Question

6. A paper mill dumps waste into a lake used by a tilapia farmer. The paper mill’s marginal private cost function of producing a tonne of paper is represented by: MPC = 5 + ½ Q and the marginal benefits can be represented by: MSB = 65 – Q. The tilapia farmer’s costs from the pollution can be represented by: MEC = ½ Q.
   1. Sketch the paper mill's marginal private cost curve, the marginal social cost curve, and the marginal social benefit of paper curve.

2. What is the efficient level of paper production? If no one owns the lake and there is no regulation of pollution, what is the quantity of paper produced per week? Illustrate the deadweight loss of the no-regulation level of production in your figure.

3. If the government introduces a tax to correct the externality, what is the tax per tonne of paper produced that achieves an efficient outcome?

4. If the tilapia farmer owns the lake, how much paper is produced per week and what does the paper mill pay the farmer per tonne? Explain you answer.

5. If the paper mill owns the lake, how much paper is produced per week? Explain.

6. Compare the quantities of paper produced in (d) and (e) and explain the relationship between these quantities.

Answer 1

A)

B)MSC=MPC+MEC=5+0.5Q+0.5Q=5+Q

Efficient outcome is where ,MSC=MBC

5+Q=65-Q

2Q=60

Q=30{ efficient outcome}

In absence of regulation,The market equilibrium,

At MPC=MBS

5+0.5Q=65-Q

Q=60/1.5=40

marginal external cost ( MEC) at market equilibrium=0.5*40=20

Deadweight loss=1/2*20*(40-30)=10*10=100

C) The efficent tax will equal to MEC at efficient outcome,

Efficient outcome=30

MEC=0.5*30=15$

15$ tax per ton paper will lead to efficient outcome

D)the efficient outcome equal to 30 ,will produced per week if farmer owns the lake.

The amount paper mill pay to farmer to dumb waste in lake is equal to total external cost of dumbing waste generate by 30 tons of paper production.

MEC=0.5Q

TEC=0.25*Q^2=0.25*30*30=225

E) If paper mill own the lake,then farmer will pay the a sum equal to profit loss of firm due to efficent level of production. And firm will produce efficient level of outcome equal to 30. The payment by farmer will be =1/2*15*10=75

F)In both equilibrium quantity,is same .The only difference is the given property right. In d) farmer had the property right so firm has to bear some loss.

In e) paper mill had the property right so farmer had to bear a 75 cost to make firm to produce efficient level of output