**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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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.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

**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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