Question

Consider the following information in the context of negative production externality:

Hint:

For negative production externality, use \(SMC=PMC+MEC\). The socially efficient equilibrium is found where demand equals social marginal cost.

Answer 1

Correct Answer: 27.07

Step 1: Identify the private supply curve.
The given supply curve is
\[ P=15+0.08Q \]
This represents the private marginal cost curve.
So,
\[ PMC=15+0.08Q \]

Step 2: Identify the marginal external cost.
The marginal external cost is given as
\[ MEC=0.06Q \]
In the case of negative production externality, social marginal cost is greater than private marginal cost.
Therefore,
\[ SMC=PMC+MEC \]

Step 3: Find the social marginal cost curve.
Substitute the values:
\[ SMC=(15+0.08Q)+0.06Q \]
\[ SMC=15+0.14Q \]

Step 4: Use the condition for socially efficient equilibrium.
Socially efficient equilibrium occurs where demand equals social marginal cost.
Demand curve is
\[ P=40-0.15Q \]
Thus,
\[ 40-0.15Q=15+0.14Q \]

Step 5: Solve for socially efficient quantity.
\[ 40-15=0.14Q+0.15Q \]
\[ 25=0.29Q \]
\[ Q=\frac{25}{0.29} \]
\[ Q=86.2069 \]

Step 6: Find the socially efficient equilibrium price.
Substitute \(Q=86.2069\) in the demand curve:
\[ P=40-0.15Q \]
\[ P=40-0.15(86.2069) \]
\[ P=40-12.9310 \]
\[ P=27.0690 \]
Rounded off to two decimal places,
\[ P=27.07 \]

Step 7: Final conclusion.
Hence, the socially efficient equilibrium price is
\[ \boxed{27.07} \]