Question

Natural gas for a typical residence has a monthly demand (in MMBtus) of D(P)=12-0.2P. The market price of natural gas is $4 per MMBtu, and natural gas has an external cost from CO2 emissions of $2.60 per MMBtu^3. Assume natural gas is competitively supplied.

1. Calculate the market equilibrium price and quantity of natural gas.

2. Calculate the social benefit of the market equilibrium (i.e. consumer surplus plus consumer surplus minus the external cost)

3. How much natural gas should be used? (i.e. calculate the socially efficient quantity of natural gas)

4. Calculate the deadweight loss of the market equilibrium. Illustrate on a graph.

Answer 1

Q = D(P) = 12 - 0.2P

P = (12 - Q)/0.2 = 60 - 5Q

(1)

In market equilibrium, P = 4

60 - 5Q = 4

5Q = 56

Q = 11.2

(2)

When Q = 0, P = 60

Consumer surplus (CS) = (1/2) x (60 - 4) x 11.2 = 5.6 x 56 = 313.6

Producer surplus (PS) = Area between MC curve and price = 0 [since P = MC = 4]

Total external cost = Unit external cost (MEC) x Quantity = 2.6 x 11.2 = 29.12

Social benefit = 313.6 + 0 - 29.12 = 284.48

(3)

In efficient outcome,

60 - 5Q = 4 + 2.6 = 6.6

5Q = 53.4

Q = 10.68

(4)

Deadweight loss = (1/2) x Unit external cost x Change in Q = (1/2) x 2.6 x (11.2 - 10.68) = 1.3 x 0.52 = 0.676

In following graph, market outcome is at point A where demand (D0) intersects MC with market price P0 (= 4) and market output Q0 (= 11.2). Efficient outcome is at point B where demand (D0) intersects MSC (= MC + MEC) with efficient price P1 (= 6.6) and efficient output Q1 (= 10.68). Deadweight loss is area ABC.