Question

Suppose that demand for electricity is given by P= 400 -(Q) , where Q is the quantity kilowatt hours demanded and P is the price of electricity. The marginal private cost of electricity production is: MC(Q) = 100 +1/2Q . Assume that electricity production exposes an external cost on society of $30 per kWh. There are no marginal external benefits from the consumption or production of electricity.

1. Find the efficiency quantity of electricity.

2. Find the efficient price per kWh of electricity.

3. Calculate the deadweight loss that will arise in the absence of government intervention.

Answer 1

1. Marginal Social cost(MPS) = Marginal private cost(MPC) + Marginal external cost(MEC)

MSC = 100 + 0.5Q + 30 = 130 + 0.5Q

The efiicient equilibrium is at the point where,

MPB = MPS

400 - Q = 130 + 0.5Q

1.5Q = 270

Q = 270 / 1.5 = 180

Thus, the efficiency quantity of electricity. is 180 Kwh.

2. P = 400 - Q = 400 - 180 = $220

Thus, the efficient price per kWh of electricity is $220.

3. The market equilibrium is where,

MPB = MPC

400 - Q = 100 + 0.5Q

1.5Q = 300

Q = 300 / 1.5 = 200    [This is market quantity]

At the efficient quantity, MPC = 100 + 0.5Q = 100 + 0.5(180) = $190

Deadweight loss = 0.5[($220 - $190) * (200 - 180)] = $300.

Thus, the deadweight loss that will arise in the absence of government intervention is $300.