Given a market where the monopolist produces at quantity Q_m and charges price P_m, while the competitive equilibrium would occur at quantity Q_c and price P_c, which of the following expressions correctly calculates the deadweight loss associated with monopoly?

• A. Deadweight loss = 0.5 \times (P_m - P_c) \times (Q_c - Q_m)
• B. Deadweight loss = (Q_c - Q_m) \times P_c
• C. Deadweight loss = (P_m - P_c) \times Q_c
• D. Deadweight loss = (P_c - P_m) \times Q_m

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of deadweight loss in the context of monopoly. Deadweight loss represents the loss of total surplus (consumer plus producer surplus) due to the monopolist producing less quantity than the socially optimal competitive quantity.
2. Step 2: Identify the relevant quantities and prices: \(Q_m\) is the monopolist's quantity, \(P_m\) is the monopolist's price, \(Q_c\) is the competitive equilibrium quantity, and \(P_c\) is the competitive equilibrium price.
3. Step 3: Recognize that the deadweight loss is the area of the triangle formed between the demand curve and the marginal cost curve between quantities \(Q_m\) and \(Q_c\). This area represents the lost trades that would have occurred under perfect competition but do not occur under monopoly.
4. Step 4: Use the formula for the area of a triangle to calculate deadweight loss: \(\text{Deadweight loss} = \frac{1}{2} \times \text{base} \times \text{height}\). Here, the base is the difference in quantities \((Q_c - Q_m)\) and the height is the difference in prices \((P_m - P_c)\).
5. Step 5: Write the deadweight loss expression as \(\text{Deadweight loss} = 0.5 \times (P_m - P_c) \times (Q_c - Q_m)\), which correctly captures the loss in total surplus due to monopoly pricing and reduced output.