Directions : The marginal control cost curves for two air pollutant sources affe

Question

Directions: The marginal control cost curves for two air pollutant sources affecting a single receptor are MC1 = $0.3q1 and MC2 = $0.5q2 , where q1 and q2 are controlled emissions. Their respective transfer coefficients are a1 = 1.5 and a2 = 1.0. With no control they would emit 20 units of emissions each. The ambient standard is 12ppm.

(a) If an ambient permit system were established, how many permits would be issued and what price would prevail?

(b) How much would each source spend on permits if they were auctioned off? How much would each source ultimately spend on permits if each source were initially given, free of charge, half of the permits?

Explanation / Answer

MC1= 0.3q1

MC2= 0.5q2

The cost of achieving a given level of pollution control is minimised by setting the marginal cost of pollution control equal for the two firms (i.e. MC1 = MC2). This implies: MC1=MC2

0.3q1 = 0.5q2

so, q1 = 1.67q2

Both the firms emit 40 units of emissions together, their ideal emission would be 12+12= 24 emissions together. That is a reduction od 40 - 24= 16 units.

Mathematically, we can write this as: q1+q2 = 16

we replace the value of q1 here, 1.67q2 + q2= 16

or, 2.67q2=16

or, q2= 9.58

so q1= 15.9986 ~`16

so 24 units of emissions would prevail. And prices are: 0.3*16 = $4.8 and 0.5*9.58= $4.79 for two air pollutant firms.

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