Consider two firms whose marginal costs of production are MC(Q1) = 10Q1; MC(Q2) = 5Q2: Suppose each unit of output produced, Q, results in one unit of emissions, E. Suppose the two firms sell their output in a perfectly competitive market, with perfectly elastic demand at a price of $90. Furthermore, suppose there is a constant external cost of emissions of $10.
Now suppose the regular decides to implement a cap and trade system to attain the socially optimal level of emissions via the Coase theorem. Firm 2 has more political clout, however, so the regulator distributes all permits to firm 2.
(a) How many permits should the regulator allocate to firm 2?
(b) Now suppose firm 2 sells permits to firm 1 such that they get to the socially optimal allocation of emissions across the two rms. How many permits would firm 2 sell to firm 1?
(c) What is the minimum price firm 2 would be willing to accept for the permits?
(d) What is the maximum price firm 1 would be willing to pay for these permits?