus_a + Monopolist's Profits) Deadweight Loss = 1152 - (288 + 576) Deadweight Loss = 1152 - 864 Deadweight Loss = 288 The value of deadweight loss from monopolization is 288.

Key concepts

Profit-Maximizing Quantity and Price

In a monopoly market structure, where a single firm dominates the market, determining the profit-maximizing quantity and price is crucial for the monopolist. Unlike firms in a perfectly competitive market that take the market price as given, a monopolist has the power to set its price.

To find the profit-maximizing output, the monopolist equates marginal revenue (MR) with marginal cost (MC). The demand curve faced by the monopolist is downward sloping, so its MR curve lies below the demand curve due to the diminishing marginal revenue with each additional unit sold. After computing the MR, the firm equates it to MC, which remains constant in our case at $5, to find the quantity that maximizes profit.

Once the optimal quantity is identified, the monopolist uses the demand curve to determine the price consumers are willing to pay for that quantity. The result is a price that is typically higher and an output that is lower than what would be observed in a perfectly competitive market, leading to higher profits for the firm but also potential inefficiencies in the market.

Perfect Competition Equilibrium

Under perfect competition, the market consists of many small firms, each with no control over the price. These firms are price takers, which means they accept the market equilibrium price where supply equals demand. In this scenario, the firm’s marginal cost (MC) curve is its supply curve.

The equilibrium in a perfectly competitive market is where the aggregate demand intersects with the aggregate supply, implying that the equilibrium price equals MC. In our exercise, if this industry were perfectly competitive, the equilibrium output would be determined by setting the price equal to MC. The output would be twice as much as the monopolist's profit-maximizing quantity, demonstrating the monopolist's power to restrict output and elevate prices above efficient levels.

Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay. It represents the economic benefit that consumers receive when they are able to purchase a product for less than the highest price they are willing to pay.

In the context of perfect competition, consumer surplus is maximized because the price equals MC, allowing the market to produce and sell as much as consumers are willing to consume at that price. This leads to an allocation of resources that satisfies consumer preferences to the greatest extent. The exercise demonstrates how consumer surplus in a competitive market exceeds the total surplus in a monopolistic market, emphasizing the loss of welfare due to monopolistic practices.

Deadweight Loss

Deadweight loss refers to the loss of economic efficiency when the equilibrium in a market is not achieved or is not achievable. In a monopoly, the deadweight loss occurs because the monopolist sets a higher price and produces fewer goods than in a perfectly competitive market. This not only reduces consumer surplus but also prevents some transactions that would have occurred if the market were competitive.

The exercise illustrates that monopolization leads to a value of deadweight loss, calculated as the difference between the higher consumer surplus in a competitive market and the sum of the monopolist's profit plus consumer surplus under monopoly. This loss is a cost to society because it represents foregone trades—transactions that could have benefitted both consumers and producers that did not happen due to the monopolist's pricing and output decisions.