Assume an electricity generator can produce electricity from two different production technologies, a dirty technology, and a clean technology. The quantity of electricity produced from the dirty technology is Qd in megawatt hours (MWh), and the amount from the clean technology is Qc. The dirty technology produces carbon emissions at a constant rate of d tons per MWh of electricity generation. The clean technology produces carbon emissions at a constant rate of c tons per MWh, where Bc < Bd. The cost functions for the two-generation technologies are C(Qd) and C(Qc). The market price of electricity is P. Under these assumptions, the firms profit function is: Profit = PQd + PQc - C(Qd) - C(Qc).

1.) To fight climate change, policymakers implement a carbon tax where the firm is charged _ dollars per ton of carbon emissions released into the atmosphere. Under this policy, the firms profit function is:

Profit = PQd + PQc - C(Qd) - C(Qc) -B(BdQd + BcQc), where the last term is the amount of carbon taxes paid (hint: check the units on these terms). Write down the firms first-order conditions for each type of electricity under the carbon tax policy. How do these expressions differ from the expressions in part 1 above?