Question

Let a monopolist demand curve be given by $Q = P^e$, where Q is output, P is price, e is the price elasticity of demand (e <-1), and Marginal Cost = Average Cost = $\alpha$. If $P^c$ and PM represent the price under perfect competition and monopoly, respectively, then which of the following is/are NOT correct?
($CS_M$ and $CS_C$ represent the consumer surplus under monopoly and perfect competition, respectively.)

• A. $P^c$ = $\alpha (\frac{e}{1+e})$
• B. $P^M$ = $\alpha(\frac{e}{1+e})$
• C. For e=2, $CS_M$ = $CS_C$.
• D. For e closer to -1, the ratio $CS_M$ / $CS_C$ increases.

Answer 1

The Correct Option is A, C

To solve the given problem, we need to analyze each of the options provided and verify if they are correct based on the given economic scenario. Let's break it down step by step:

1. Perfect Competition Price, \(P^c\):
   Under perfect competition, the price in the market is usually equal to the marginal cost, as firms are price takers. In the given options, it suggests \(P^c = \alpha \left(\frac{e}{1+e}\right)\). However, intuitively, \(P^c\) should equal \(\alpha\), the marginal cost. Therefore, the formula given is incorrect, implying this condition is not correct.
2. Monopoly Price, \(P^M\):
   In monopolistic markets, the price is usually higher than marginal cost, accounting for profit maximization strategies. The common formula for monopolistic pricing derives from setting marginal revenue equal to marginal cost. The option stating \(P^M = \alpha \left(\frac{e}{1+e}\right)\) aligns with monopolistic price derivations and is considered correct.
3. Consumer Surplus under e=2:
   This statement asserts that consumer surplus under monopoly \((CS_M)\) equals the consumer surplus under perfect competition \((CS_C)\) for \(e = 2\). Under normal economic laws, perfect competition provides higher consumer surplus compared to monopoly due to lower prices. This condition is typically not correct.
4. CS Ratio when e is closer to −1:
   As the price elasticity of demand \((e)\) approaches -1, the demand becomes less elastic, and monopolists can charge higher markup prices. Consequently, the consumer surplus under monopoly relative to perfect competition may increase. This statement is quite reasonable and is correct based on behavior in less elastic demand settings.

In conclusion, examining all options, we conclude that the statements "\(P^c = \alpha \left(\frac{e}{1+e}\right)\)" and "For \(e=2\), \(CS_M = CS_C\)" are incorrect.