QQuestionEconomics
QuestionEconomics
The deadweight loss from monopoly arises because the monopoly firm makes higher profits than a competitive firm would. some potential consumers who forgo buying the good value it more than its marginal cost consumers who buy the good have to pay more than marginal cost, reducing their consumer surplus the monopoly firm chooses a quantity that fails to equate price and average revenue.
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Step 1:: Begin by defining the deadweight loss (DWL) in a monopoly market.
\text{DWL} = (\text{Competitive Output} - \text{Monopoly Output}) \times (\text{Price} - \text{Marginal Cost at Monopoly Output})
DWL is the difference between the competitive output level and the monopoly output level, multiplied by the difference in price and marginal cost at the monopoly output level.
Step 2:: The competitive output level is where price equals marginal cost (P = MC).
\text{Competitive Output:} \quad Q_c = \text{arg} \min_Q (P - MC)
In a competitive market, firms produce where P = MC, so we can express competitive output as:
Step 3:: In a monopoly market, the monopolist chooses the quantity where marginal cost equals marginal revenue (MC = MR).
\text{Monopoly Output:} \quad Q_m = \text{arg} \min_Q (MC - MR)
We can express monopoly output as:
Step 4:: To calculate the DWL, we first need to find the price and marginal cost at the monopoly output level.
MC(Q_m) = MR(Q_m) = P(Q_m) - \frac{d}{dQ} \left[ \int_{Q_m}^{+\infty} MR(Q) dQ \right]
Since the monopolist chooses the quantity where MC = MR, we can rewrite the equation as:
Step 5:: Now, we can calculate DWL using the equations from Steps 1, 4, and the given information about the monopoly firm making higher profits than a competitive firm would.
\text{DWL} = (Q_c - Q_m) \times (P(Q_m) - MC(Q_m))
Final Answer
The deadweight loss from monopoly is given by the equation: \text{DWL} = (Q_c - Q_m) \times (P(Q_m) - MC(Q_m)) Where: - $Q_c$ is the competitive output level - $Q_m$ is the monopoly output level - $P(Q_m)$ is the price at the monopoly output level - $MC(Q_m)$ is the marginal cost at the monopoly output level Note that DWL is positive, indicating that there is a loss of economic efficiency in a monopoly market compared to a competitive market.
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