Question

1. Consider the market for electricity. Suppose demand (in megawatt hours) is given by Q = 42 − P and that the marginal private cost of generating electricity is $10 per megawatt hour (P is in the same units). Suppose further that smoke is generated in the production of electricity in direct proportion to the amount of electricity generated. The health damage from the smoke is $15 per megawatt hour generated. (What is meant here is that MC and MD are 10 and 15 respectively, not 10Q and 15Q.)

(a) Suppose the electricity is produced by an unregulated monopolist. What price will be charged, and how much electricity will be produced?

(b) In part (a), what is the consumer surplus from the electricity generation? What is the total surplus, taking into account the pollution damage?

Answer 1

a)

Electricity Produced by a monopolist

marginal external cost(MEC)=15xQ

(a) In competitive equilibrium, profit is maximized when Price equals marginal cost (MC).

Q = 42 - P

P = 42 - Q

Equating with MC,

42 - Q = 10

Q = 32

P = MC = $10

(0R)

a) inverse demand function is p=42-Q

marginal revenue =d(pxQ)/dQ

10=d(42-Q)Q/dQ . .(as per p=42-Q)

10=(42-Q)dQ/dQ

10=42-Q

Q=32

p=42-32=mc=$10

For unregulated monopolist, profit is maximized when marginal revenue (MR) equals marginal cost (MC).

Q = 42 - P

P = 42 - Q

Total revenue, TR = P x Q = 42Q - Q²

MR = dTC/dQ = 42 - 2Q

Equating with MC,

42 - 2Q = 10

2Q = 42

Q = 16

P = 42 - Q = 42 - 16 = $26

(b)

From demand curve, When Q = 0, P = $50 [Reservation price]

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

(i) In competitive equilibrium, CS = (1/2) x $(42 - 10) x 40 = (1/2) x $32x 40 = $640

(ii) In monopoly, CS = (1/2) x $(42 - 16) x 20 = (1/2) x $26 x 20

Pollution damage will increase MC to Social Marginal cost (SMC), where

SMC = MC + MEC = $10 + $15Q

(i) In competitive equilibrium, equating Demand with SMC,

32 - Q = 10 + 15Q

16Q = 22

Q = 1.375

P = 42- 1.375 = $40.625

Compared to private equilibrium, Net Surplus = (1/2) x Difference in price x Difference in quantity

= (1/2) x $($40.625 - 10) x (32- 1.375) = (1/2) x $30.625 x30.625  = $468.125

(ii) In monopoly, equating MR with SMC,

42 - 2Q = 10 + 15Q

17Q = 32

Q = 1.88

P = 42 - 1.88 = $40.12

Compared to private equilibrium, Net Surplus = (1/2) x Difference in price x Difference in quantity

= (1/2) x $(40.12 - 30) x (20 -1.88 ) = (1/2) x $12.12 x 18.5 = $32.51