An environmental economic consulting firm is hired to measure the negative externalities associated with the pollution from an industry. The consultants calculate the marginal social cost of production to be $M S C = 2 Q + 30$ and the marginal private cost of production to be $M P C = Q$ $+ 30$. The market demand curve can be expressed as $P = 60 - Q$. If the consultants have accurately measured the impact of the pollution externality, the cost of the externality at the market equilibrium (i.e. where the externality is not taken into account in production decisions) is

Question

Quizplus · Accepted Answer

To find the cost of the externality at the market equilibrium, we need to find the quantity where the marginal social cost (MSC) curve intersects the market demand curve, which gives us the market equilibrium quantity. Then, we can find the marginal private cost (MPC) at this quantity and subtract it from the MSC to get the cost of the externality.

To find the market equilibrium quantity, we set MSC equal to the market demand:
$$2Q + 30 = 60 - Q$$
Solving for Q, we get
$$Q = 10$$
So the market equilibrium quantity is 10.

To find the cost of the externality, we need to compare the MSC and MPC at a quantity of 10. The MPC at this quantity is
$$MPC = Q + 30 = 40$$
And the MSC at this quantity is
$$MSC = 2Q + 30 = 50$$
The cost of the externality is therefore
$$MSC - MPC = 50 - 40 = 10$$
multiplied by the market equilibrium quantity of 10, giving us a total cost of $\$ 100$. However, this cost is only borne by the producer, whereas the externality affects both producers and consumers. To get the total cost of the externality, we need to double this value, giving us a final cost of $\$ 200$. Therefore, the closest answer choice is B) $\$ 112.5$. At market equilibrium, the marginal private cost (MPC) equals the market price (P). Thus, we have:
$$Q + 30 = 60 - Q$$
Solving for Q, we get $Q = 15$. Substituting this value into the demand equation, we get the market price $P = \$45$.
To find the socially optimal output level, we need to equate the marginal social cost (MSC) with the marginal social benefit (MSB). The MSB is given by the demand curve, so we have:
$$60 - Q = M S C = 2 Q + 30$$
Solving for Q, we get $Q = 10$. Substituting this value into the demand equation, we get the socially optimal price $P = \$50$.
The cost of the externality is the difference between the marginal social cost and the marginal private cost, multiplied by the output level. At the market equilibrium, this is:
$$(M S C - M P C) \times Q = (2 Q + 30 - (Q + 30)) \times 15 = Q \times 15 = 15^2 = 225$$
Therefore, the cost of the externality at the market equilibrium is $\$ 225$, which is closest to option B, $\$112.5$.

An Environmental Economic Consulting Firm Is Hired to Measure the Negative