question archive Suppose the marginal costs of mitigating Greenhouse Gas emissions for two coal producers are given as follows
Suppose the marginal costs of mitigating Greenhouse Gas emissions for two coal producers are given as follows
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Suppose the marginal costs of mitigating Greenhouse Gas emissions for two coal producers are given as follows.
Producer 1: MC1=10Q1MC1=10Q1
Producer 2: MC2=40Q2MC2=40Q2
where MC1MC1 and MC2MC2 are the marginal control costs and Q1Q1 and Q2Q2 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)?
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A.
We have, according to the equimarginal principle,
MC1=MC210Q1=40Q2Q1=4Q2Q1+Q2=504Q2+Q2=505Q2=50Q2=10Q1=40MC1=MC210Q1=40Q2Q1=4Q2Q1+Q2=504Q2+Q2=505Q2=50Q2=10Q1=40
Thus, the cost-effective allocation of producer 1 is 40 units and producer 2 is 10 units.
B.
The government would charge the tax equal to abatement (control) cost per unit of the firm. The total abatement cost is:
MC1=10(40)=400MC2=40(10)=400MC1=10(40)=400MC2=40(10)=400
Thus, for producer 1, the government should charge an emission tax of 400/40, which is 10 per unit.
For producer 2, the government should charge an emission tax of 400/10, that is 40 per unit.
C.
By charging this, the government would get a revenue of 400 each, that is a total of 800 from the two producers.
