Two firms can control emissions at the following marginal costs: MC1 = 200q1, MC
ID: 1231362 • Letter: T
Question
Two firms can control emissions at the following marginal costs: MC1 = 200q1, MC2= 100q2, where q1 and q2 are the amount of emissions reduced by the first and second
firm. Assume with no control each firm would emit 20 units or a total of 40 units.
a. Compute the allocation that would result if 10 tradable effluent permits
were given to the second source and 9 were given to the first source. What
would be the market permit price? How many permits would each source
end up with after trading? What would the net permit expenditure be for
each source after trading?
b. Suppose a new source entered the area with a constant marginal cost of
control equal to $1,600 per unit of emissions reduced. Assume further that
it would add 10 units in the absence of any control. What would be the
resulting allocation of control responsibility if the cap of only 19 units of
effluent allowed were retained? How much would each firm clean up?
What would happen to the permit price? What trades would take place?
Explanation / Answer
a) Initially firm 1 has a higher MC, this means the amount firm 1 is willing to pay to control one LESS unit (by purchasing permit) is higher than the amount firm 2 is willing to receive in order for it to control 1 MORE unit. Thus a number of permit will be trade such that MC1 = MC2, at which neither firm will benefit by trading more. We also know the total reduction of the two firms must be 21, because there are only 19 permits, 40-21=19. Thus: set MC1 = MC2 : 200q1 = 100q2 2q1 = q2 solve: q1 + q2 = 21 q1 + 2q1 = 21 q1 = 21/3 = 7 therefore q2 = 2*7 = 14 the market permit price is the MC of the firms, which is 1400. In equilibrium, firm 1 end up reducing 7, so it has 20-7 = 13 permit. firm 2 reduces 14, so it has 6 permit. Since firm 1 bought 4 permits, it spent 4*1400 = 5600, while firm 2 earns 5600 on permits sold. b) by setting MC1 = MC2 = MC3, 100q2 = 200 q1 = 1600q3, so that q1 = 8q3, q2 = 16q3 total control must be (20 + 20 + 10) - 19 = 31 8q3 + 16q3 + q3 = 31 q3 = 31/25 = 1.24, so q2 = 19.84 and q1 = 9.92 so that firm 3 buys 8.76 permits from firm 2, and firm 1 buys 1.08 from firm 2. permit price is the MC of the firms, which is 1600*1.24 = 100*19.84 = 200*9.92 = 1984 sorry i didn't realize i could input equations, i'm new to this. If you have trouble reading you can ask me samc_998110@hotmail.com
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