Suppose demand is given by P = 39 - 1.2Q, supply is given by P = 7 + 2Q, and marginal external cost is given by P = 0.8Q.

Given the information about demand, supply, and marginal external cost (MEC), we can analyze the situation in the context of market equilibrium and externalities.

### 1. **Market Equilibrium without Considering Externality:**

To find the market equilibrium, we equate the demand and supply functions. 

- **Demand:** \( P = 39 - 1.2Q \)
- **Supply:** \( P = 7 + 2Q \)

Set the demand equal to the supply:

\[
39 - 1.2Q = 7 + 2Q
\]

Solve for \( Q \):

\[
39 - 7 = 2Q + 1.2Q
\]
\[
32 = 3.2Q
\]
\[
Q = \frac{32}{3.2} = 10
\]

Now, substitute \( Q = 10 \) into either the demand or supply equation to find the equilibrium price \( P \).

Using the demand equation:

\[
P = 39 - 1.2(10) = 39 - 12 = 27
\]

So, the market equilibrium is at \( Q = 10 \) units and \( P = 27 \) dollars.

### 2. **Considering Marginal External Cost (MEC):**

The marginal external cost is given by \( P = 0.8Q \). This cost represents the additional cost to society that is not accounted for in the market equilibrium.

#### Socially Optimal Quantity:

To find the socially optimal quantity, we consider the social marginal cost (SMC), which is the sum of the private marginal cost (supply) and the marginal external cost.

- **Supply (Private Marginal Cost):** \( P = 7 + 2Q \)
- **Marginal External Cost:** \( P = 0.8Q \)

So, the **Social Marginal Cost (SMC)** is:

\[
SMC = (7 + 2Q) + 0.8Q = 7 + 2.8Q
\]

The socially optimal quantity occurs where the demand curve intersects the SMC curve:

\[
39 - 1.2Q = 7 + 2.8Q
\]

Solve for \( Q \):

\[
39 - 7 = 2.8Q + 1.2Q
\]
\[
32 = 4Q
\]
\[
Q = \frac{32}{4} = 8
\]

Now, substitute \( Q = 8 \) into the demand equation to find the socially optimal price \( P \):

\[
P = 39 - 1.2(8) = 39 - 9.6 = 29.4
\]

### Summary:

- **Market Equilibrium (without externality):** \( Q = 10 \), \( P = 27 \)
- **Socially Optimal Outcome (with externality):** \( Q = 8 \), \( P = 29.4 \)

### Do you want more details or have any questions?

### 5 Related Questions:
1. How does the introduction of a tax equivalent to the marginal external cost affect the market equilibrium?
2. What would happen if the government imposes a price floor above the market equilibrium price?
3. Can you explain the concept of deadweight loss in this context?
4. What is the significance of the socially optimal quantity compared to the market equilibrium quantity?
5. How would subsidies influence the market equilibrium in this scenario?

### Tip:
When analyzing externalities, always consider both the private and social costs to identify potential inefficiencies in the market.

Explore the calculation of market equilibrium and socially optimal outcomes considering externalities. Understand how to solve linear equations representing demand, supply, and marginal external costs. This problem is ideal for undergraduate students studying economics.

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