Suppose the marginal control costs (MC) and the total costs (TC) of reducing emi

Question

Suppose the marginal control costs (MC) and the total costs (TC) of reducing emissions for two steel producers are:

Producer 1: MC1 = 10Q1 TC1 = 5(Q1)2

Producer 2: MC2 = 40Q2 TC2 = 20(Q2)2 Where MC1 and MC2 are the marginal control costs and Q1 and 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. Suppose the government allocates emissions reductions equally among the two producers to reduce total emission by half (that is each firm has to reduce emissions by 25 units). Calculate the total cost to each firm (Hint: use the total cost function TC). (2 points)

b. Calculate the cost-effective allocation of control responsibility if a total reduction of 50 emission units is required. What is the total control cost and how does this compare to part a? (4 points)

c. If the government wants to charge an emission tax, what per unit tax should they impose? (2 points)

d. How much total revenue would the Government collect from the emission tax in part b (2 points)

e. If instead the government used a cap and trade scheme and, based on histrocial emissions, allocated 25 units to each firm. What is the pattern of trade expected? What is the equilibrium price of permits? (4 points)

Explanation / Answer

Answer:

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.

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.

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.

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