Question

1. Due to the large fixed costs involved in providing electricity to a city (running cables, electric plants, etc.) the market for electricity is a natural monopoly. If marginal cost is $20, fixed cost is $1,000, and the demand is given by Q = 100 - P
   1. Calculate quantity, price, and profit.
   2. Calculate consumer surplus and social welfare
   3. If you were to regulate the price in this market, what price will maximize society’s welfare?
   4. Following your answer in part c), how will this price regulation change quantity, profit, consumer surplus, and social welfare?

Answer 1

Total cost (TC) = Fixed cost + (MC x Q) = 1,000 + 20Q

Q = 100 - P, so

P = 100 - Q

(a)

Profit is maximized when MR = MC.

TR = P x Q = 100Q - Q²

MR = dTR/dQ = 100 - 2Q

100 - 2Q = 20

2Q = 80

Q = 40

P = 100 - 40 = 60

Profit = TR - TC = (60 x 40) - (1,000 + 20 x 40) = 2,400 - (1,000 + 80) = 2,400 - 1,080 = 1,320

(b)

From demand function, when Q = 0, P = 100 (Vertical intercept of demand curve).

Consumer surplus (CS) = Area between demand curve & price = (1/2) x (100 - 60) x 40 = 20 x 40 = 800

From MR function, when q = 40, MR = MC = 20.

Producer surplus (PS) = Area between MC curve & price = (60 - 20) x 40 = 40 x 40 = 1,600

Social surplus (TS) = CS + PS = 800 + 1,600 = 2,400

(c)

Social surplus is maximized when P = MC.

100 - Q = 20

Q = 80

P = MC = 20

(d)

When P = 20 and Q = 80,

(i) Quantity increases by (80 - 40) = 40.

(ii) Price decreases by (60 - 20) = 40.

(iii) Profit = (20 x 80) - (1,000 + 20 x 80) = 1,600 - (1,000 + 1,600) = 1,600 - 2,600 = - 1,000 (loss)

Profit decreases by (1,320 + 1,000) = 2,320

(iv) CS = (1/2) x (100 - 20) x 80 = 40 x 80 = 3,200

CS increases by (3,200 - 800) = 2,400.

(v) Since P = MC, producer surplus is zero and TS = CS = 3,200.

TS increases by (3,200 - 2,400) = 800.