Suppose the demand for electricity is given by P = 100-2Q, and the supply schedu

Question

Suppose the demand for electricity is given by P = 100-2Q, and the supply schedule is given by P = 10+4Q.

a)Determine the equilibrium P & Q in this market. Calculate CS, PS, and TS. Now suppose that producing electricity entails emission of pollutants which generate external costs constant at $6 per unit.

b) What is the efficient quantity of electricity provision? Calculate TS at this level of provision. What is the efficiency loss if the market is left to its own devices (part (a))?

c) What Pigouvian tax could you impose to get the market allocation to be efficient? Show your work.

Explanation / Answer

a) When there is no externality, market equilibrium is societal equilibrium at which demand = supply

100-2Q =10+4Q

90 = 6Q

Q = 15 and P = 100 - 2*15 = $70

CS = 0.5*(Max price - current price)*qty = 0.5*(100 - 70)*15 = 225

PS = 0.5*(Current price - minimum price)*qty = 0.5*(70 - 10)*15 = 450

TS = PS + CS = 450 + 225 = 675

b) With an external cost of $6, efficient outcome occurs with demand equals social supply. This implies the supply cirve shifts up by $6 to become P = 10 + 4Q + 6 or P = 16 + 4Q

Efficient equilibrium has

100 - 2Q = 16 + 4Q

84 = 6Q

Q = 14 and P = 100 - 2*14 = $72. Efficient quantity is 14 units

TS = 0.5*(100 - 10)*14 = 630. Efficiency loss if the market is left to its own devices = DWL loss = 0.5*6*1 = $3

c) The Pigouvian tax would be equivalent to the external cost at socially efficientb quantity which is $6 per unit.

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