Question

Question 3. Externality and Market Power, 30 points) Consider an electricity market. Assume that the demand for electricity is P = 40 - Q amd the cost of producing electivity is C(q) = 20+ 0.50Q2. We assume that the production of electiricity may lead to emission to the society. We assume that each unit of production creates an externality. which amounts to 10 (per unit of production). 1. Derive a socially efficient amount of production. 2. Derive an equilibrium quantity in a competitive market. Calculate the Pigou tax that leads to the socially efficient level of production. 3. Assume that there is only firm in the electricity market so that it is a monopoly market. What is an equilibrium level of production? Suppose that the government want to implement the socially efficienct amount of production. Do they need to provide tax or subsdies? Calculuate it (as a per unit of production)

Answer 1

(1)

Marginal private cost (MPC) = dC(Q)/dQ = Q

Marginal social cost (MSC) = MPC + Externality cost = Q + 10

Socially efficient outcome is obtained by equating demand with MSC.

40 - Q = Q + 10

2Q = 30

Q = 15

(2)

In competitive equilibrium, P = MPC.

40 - Q = Q

2Q = 40

Q = 20

Pigouvian tax = Externality cost per unit = 10

(3)

A monopoly equilibrium is obtained by equating MR and MPC.

Total revenue (TR) = P x Q = 40Q - Q²

MR = dTR/dQ = 40 - 2Q

40 - 2Q = Q

3Q = 40

Q = 13.33

P = 40 - 13.33 = 26.67

When Q = 13.33, MSC = 10 + 13.33 = 23.33

Therefore, monopoly has to be given a subsidy of (26.67 - 23.33) = 3.34 per unit.