Problem 08-06: The Diagram Below Shows The Demand And Margin
Problem 08 06the Diagram Below Shows The Demand Marginal Revenue And
Problem 08-06 The diagram below shows the demand, marginal revenue, and marginal cost of a monopolist. a. Determine the profit-maximizing output and price. Profit-maximizing output: units Profit-maximizing price: $ b. What price and output would prevail if this firm’s product was sold by price-taking firms in a perfectly competitive market? Price: $ Output: units c. Calculate the deadweight loss of this monopoly.
Paper For Above instruction
Introduction
The analysis of monopoly versus perfect competition is fundamental in understanding market efficiency and welfare economics. Monopoly pricing strategies, profit maximization, and deadweight loss are central concepts in economic theory, providing insights into how market power influences resource allocation and consumer welfare. This paper explores a given demand, marginal revenue, and marginal cost diagram of a monopolist to determine the profit-maximizing output and price, compare it with a perfectly competitive market outcome, and compute the associated deadweight loss.
Profit-Maximizing Output and Price for the Monopoly
In monopolistic markets, profit maximization occurs where marginal revenue (MR) equals marginal cost (MC). The diagram provides the demand curve (D), the marginal revenue curve (MR), and the marginal cost curve (MC). To identify the profit-maximizing output, one finds the point where MR intersects MC. From this point, a vertical line is drawn to the quantity axis, revealing the profit-maximizing quantity (Qm).
Once the optimal quantity (Qm) is determined, the monopolist sets the price (Pm) by moving upward along the demand curve to the corresponding price level at Qm. This point on the demand curve indicates the market price consumers are willing to pay for the profit-maximizing quantity. For example, if Qm corresponds to 10 units and the demand curve at this quantity intersects at a price of $15, then:
Profit-maximizing output: 10 units
Profit-maximizing price: $15
It is important to note that these numbers are illustrative; actual values depend on the specifics of the diagram provided.
Competitive Market Price and Output
In a perfectly competitive market, firms are price takers, and the market price equals marginal cost at equilibrium. With the supply curve reflecting MC, the equilibrium price (Pc) is found where the industry supply equals demand, or simply at the point where Price (P) equals MC on the demand curve.
Assuming the same MC curve intersects the demand curve at a point where:
Price: $12
Output: 12 units
In this scenario, the competitive equilibrium involves the firm producing at point where P = MC, resulting in a higher or lower quantity depending on the shape of the curves. Comparing this to the monopoly outcome highlights differences in market efficiency and consumer surplus.
Calculating Deadweight Loss
Deadweight loss (DWL) measures the welfare loss due to market inefficiency, primarily caused by monopoly pricing. It is represented by the triangle between the monopolist’s quantity (Qm) and the competitive equilibrium quantity (Qc), bounded by the demand and supply (or MC) curves.
Using the diagram, DWL can be calculated as:
\[ \text{DWL} = \frac{1}{2} \times (Q_c - Q_m) \times (P_m - P_c) \]
Where:
- \(Q_c\) = competitive equilibrium quantity
- \(Q_m\) = monopolist’s quantity
- \(P_m\) = monopolist price
- \(P_c\) = competitive market price
Suppose, from the diagram, \(Q_c = 15\) units, \(Q_m = 10\) units, \(P_m = 15\) dollars, and \(P_c = 12\) dollars, then:
\[ \text{DWL} = \frac{1}{2} \times (15 - 10) \times (15 - 12) = \frac{1}{2} \times 5 \times 3 = 7.5 \text{ dollars} \]
This value indicates the loss of consumer and producer surplus caused by monopolistic restrictions on output.
Conclusion
The analysis reveals that monopolists tend to produce less and charge higher prices than perfectly competitive firms, leading to allocative inefficiency and deadweight loss. The profit-maximizing output is determined where MR equals MC, resulting in higher prices and reduced output compared to a competitive market. The deadweight loss quantifies the overall welfare loss to society, highlighting the importance of regulatory measures or competitive policies to improve market efficiency.
References
- Krugman, P. R., & Wells, R. (2018). Economics (5th ed.). Worth Publishers.