Question

17.17. The demand for energy-efficient appliances is given by P = 100/Q, while the inverse supply (and marginal private cost) curve is MPC = Q. By reducing demand on the electricity network, energy-efficient appliances generate an external marginal benefit according to MEB = eQ.

a) What is the equilibrium amount of energy-efficient appliances traded in the private market?

b) If the socially efficient number of energy-efficient appliances is Q = 20, what is the value of e?

c) If the government subsidized production of energy efficient appliances by $S per unit, what level of the subsidy would induce the socially efficient level of production?

Answer 1

Answer 17.17

(a)

In the Private market equilibrium occurs when Marginal Private Benefit(i.e. Price) = Private marginal cost(MPC)

Here MPB = P = 100/Q and MPC = Q

MPB = MPC => 100/Q = Q => Q = 10.

Hence, the equilibrium amount of energy-efficient appliances traded in the private market is Q = 10.

(b)

Social efficient quantity occurs when Marginal Social Cost(MSC) = Marginal Social Benefit(MSB).

Here there is Positive externality hence MPC = MSC = Q and MSB = MPB + MEB = 100/Q + eQ

MSC = MSB => Q = 100/Q + eQ

As social efficient quantity is Q = 20

=> 20 = 100/20 + 20e

=> e = 15/20 = 0.75

Hence, The value of e = 0.75

(c)

When Government subsidize the Production then Inverse Supply(MPC) will shift to the Right and Let Subsidy = S

Hence previously for P he is willing to supply Q = P and Now he is willing to supply Q = P + S

Hence New inverse supply curve: Q = P + S => P = Q - S

Now efficient quantity = 20 and MPB = P = 100/Q

At equilibrium supply = demand => Q - S = 100/Q and Q = 20(Efficient quantity)

Hence 20 - S = 100/20 = 5

=> S = 15

Hence, level of the subsidy would induce the socially efficient level of production is S = $15