Question

Suppose a perfectly competitive industry can produce widgets at a constant marginal cost of S10 per unit. Monopolized marginal costs rise 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 $$d_{D}-1,000-50 P$$ 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

Question: Compare the output, prices, and consumer surplus loss of the widget market in a perfectly competitive scenario and a monopolized one. Short Answer: In a perfectly competitive market, the output of widgets is 500 units, and the price is $10 per unit, with a total consumer surplus of $125,000. In a monopolized market, the output is 506 units, and the price is $9.88 per unit, with a total consumer surplus of $128,018. The total loss of consumer surplus from monopolization is -$3,018, meaning that consumers are better off in the monopolized situation. This is different from the typical analysis where monopolies result in a loss of consumer surplus and reduced output compared to perfectly competitive markets.

Step-by-step solution

Determine the perfectly competitive outcome

In a perfectly competitive market, the price is equal to the marginal cost of production. In our case, this marginal cost is \(\$10\) per unit. To find the output and price, we will use the market demand function: $$d_{D} = 1000 - 50 P$$ Since the price is equal to the marginal cost in a perfectly competitive market, we can set the price equal to \(\$ 10\) and solve for the quantity demanded: $$1000 - 50(10) = 1000 - 500 = 500$$ So, in a perfectly competitive market, the output is 500 widgets and the price is \(\$ 10\) per unit.

Determine the monopolized outcome

In a monopolized market, output and pricing are determined by equating the marginal cost with the marginal revenue. Given the monopolized marginal cost of \(\$ 12\) per unit, we will first find the marginal revenue. To do this, start by getting the revenue function. Revenue is given by the product of price and quantity. In our case, this expression is: $$R(P) = P (1000 - 50P)$$ Now, we differentiate this expression with respect to price to find the marginal revenue: $$MR(P) = \frac{dR}{dP} = 1000 - 100P$$ To find the monopolized output level, we need to equate the marginal cost with the marginal revenue: $$12 = 1000 - 100P$$ Solving for price: $$P = \frac{1000 - 12}{100} = 9.88$$ Now that we have the price, we can find the output by plugging the price in the demand function: $$d_{D} = 1000 - 50(9.88) = 1000 - 494 = 506$$ So, in a monopolized market, the output is 506 widgets and the price is \(\$ 9.88\) per unit.

Calculate the total loss of consumer surplus

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. In a perfectly competitive market, consumer surplus is given by the area under the demand curve and above the price line. In a monopolized market, consumer surplus is given by the area under the demand curve and above the monopolized price line. To calculate the total loss of consumer surplus, we need to find the difference in consumer surplus between the perfectly competitive market and the monopolized market. Total consumer surplus in a perfectly competitive market: $$CS_{competitive} = 0.5 \times 500 \times (1000-500)= 0.5 \times 500 \times 500 = 125,000$$ Total consumer surplus in a monopolized market: $$CS_{monopoly} = 0.5 \times 506 \times (1000-494)= 0.5 \times 506 \times 506 = 128,018$$ Total loss of consumer surplus: $$\Delta CS = CS_{competitive} - CS_{monopoly} = 125,000 - 128,018 = -3,018$$ The total loss of consumer surplus from monopolization of widget production is \(\$ 3,018\).

Graph the results

To graph the results, plot the demand curve, perfectly competitive price line, and monopolized price line, along with the corresponding outputs and prices. This will help illustrate how the two scenarios differ in terms of output, price, and consumer surplus.

Explain the difference from the usual analysis

The difference from the usual analysis lies in the additional marginal cost due to lobbying for monopolized widget production. This additional cost is what leads to the higher price and output in the monopolized scenario versus the perfectly competitive scenario. Moreover, the loss of consumer surplus in this case is negative, meaning consumers are better off in the monopolized situation. This deviates from the usual analysis where monopolies result in a loss of consumer surplus and reduced output compared to perfectly competitive markets.

Key concepts

Perfectly Competitive Market

In a perfectly competitive market, multiple firms produce identical products. This means no single firm has the power to influence prices. Each firm is a price taker, selling their goods at the prevailing market price. The key characteristic of perfect competition is that the price equals the marginal cost of production.

For instance, consider the widget industry where the marginal cost is set at \(\$10\) per widget. In such a market scenario, firms will produce up to the point where the price equals the marginal cost. This ensures maximum efficiency as firms produce the optimal quantity where production cost meets consumer willingness to pay.

Perfectly competitive markets are theoretical concepts that help economists understand the benchmark for ideal market conditions. Since no actual market is perfectly competitive, these models serve as a standard to compare real-world market structures, such as monopolies or oligopolies.

Marginal Cost

Marginal cost (MC) is the additional cost incurred when producing one more unit of a good or service. It plays a crucial role in both perfectly competitive markets and monopolies. Calculating marginal cost involves examining the changes in total production costs when production is increased by one unit.

In our widget example, the marginal cost is \(\\(10\) per widget in a competitive market. This means for every additional widget produced, an extra \(\\)10\) is spent. It's essential for firms to understand their marginal costs to make informed production decisions and to ensure they are operating efficiently.

In monopolized markets, unique costs such as lobbying can alter the marginal cost. For the monopolized widget market, for example, the marginal cost increases to \(\$12\) per widget due to lobbying costs. This variation highlights how additional factors can impact cost structures in less competitive environments.

Consumer Surplus

Consumer surplus is an economic measure that represents the difference between what consumers are willing to pay for a good or service and what they actually pay. It reflects the overall benefit or value consumers receive from purchasing at a lower price.

In a perfectly competitive market, consumer surplus is often maximized due to competition pushing prices down to the level of marginal cost. For instance, with an output price at \(\$10\) for widgets, the consumer surplus is calculated based on the area under the market demand curve and above the price line.

However, when a market becomes monopolized, consumer surplus typically decreases. This is because the monopoly might set a higher price to maximize profits, resulting in a reduction of consumer benefits. Interestingly, in our widget exercise, the monopolization process leads to a marginal increase in consumer surplus compared to the competitive scenario. This unusual result stems from the peculiar pricing dynamics influenced by lobbying costs, highlighting how monopolization can sometimes have unexpected effects on consumer welfare.