Question

1. Consider a popular food truck (EMT, perhaps?) The owner faces a marginal private cost (MPC) and a marginal benefit (MB) for each hour it operates. Consider the quantity (Q) of the activity to be hours of serving food (although you can see how that relates to quantity of food sold).

            MPC = 4Q

            MB = 36 – 2Q

1. Based on this information, how many hours will the truck operate? I.e. what is the “private solution.”
2. The food truck creates a negative externality – it releases exhaust while it is running. That air pollution can be represented by the marginal damage (felt by the community): MD = 6. What is the marginal social cost (MSC) equation of operating the food truck in terms of Q?
3. What is the socially optimal number of hours to operate?
4. Graph this scenario. Label all intercepts, curves and axes.
5. If the City of Columbia decides to implement a Pigouvian tax on food trucks based on how many hours they operate, what should it equal in order to achieve the socially optimal number of hours?
6. How much surplus does the truck owner lose by reducing to the socially optimal quantity?
7. How much does the truck owner pay in taxes?
8. How much does the community gain in reduced damage because the owner has reduced the hours of operation?

Answer 1

(a) In private equilibrium, MB = MPC

36 - 2Q = 4Q

6Q = 36

Q = 6

P = 4 x 6 = 24

(b) MSC = MPC + MD = 4Q + 6

MSC = 4Q + 6

(c) In social optimum, MB = MSC.

36 - 2Q = 4Q + 6

6Q = 30

Q = 5

P = (4 x 5) + 6 = 20 + 6 = 26

(d)

From MB function,

When Q = 0, MB = 36 (Vertical intercept) & when MB = 0, Q = 36/2 = 18 (Horizontal intercept).

From MPC function,

When Q = 0, MPC = 0 (Vertical intercept).

From MSC function,

When Q = 0, MSC = 6 (Vertical intercept).

In following graph, private equilibrium is at point A where MB intersects MPC with price P0 (= 24) and quantity Q0 (= 6). Socially optimal equilibrium is at point B where MB intersects MSC with price P1 (= 26) and quantity Q1 (= 5).

NOTE: As per Answering Policy, 1st 4 parts are answered.