Question

3. Suppose you have been asked to advise the Energy Ministry of Mexico on their reform of the electricity sector. The Ministry wants to impose a tax per unit of electricity generated by heavy fuel oil (HFO) generation plants. The amount of the tax is meant to offset the damage incurred by the Mexican population from respiratory health diseases and decreased crop yields resulting from SO2 emissions which are a by-product of HFO power plants. Suppose demand (in MWh) is given by Qd = 140 − P where P is the price in pesos per MWh and Qd is the quantity demanded. The supply of electricity (in MWh) from HFO plants is given by Qs = 4P −200 where P is the price in pesos per MWh and Qs is the quantity supplied. Suppose further that the damage caused by the SO2 emissions is given by 0.125Q2 pesos where Q is electricity generated in MWh. (a) (7 points) In the absence of a tax for SO2 emissions, what will be the equilibrium price and quantity of HFO-generated electricity in the market? (b) (6 points) What is the socially optimal amount of electricity production from HFO power plants, taking into account the SO2 emissions damage? (Ignore damage from other emissions such as NOx, particulate matter, carbon etc. Note that the marginal damage from the SO2 emissions is given by the derivative of 0.125Q2 with respect to electricty generated, i.e. 0.25Q.) (c) (4 points) Suppose the Ministry is considering a tax of $T per MWh generated by HFO plants. Find the level of the tax, T, that ensures that the socially optimal amount of HFO-generated power will be produced in competitive equilibrium. (d) (4 points) Compute the deadweight loss which is eliminated by imposition of the tax. (e) (4 points) In general, do all taxes eliminate deadweight losses? If yes, state why. If not, state why not.

Answer 1

(a) At the equilibrium, demand equals the supply in the market. That is,

140 - P = 4P - 200

5P = 340

P = 340/5

P = $68

Substituting this into the demand or supply function, we get the equilibrium quantity.

Q = 140 - P

Q = 140 - 68

Q = 72

(b) Damage from pollution = 0.125Q²

MC of pollution= d( 0.125Q²) / dQ = 0.25Q

MC of producing (along with social cost) = (0.25Qs + 50) + 0.25Qs

(Social + Private) MC = 0.5Qs + 50

Equilibrium in competitive market => MC = P

0.5Qs + 50 = 140 - Qs

At market equilibrium, Qd = Qs = Q. This implies,

0.5Q + 50 = 140 - Q

1.5Q = 90

Q = 60

Thus, socially optimal production = 60.

(c) Tax => Marginal social cost of production

Therefore, Tax = 0.25 * Q = 0.25 * 60

Tax = $15 per unit

(d) Deadweight loss negated = 1/2 * (72 - 60) * (Social cost at Q = 72)

Social Cost = 0.25 * 72 = 18

DWL negated due to tax imposition =1/2 * 12 * 18

DWL negated due to tax imposition = 108

(e) Deadweight loss is not eliminated by all form of taxes imposed. Some form of taxations give rise to deadweight losses in the market.

Deadweight losses arise when taxes are imposed on socially optimal production levels that are estimated after total marginal costs (social plus private) are equated to price levels.