Suppose That A Firm Has A Monopoly On A Good With The Follow

Suppose That A Firm Has A Monopoly On A Good Withthe Following Deman

Suppose that a firm has a monopoly on a good with the following demand schedule:

• Quantity 0, Price $10
• Quantity 1, Price $9
• Quantity 2, Price $8
• Quantity 3, Price $7
• Quantity 4, Price $6
• Quantity 5, Price $5
• Quantity 6, Price $4
• Quantity 7, Price $3
• Quantity 8, Price $2
• Quantity 9, Price $1
• Quantity 10, Price $0

The monopolist faces a constant marginal cost of $4. The assignment asks to determine the monopolist's profit-maximizing price and quantity and to calculate the deadweight loss compared to a perfectly competitive market.

Paper For Above instruction

The analysis of monopoly pricing and output decisions is fundamental in understanding market inefficiencies and the impacts of market power. Given the demand schedule provided, the monopoly's decision hinges on maximizing profit, which involves comparing marginal revenue (MR) with marginal cost (MC). Since the demand schedule is discrete and linear between points, we can derive the marginal revenue from the demand data and determine the optimal output level accordingly.

First, we analyze the demand schedule to identify the relevant points. The data provides prices and quantities, allowing us to plot or understand the demand curve and subsequently compute the total revenue (TR) and marginal revenue at each quantity. The total revenue at each quantity (Q) is the product of price (P) and quantity (Q): TR = P * Q. Marginal revenue, which reflects the change in total revenue when one additional unit is sold, can be approximated between data points or derived from the linear demand equations.

Calculating Marginal Revenue

For the demand schedule, the slope between points is consistent if we consider the incremental changes. Between each pair of points, the change in price is -1, and the change in quantity is 1. This suggests the demand curve is linear with a negative slope, specifically: P = 10 - Q, for Q from 0 to 10.

Given this, total revenue (TR) at any quantity Q is: TR = P Q = (10 - Q) Q = 10Q - Q^2.

Marginal revenue (MR) is the derivative of TR with respect to Q, which yields: MR = d(TR)/dQ = 10 - 2Q.

Finding the Profit-Maximizing Quantity and Price

The monopolist maximizes profit where MR = MC. The given marginal cost is $4, so setting MR equal to 4 yields:

10 - 2Q = 4

2Q = 6

Q = 3

At Q = 3, the corresponding price on the demand curve is:

P = 10 - Q = 10 - 3 = $7.

Therefore, the monopolist will produce 3 units and charge a price of $7 to maximize profits.

Calculating Deadweight Loss

In a perfectly competitive market, equilibrium occurs where price equals marginal cost. The competitive quantity (Q*) is found by setting P = MC. Using the demand equation:

Price P = 10 - Q

Set P = 4 (the marginal cost):

4 = 10 - Q

Q* = 10 - 4 = 6

At the competitive quantity Q* = 6, the price would be:

P = 10 - 6 = $4, which equals marginal cost, aligning with perfect competition assumptions.

The deadweight loss (DWL) arises from the inefficiency of producing less than the competitive quantity. The DWL is the loss in consumer and producer surplus due to the reduced output, represented visually as the area of a triangle between the monopoly quantity and the competitive quantity, bounded by the demand curve and the marginal cost line.

The formula for DWL in this context is:

DWL = 0.5 (Q_c - Q_m) (P_m - P_c)

Where:

• Q_c = 6 (competitive quantity)
• Q_m = 3 (monopoly quantity)
• P_m = $7 (monopoly price at Q=3)
• P_c = $4 (price at Q=6, marginal cost)

Calculating the DWL:

DWL = 0.5 (6 - 3) (7 - 4) = 0.5 3 3 = 4.5

Thus, the deadweight loss due to monopoly power is $4.50, representing the value of the lost efficiency from producing fewer units than would be produced in a competitive market.

Conclusion

The monopoly maximizes profit by producing 3 units and charging a price of $7. This results in a deadweight loss of approximately $4.50, illustrating the inefficiency created by monopolistic market power. The analysis underscores the importance of considering regulatory policies or market interventions to mitigate such inefficiencies and promote allocative efficiency in the economy.

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