Question

1. Assume that a firm produces natural gas, but emits some air pollution as part of the process. The market functions for natural gas demand and supply, as well as the external damage that the air pollution causes, is shown below, where P is price in $/British Thermal Unit (BTU) and Q is quantities in BTUs :

Demand: P = 1000 – 0.2Q

Marginal Private Cost: P = 100 + 0.4Q

Marginal External Cost: $500

Marginal Social Cost: P = 600 + 0.4Q

This information is provided for you to determine the impact of the pollution. Based on the above information, do the following:

1. Draw and fully label the demand and supply functions provided above for this natural gas market.         [5 marks]
2. Calculate the equilibrium P, Q, and total gross gains from trade (total surplus), assuming no regulation.       [5 marks]
3. c. Solve for the total external cost at the market equilibrium. [3 marks]

d. Solve for the private true or net gains from trade, assuming no regulation.

[3 marks]

e. What is the Pigouvian Tax in this case?                                                        [2 marks]

        f. Explain briefly how it can be applied in this problem to reduce emissions.          

                                                                                                                                      [4 marks]

Answer 1

a. In the diagram below, we have shown marginal private cost, marginal social cost and demand curves for the given natural gas market:

b. With no regulations, equilibrium can be obtained at a point where MPC = Demand

or, 100+0.4Q = 1000-0.2Q

or, 0.6Q = 900

or, Q =1500 BTU

and P = 1000-(0.2*1500) = $ 700 per BTU

Now, Total gain = Consumer surplus + Producer surplus = 1/2*(1000-100)*1500 = $ 675,000

c. Total cost at market at market equilibrium = 600+0.4Q = 600+(0.4*1500) = $1200 per BTU

Then, external cost = Total cost (or MSC) at market equilibrium - Equilibrium price (MPC) = $1200 /BTU - $700 /BTU = $500/BTU

d. With regulation, equilibrium can be obtained at a point where MSC = Demand

or, 600+0.4Q = 1000-0.2Q

or, 0.6Q = 400

or, Q = 666.67 BTU

and P = 1000-(0.2*666.67) = $ 866.67 per BTU

Now, total gain = Consumer surplus + Producer surplus = 1/2*(1000-600)*666.67 = $ 133,334

e. Pigouvian tax = Marginal external cost (Negative externality) = $500

f. With pigouvian tax of $500, equilbrium quantity has fallen from 1500 BTU to 666.67 BTU. Again, equilibrium price has increased from $700 per BTU to $866.67 per BTU. There is a loss in total surplus. This will help in reducing extractions of natural gas and thereby, reduce emissions.