# Suppose the marginal costs of mitigating Greenhouse Gas emissions for two coal producers are given as follows: Producer 1: MC1 = 10Q1 Producer 2: MC2 = 40Q2 where MC1 and MC2 are the marginal control costs and Q1and Q2 are the volumes of emissions reduced by Producers 1 and 2 respectively. With no controls at all, each firm emits 50 units totalling 100 units. (a) Compute the cost-effective allocation of control responsibility if a total reduction of 50 emission units is required. (b) If the Government wants to charge an emission tax, what per unit tax should they impose? (c) How much total revenue would the Government collect from the emission tax of section (b)?

Suppose the marginal costs of mitigating Greenhouse Gas emissions for two coal producers are given as follows:

Producer 1:                           MC1 = 10Q1

Producer 2:                           MC2 = 40Q2

where MC1 and MC2 are the marginal control costs and Q1and Q2 are the volumes of emissions reduced by Producers 1 and 2 respectively. With no controls at all, each firm emits 50 units totalling 100 units.

(a)            Compute the cost-effective allocation of control responsibility if a total reduction of 50 emission units is required.

(b)            If the Government wants to charge an emission tax, what per unit tax should they impose?

(c)             How much total revenue would the Government collect from the emission tax of section (b)?

a)

We have to equate the marginal cost for a cost-effective allocation; the marginal costs must be equilibrated:

MC1=MC2

10Q1=40Q2

Q1=4Q2

As the total reduction of 50 units is required, thus we have Q1+Q2=50. Solving the two equations we get:

Q1+Q2=50

4Q2+Q2=50

Q1=40

Q2=10

Therefore required reduction by firm 1 is 40 units and by firm 2 is 10 units.

b)

If the government is willing to charge a tax on emission then it must charge a tax which is equivalent to the marginal cost of such reduction. From part a) we conclude that this amounts to:

T=MC1=MC2

10*40=40*10=400

or T=\$400

Thus, the per unit tax of \$400 should be imposed.

c)

As currently the firms are emitting 50 units of pollution thus the total amount of revenue that can be earned by the government is calculated as:

TR=T(20-Q1) + T(20-Q2)

or, =400*(50-40) + 400(50-10) = 20,000

Government should earn a total of \$20,000 in the form of emission charges.

Asked on February 15, 2018 in