Question

Suppose a perfectly competitive industry can produce widgets at a constant marginal cost of \(\$ 10\) per unit. Monopolized marginal costs increase to \(\$ 12\) per unit because \(\$ 2\) per unit must be paid to lobbyists to retain the widget producers' favored position. Suppose the market demand for widgets is given by \\[Q_{D}=1,000-50 P.\\] a. Calculate the perfectly competitive and monopoly outputs and prices. b. Calculate the total loss of consumer surplus from monopolization of widget production. c. Graph your results and explain how they differ from the usual analysis.

Short answer

Answer: The total loss of consumer surplus from monopolization of widget production is $11,500.

Step-by-step solution

Calculate the perfectly competitive output and price

In a perfectly competitive market, the price is equal to the marginal cost. The marginal cost in this case is given as \(\$10\) per unit. The demand function is given by: \\[Q_{D} = 1000 - 50P,\\] To calculate the perfectly competitive output and price, set the marginal cost equal to the price in the demand function: \\[10 = P.\\] Now, substitute the price back into the demand function to find the quantity: \\[Q_{D} = 1000 - 50(10) = 1000 - 500 = 500.\\] Therefore, the perfectly competitive output is 500 units and the price is \(\$10\).

Calculate the monopoly output and price

In a monopoly, the monopolized marginal cost is given as \(\$12\) per unit. To find the output and price in a monopolized market, we need to set the monopolized marginal cost equal to the marginal revenue derived from the demand function. First, we need the total revenue: \\[R = PQ = (1,000 - 50P)P.\\] Now, calculate the marginal revenue by differentiating the total revenue with respect to quantity: \\[\frac{dR}{dQ} = \frac{d}{dQ}(20,000 - 100P) = -100 + 2P.\\] Now, set the monopolized marginal cost (\(12\)) equal to the marginal revenue and solve for the price: \\[12 = -100 + 2P.\\] This gives: \\[P = \frac{112}{2} = \$56.\\] Now, substitute the price back into the demand function to find the quantity: \\[Q_{D} = 1000 - 50(56) = 1000 - 2800 = -1800.\\] Therefore, the monopoly output is 1800 less units compared to the perfectly competitive scenario and the price is \(\$56\).

Calculate the total loss of consumer surplus

Consumer surplus is the area under the demand curve and above the market price. In a perfectly competitive market, the consumer surplus is the area of the triangle formed by the demand curve, the price, and the quantity. In the monopolized scenario, the consumer surplus is the area under the demand curve and above the monopolized price up to the monopolized output. Loss of consumer surplus can be calculated as the difference in the areas under the curve: Loss of consumer surplus = (Area under the curve in a perfectly competitive market) - (Area under the curve in a monopolized market) In this case: Loss of consumer surplus = (0.5 × base × height) - (0.5 × base × height) Base and height refer to the respective dimensions of the triangular areas of consumer surplus under the demand curve. Loss of consumer surplus = (0.5 × 500 × 10) - (0.5 × 500 × 46) Loss of consumer surplus = 11,500 Therefore, the total loss of consumer surplus from monopolization of widget production is $11,500.

Graph your results and explain the differences

A graph comparing the perfectly competitive market and monopolized market can be drawn, with the x-axis representing the quantity and the y-axis representing the price. The demand curve will be a downward-sloping linear function intersecting the y-axis at P = 20 and the x-axis at Q = 400. The perfectly competitive equilibrium (price = \(10, quantity = 500) will be a point on the demand curve, while the monopolized equilibrium (price = \)56, quantity = -1800) will be below and to the left of the perfectly competitive equilibrium on the demand curve. The key differences between the perfectly competitive and monopolized scenarios are the prices and quantities produced. In the perfectly competitive market, the quantity produced is higher, and the price is lower, resulting in a larger consumer surplus. In the monopolized market, the quantity produced is lower, and the price is higher, resulting in a smaller consumer surplus and a total loss in consumer surplus due to monopolization.

Key concepts

Perfect Competition

Perfect competition is a theoretical market structure where numerous small firms, all producing identical products, compete against each other. In this idealized scenario, no single firm can influence the market price because the supply of the product is so vast. This results in each firm being a price taker, meaning they sell their products at the same price determined by the industry's overall supply and demand.
In a perfectly competitive market, the price equals the marginal cost of production. This efficiency leads to the maximum output being produced at the lowest price. For example, in the given exercise, the marginal cost is \(\$10\) per unit, aligning perfectly with the competitive price.
The perfectly competitive market results in the most consumer surplus and economic welfare, as goods are supplied at the minimum cost to consumers.

Consumer Surplus

Consumer surplus measures the benefit to consumers because they can purchase a product for less than the maximum price they are willing to pay. It is depicted as the area between the demand curve and the price consumers actually pay, up to the quantity purchased.
In competitive markets, maximum consumer surplus is achieved because products are priced at their marginal cost. In the exercise, this is shown as consumers pay \(\$10\) per unit, while they might have been willing to pay more at different levels.
When monopolistic behavior enters the market, the price rises due to decreased competition, and consumer surplus decreases. This loss is calculated in the exercise as the difference in areas under the demand curve, highlighting the monetary losses consumers face in a monopolized situation.

Marginal Cost

Marginal cost is the cost of producing one additional unit of a good. Understanding marginal cost is crucial, as firms aim to produce up to the point where marginal cost equals marginal revenue for profit maximization.
In perfect competition, the price is equal to the marginal cost, ensuring efficient allocation of resources. The original exercise shows the marginal cost of widget production as \(\\(10\) per unit. This aligns directly with the equilibrium price in a perfectly competitive market.
Under monopolization, marginal costs can rise due to additional expenses like lobbying costs. In the example, marginal costs become \(\\)12\), which disrupts the balance between cost and consumer pricing, moving away from efficiency.

Market Demand

Market demand refers to the total quantity of a good or service that consumers are willing and able to purchase at different price levels during a given period. The market demand schedule reflects the relationship between price and quantity demanded, and is typically illustrated by a downward-sloping curve.
This concept is crucial in determining market equilibrium, where supply meets demand. In the exercise, the market demand equation \(Q_D = 1000 - 50P\) is given, and it helps calculate equilibrium in both perfectly competitive and monopolistic scenarios.
Changes in price affect the quantity demanded, which is why monopolies can significantly impact market demand by charging higher prices and reducing the quantity available to consumers.