Question

The informal settlements surrounding Rio de Janeiro (known as favelas) have no formal infrastructure to supply them with electricity. Instead, many residents have improvised theirown connections to the electricity grid. These connections are dangerous and unreliable, butthey provide users with free electricity.

The monthly electricity demand for a Brazilian household is:Q= 300?10P. P Is the price of electricity cents per kWh, and Q is the household’s monthly consumption in kWh.What is the monthly electricity consumption of a household ? (Remember The marginal price of electricity for such a household is zero). What is the monthly consumer surplus per household?

Answer 1

Q = 300 - 10P

10P = 300 - Q

P = 30 - 0.1Q

For a downward sloping demand function, optimal point is at equality of Marginal revenue (MR) and MC.

Total revenue (TR) = P x Q = 30Q - 0.1Q²

MR = dTR/dQ = 30 - 0.2Q

Equating with MC,

30 - 0.2Q = 0

0.2Q = 30

Q = 150 kWH

P = 30 - (0.1 x 150) = 30 - 15 = 15 cents

From demand function, when Q = 0, P = 30 (Reservation price)

Consumer surplus = Area between demand curve & market price = (1/2) x (30 - 15) x 150 = 75 x 15 = 1,125 cents