Question

1) At equilibrium:

Marginal benefit = Marginal private cost

9 - Q = 2Q

9 = 3Q

Q = 3 units

2. Market price, P = 9 - 3 = $ 6

3. Social optimal:

Marginal benefit = Marginal social cost i.e. MPC + MEC

9 - Q = 2Q + Q

9 = 4Q

Q = 2.25 units

4. Social optimal price = 9 - 2.25 = $ 6.75

-------What is the deadweight loss?

------How much would a corrective (Pigouvian) tax need to be to move the market equilibrium to a socially optimal equilibrium?

Answer 1

From the information we see that MB = 9 - Q, MPC = 2Q and MEC = Q so that MSC = 3Q. Market equilibrium has a price of $6 and the quantity of 3 units while the socially efficient equilibrium has a price of $6.75 units and quantity of 2.25 units.

Here the deadweight loss is the area found between the market outcome and socially efficient outcome.

DWL = 0.5*(difference in quantities)*(MSC at market efficient quantity - MPC at market efficient quantity)

= 0.5*(3 - 2.25)*(3*2.25 - 2*3)

= 0.28125

A corrective Pigouvian tax that is need to be to move the market equilibrium to a socially optimal equilibrium is the marginal external cost. Here such a tax is Qe or $3 per unit.