Question

Consider the market for electricity. Suppose demand (in megawatt hours) is given by Q=50-P and that the marginal private cost of generating electricity is $10 per megawatt hours. Suppose further that smoke is generated in the production of electricity in direct proportion to the amount of electricity generated. The health damage from smoke is $15 per megawatt hour generated.

A.) Suppose the electricity is produced by competitive producers, without consideration of the externality. What price will be charged and how much electricity will be produced? Graph the demand and marginal cost curve with quantity, Q, on the horizontal axis and price, P, on the vertical axis. (Hint: This will require solving for the inverse demand curve.)

B.) How would your answer in part a change if electricity were produced by an unregulated monopolist? (Remember that the marginal revenue curve for a monopolist falls twice as fast as the inverse demand curve, assuming a linear demand curve.) Graph the demand and marginal cost curve with quantity, Q, on the horizontal axis and price, P, on the vertical axis.

C.) In parts a and b, what is the consumer surplus from the electricity generation? What is the net social surplus, taking into account the pollution damage?

Answer 1

Q = 50 - P

P = 50 - Q

(A) In unreglated competiive equilibrium, Price equals Private marginal cost (PMC).

50 - Q = 10

Q = 40

P = PMC = $10

From demand function, when Q = 0, P = 50 (Vertical intercept) & when P = 0, Q = 50 (Horizontal intercept).

In following graph, AB is the demand curve intersecting PMC at point E with price P0 (= 10) and quantity Q0 (= 40).

(B) Monopolist will equate Marginal revenue (MR) with PMC.

Total revenue (TR) = P x Q = 50Q - Q²

MR = dTR/dQ = 50 - 2Q

Equating with PMC,

50 - 2Q = 10

2Q = 40

Q = 20

P = 50 - 20 = 30

In above graph, AC is the MR curve and monopoly equilibrium is at point D where MR intersects PMC with price P1 (= 30) and quantity Q1 (= 20).

(C) Consumer surplus (CS) = Area between demand curve & market price

In competitive outcome, CS = Area AEP0 = (1/2) x $(50 - 10) x 40 = 20 x $40 = $800

In monopoly outcome, CS = Area AFP1 = (1/2) x $(50 - 30) x 20 = 10 x $20 = $200

When we consider pollution damage, Social marginal cost (SMC) = PMC + 15 = 10 + 15 = 25

Socially efficient outcome is at intersection of demand curve and SMC:

50 - Q = 25

Q = 25

P = 50 - 25 = 25

In above graph, socially efficient outcome is at point G where Demand intersects SMC with price P2 (= 25) and quantity Q2 (= Point C = 25). Net social surplus is area EGH, equal to

Net social surplus = (1/2) x (25 - 10) x (40 - 25) = (1/2) x 15 x 15 = 112.5