Question

Dayna's Doorstops, Inc. (DD) is a monopolist in the doorstop industry. Its cost is \(C=100-5 Q+Q^{2}\), and demand is \(P=55-2 Q\) a. What price should DD set to maximize profit? What output does the firm produce? How much profit and consumer surplus does DD generate? b. What would output be if \(D D\) acted like a perfect competitor and set \(\mathrm{MC}=P ?\) What profit and consumer surplus would then be generated? c. What is the deadweight loss from monopoly power in part (a)? d. Suppose the government, concerned about the high price of doorstops, sets a maximum price at \(\$ 27\) How does this affect price, quantity, consumer surplus, and DD's profit? What is the resulting deadweight loss? e. Now suppose the government sets the maximum price at \(\$ 23 .\) How does this decision affect price, quantity, consumer surplus, DD's profit, and deadweight loss? f. Finally, consider a maximum price of \(\$ 12 .\) What will this do to quantity, consumer surplus, profit, and deadweight loss?

Short answer

The solutions would depend on the algebraic results of the prior steps. It covers various market scenarios, effects of government interference, and the resultant deadweight loss in each case.

Step-by-step solution

Monopoly Pricing

Here the first step is to find the profit maximizing quantity where Marginal Cost (MC) is equal to Marginal Revenue (MR) for a monopolist. MR is derived from the demand function and MC from the cost function. Then substitute the optimal quantity in the price function to find the monopolistic price. Consumer surplus can be calculated as half the product of quantity and difference between highest price consumers are willing to pay and monopolistic price. Profit is the difference between Total Revenue (TR) and Total Cost (TC).

Perfect Competition Pricing

In a perfect competition scenario, the firm sets its price equal to marginal cost. The output is determined by setting MC equal to price from demand function. After finding the optimal quantity, consumer surplus and profit can be calculated similarly as in Step 1.

Calculation of Deadweight Loss in Monopoly

Deadweight Loss refers to the economic inefficiency, in this case caused by monopoly pricing. It is calculated as the difference between the Consumer’s Surplus (CS) and Producer’s Surplus (PS) under perfect competition and monopoly.

Price Ceiling at $27

A price ceiling means the products cannot be sold at a price higher than the ceiling. Now set the price from demand function equal to $27 and solve for quantity. Then calculate the impact on price, quantity, consumer surplus, firm's profit and the resulting deadweight loss.

Price Ceiling at $23

Repeat step 4 but with the price ceiling now set at $23. Again, calculate the impacts.

Price Ceiling at $12

Finally, repeat step 4 but now with a price ceiling set at $12 and calculate the resulting quantity, consumer surplus, firm's profit and the deadweight loss.

Key concepts

Marginal Cost

When analyzing a company's pricing strategies, understanding marginal cost (MC) is critical. Marginal cost refers to the expense of producing one additional unit of a good. In economic terms, it's the slope of the total cost curve. Businesses use MC to determine the optimal level of production: they can increase production as long as the revenue from an additional unit exceeds the marginal cost of producing it.

For monopolists like Dayna's Doorstops, Inc. (DD), equating marginal cost to marginal revenue helps find the profit-maximizing output. This relationship is central to monopoly pricing strategy, as monopolists can adjust their output to influence market prices. In a competitive market, firms have less control and typically set prices equal to their marginal cost to remain competitive.

Marginal Revenue

Marginal revenue (MR) is the additional income from selling one more unit of a good. For monopolies, MR diminishes with each additional unit sold due to the downward sloping demand curve: to sell more, they must lower the price, which affects revenue from units they could have sold at a higher price. By contrast, in perfect competition, the price remains constant as firms are price takers, and thus marginal revenue equals the market price.

In the exercise, DD derives its marginal revenue from its demand curve and looks for the quantity where MR equals MC to maximize profits. Monopoly pricing strategies hinge on this balance, with monopolists manipulating output to manage scarcity and prices.

Deadweight Loss

Deadweight loss measures inefficiency in a market—value that is lost to consumers or producers because the market is not operating at an optimal point. Under perfect competition, markets tend to be efficient with minimal deadweight loss. In a monopoly, however, the monopolist sets the price above marginal cost, leading to reduced output and a higher price than in a competitive market. This results in a deadweight loss, which is the social cost of market inefficiency.

The exercise highlights how DD's monopoly generates deadweight loss by comparing hypothetical consumer and producer surplus in both monopoly and perfect competition scenarios. Knowing the size of deadweight loss can help governments decide on policies like price ceilings to correct inefficiencies.

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 serves as an indicator of the economic benefit to consumers, representing the area under the demand curve and above the market price. In the case of DD, consumer surplus is calculated by evaluating the area between the demand curve and the price DD sets for its doorstops.

A monopoly typically reduces consumer surplus as it restricts output and raises prices above marginal cost. As shown in the exercise, consumer surplus under a monopolistic scenario is less than what would have been under perfect competition—where the price equals MC.

Perfect Competition

In an ideal perfect competition market structure, numerous small firms compete, none having significant market power. Each firm in such a market is a price taker—they cannot influence market price, which is determined solely by supply and demand. Firms compete by setting their price equal to marginal cost.

The comparison analysis in the exercise shows that if DD would have acted like a firm under perfect competition, it would set the price equal to its marginal cost, resulting in a different quantity of output and consumer surplus than in the monopoly scenario. Perfect competition generally maximizes consumer surplus and minimizes deadweight loss, offering a stark contrast to the monopoly outcome.

Price Ceiling

A price ceiling is a government-imposed limit on how high a price can be set for a product. It is typically set below the equilibrium price in an attempt to make goods more affordable for consumers. In the exercise, the government sets price ceilings at \(27, \)23, and $12 to curb DD's monopoly pricing. Such interventions can increase consumer surplus by reducing prices and can potentially decrease deadweight loss.

When enforced, a price ceiling may lead to shortages if the ceiling is below the market-clearing price, as it discourages production. In the analysis of DD's situation, we see how different price ceiling levels have varying impacts on price, quantity, consumer surplus, DD's profit, and deadweight loss.