Question

1. A country that does not tax gasoline is considering the introduction of a tax ($3.00 per gallon). The economic advisors to the country estimate the supply and demand curves for gasoline as:
Demand: P = 18-2.5Qd
Supply: P = 0.5Qs
where Qd is the quantity demanded, Qs is the quantity supplied, and P is the price per gallon. Assume the country does not trade gasoline with other countries. Suppose the country’s health advisor found that gasoline consumption generates negative externalities. The estimated the marginal external cost to be: MEC = 1.5Q

a) Compute the efficient level of gasoline consumption given the information.

b) Compute the DWL when no tax is imposed.

c) Compute the tax rate necessary to achieve the efficient gasoline consumption. Is the above tax ($3 per gallon) too low or too high to achieve the efficient level?

d) Provide a graph that includes the externality cost. Label prices and quantities accordingly, including their numeric values (Pe, P*, Qe, Q*). Identify the DWL and explain what the DWL is from

Answer 1

(a)

Marginal social cost (MSC) = Private Supply (MPC) + MEC = 0.5Q + 1.5Q = 2Q

Efficient outcome is obtained when Demand equals MSC.

18 - 2.5Q = 2Q

4.5Q = 18

Q = 4

(b)

Private equilibrium outcome is obtained when Demand equals Supply.

18 - 2.5Q = 0.5Q

3Q = 18

Q = 6

P = 0.5 x 6 = 3

When Q = 6, MEC = 1.5 x 6 = 9

Therefore, DWL (in absence of tax) = (1/2) x MEC x Change in quantity = (1/2) x 6 x (6 - 4) = 3 x 2 = 6

(c)

When Q = 4, MEC = 1.5 x 4 = 6

The optimal tax per unit is equal to MEC (= $6). Hence, proposed tax of $3 is too low compared to the efficient/optimal tax.

(d)

In following graph, private equilibrium outcome is at point A where Demand (D) intersects Supply (MPC) with price P* and quantity Q*. Socially efficient outcome is at point B where Demand (D) intersects MEC with price Pe and quantity Qe, with Pe > P* and Qe < Q*. DWL equals area of triangle ABC. The DWL generates since in private market equilibrium, the firm is overproducing at lower-than-optimal price.