Find The Total Revenue Of A Monopolist When Selling 6 Units

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Find the total revenue of the monopolist when it sells 6 units of the commodity without practicing any form of price discrimination. What is the value of the consumers’ surplus? What would be the total revenue of the monopolist if it practiced first-degree price discrimination? What if the monopolist charged P=$5.50 for the first 3 units of the commodity and P=$4 for the next 3 units—what type of price discrimination is this?

Paper For Above instruction

Understanding the dynamics of monopoly pricing strategies is crucial for comprehending how market power influences both producer and consumer welfare. In this paper, we analyze the total revenue generated by a monopolist at a sales volume of six units under different pricing regimes: no price discrimination, first-degree price discrimination, and a specific two-tier pricing structure. The analysis involves deriving total revenue and consumer surplus for each scenario, illustrating how the monopolist’s pricing decisions impact market outcomes.

Introduction

A monopolist operates as the sole supplier of a good or service in a market, wielding significant pricing power. Unlike perfect competition, where prices are determined by market forces, a monopoly can set prices to maximize profits. The choice of pricing strategy profoundly affects total revenue, consumer surplus, and overall market efficiency. This paper evaluates three scenarios involving a monopolist selling six units, focusing on the nature of price discrimination and its implications.

Theoretical Framework and Assumptions

To analyze these scenarios, we assume the monopolist faces a downward-sloping demand curve, which reflects consumers’ willingness to pay at various quantities. The demand function, consumer surplus, and the relevant price points are key variables. Although the exact demand function is not specified, typical assumptions based on common economic models will be used to approximate the calculations.

Total Revenue Without Price Discrimination

When a monopolist sells six units without discriminating prices, it must choose a single price per unit that maximizes total revenue. Total revenue (TR) is calculated as the product of price (P) and quantity (Q): TR = P × Q. If the demand curve at six units corresponds to a price P, then TR is straightforward to compute. Consumer surplus, on the other hand, measures the value consumers derive from the product beyond what they pay, typically represented visually as the area between the demand curve and the price level up to the quantity sold.

Case 1: Total Revenue at Six Units without Price Discrimination

Suppose the demand curve indicates that at a quantity of 6 units, consumers are willing to pay a maximum of $6 per unit. The monopolist, aiming to maximize revenue, might choose this combined price. Therefore, TR equals 6 units × $6 = $36. Consumer surplus in this case would be the area under the demand curve above the price level over the quantity of 6 units. Assuming the demand curve is linear, the consumer surplus can be computed as the area of a triangle with a height of the difference between the maximum willingness to pay and the market price, over the 6 units.

Case 2: Total Revenue Under First-Degree Price Discrimination

First-degree price discrimination involves charging each consumer their maximum willingness to pay, capturing all consumer surplus as profit. The total revenue in this case equals the sum of individual willingness to pay for each unit sold. If the demand function is known, integrating it from zero to six units yields the total revenue. In practical terms, the monopolist effectively captures the entire area under the demand curve up to the sixth unit. This results in the highest possible total revenue for the monopolist, often equal to the total consumer surplus plus the total producer surplus, effectively converting consumer surplus into producer surplus.

Case 3: Two-Tier Price Discrimination (Charging Different Prices for Different Units)

In the third scenario, the monopolist charges P=$5.50 for the first 3 units and P=$4 for the next 3 units. This represents a form of third-degree price discrimination, where the monopolist segments the market into groups or applies different prices based on quantities sold. This method is often used when the monopolist can segment consumers by their willingness to pay or by the quantity purchased. The total revenue here is calculated as:

• Revenue from first 3 units: 3 units × $5.50 = $16.50
• Revenue from next 3 units: 3 units × $4 = $12

Total revenue thus sums to $28.50. This strategy allows the monopolist to increase revenue compared to uniform pricing but typically yields less than first-degree price discrimination because it does not capture each consumer's maximum willingness to pay, only specific segments.

Conclusion

The analysis of the monopolist's total revenue under different pricing strategies demonstrates the significant impact of price discrimination on market outcomes. Without discrimination, revenue is constrained by the single price point; with first-degree discrimination, revenue maximizes at the expense of consumer surplus. The selected two-tier pricing scheme illustrates a practical approach to segment markets and increase profits, though it does not fully extract consumer surplus. Understanding these dynamics is vital for policymakers concerned with market efficiency and consumers' welfare, especially in the context of monopolistic markets and their regulation.

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