Question

Question text Suppose there is a market characterized by the following demand and supply curves: MB = P = 22 - 1/3Q MC = P = Q/2 + 2 Suppose there is a negative externality of $5 per unit in this market that is not corrected for by the market. What is the efficient amount of production/consumption? (Hint: Efficient level of production/consumption is where SMC=SMB)

Answer 1

Given Information :-

Marginal Benefit = P = 22 - 1/3Q

Marginal Cost = P = Q/2 + 2

Negative Externality = $5 per unit

As we know under Negative Externality of production :-

Social Marginal Cost (SMC) = Marginal Cost + Total Negative Externality created

& Social Marginal Benefit (SMB) = Marginal Benefit

​​​​​​As Negative Externality = $5 per unit

So, Total Negative Externality = 5Q

Hence,

We Know Market Equilibrium is at :-

On solving the above quadratic Equation we get :-

So Efficient amount is 3.619 or 0.0167 units

Answer 2

Given Information :-

Marginal Benefit = P = 22 - 1/3Q

Marginal Cost = P = Q/2 + 2

Negative Externality = $5 per unit

As we know under Negative Externality of production :-

Social Marginal Cost (SMC) = Marginal Cost + Total Negative Externality created

& Social Marginal Benefit (SMB) = Marginal Benefit

​​​​​​As Negative Externality = $5 per unit

So, Total Negative Externality = 5Q

Hence,

We Know Market Equilibrium is at :-

On solving the above quadratic Equation we get :-

So Efficient amount is 3.619 or 0.0167 units