5) The demand and supply curves for product X are given by D(P)=300-2P and S(P)=3P-100 respectively. Unfortunately, the production of X results in a negative externality with a constant external marginal cost of $5 per unit produced. Find the deadweight loss.
5) The demand and supply curves for product X are given by D(P)=300-2P and S(P)=3P-100 respectively. Unfortunately, the production of X results in a negative externality with a constant external marginal cost of $5 per unit produced. Find the deadweight loss.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:**Problem 5 Analysis: Demand and Supply Curves with Externalities**
**Description:**
The demand and supply functions for product X are provided as follows:
- Demand Curve: \( D(P) = 300 - 2P \)
- Supply Curve: \( S(P) = 3P - 100 \)
However, the production of product X generates a negative externality, resulting in an additional external marginal cost of $5 per unit produced.
**Objective:**
Determine the deadweight loss caused by the negative externality.
**Solution:**
1. **Equilibrium Without Externality:**
- Equate quantity demanded (\( Q_d \)) to quantity supplied (\( Q_s \)):
\( 300 - 2P = 3P - 100 \)
- Solving for \( P \):
\( 300 + 100 = 3P + 2P \)
\( 400 = 5P \)
\( P = 80 \)
- Substitute \( P = 80 \) back into the demand or supply equation to find equilibrium quantity \( Q \):
\( Q = 300 - 2(80) = 140 \)
2. **Socially Optimal Quantity with Externality:**
- Include the external marginal cost in the supply function:
New Supply Curve: \( S'(P) = 3P - 100 + 5 = 3P - 95 \)
- Determine the new equilibrium by equating \( D(P) \) and \( S'(P) \):
\( 300 - 2P = 3P - 95 \)
- Solving for \( P \):
\( 300 + 95 = 3P + 2P \)
\( 395 = 5P \)
\( P = 79 \)
- Substitute \( P = 79 \) back into the demand or new supply equation to find socially optimal quantity \( Q \):
\( Q = 300 - 2(79) = 142 \)
3. **Deadweight Loss:**
- The deadweight loss (DWL) due to the negative externality can be calculated by finding the difference in quantities and the external marginal cost:
DWL = External Marginal Cost * (Equilibrium Quantity - Socially Optimal Quantity)
DWL = $5 * (140 - 142) =
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