Question

The market demand for reality TV is defined as Q_D = 4700 - 75P and the market supply for these shows is Q_S = -500 + 125P.

a) What is the equilibrium price and quantity?

b) Some critics of this type of entertainment claim that it imposes a negative externality on society. If the marginal external cost of reality TV is MEC(Q) = 8, what is the efficient price and quantity?

c) What is the fee or tax you would need to levy on producers to move this market to the efficient outcome? Explain.

d) Would the fee be larger/smaller/identical if MEC(Q) = 0.01Q? Provide evidence.

Answer 1

Part 1 :-

As we know that, for equilibrium, Qs = Qd. Therefore,

4700 - 75P = - 500 + 125P

P = 26 (This is the equilibrium price)

Q = 2750 (This is the equilibrium quantity)

Part 2 :-

SMC = PMC + MEC, therefore

New supply will be given by,

Qs' = - 500 + 125 x (P - 8)

For new equilibrium;

4700 - 75P = - 1500 + 125P

P = 31 (this is the new equilibrium price also called as efficient price)

Q = 2375 (this is the new equilibrium quantity also called as efficient quantity)

Part 3 :-

In order to attain efficient outcome:

Tax = MEC = 8

As we know that the difference between PMC and SMC at the efficient quantity is the fee or tax which would need to be levied on producers to move this market to the efficient outcome. Therefore the tax must be levied equal to 8

Part 4 :-

It is given the condition that,

If MEC(Q) = 0.01Q

Marginal social cost = 0.008Q + 4 + 0.01Q = 0.018Q + 4, by equating these values with the demand, we get

0.018Q + 4 = (4700-Q)/75

Q = 1872 (approx), this will be the required efficient quantity.

At Q = 1872, the marginal external cost will be

MEC = 0.01×1872 = 18.72

From the above data it is clear that the fee must be levied if MEC(Q) = 0.01Q is 18.72, which is larger than the fee levied when MEC= 8