Take the partial derivative of profit with respect to each output (Qd and Qc) and set each equal to zero to find the profit maximizing (“first-order”) conditions for each type of electricity. Denote marginal costs of each type of electricity as MCd and MCc. Write down and interpret these first-order conditions. (Hint: Are these expressions consistent with the behavior of a profit-maximizing firm?)
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 firm’s profit function is: Profit = PQd + PQc - C(Qd) - C(Qc).
1.) Take the partial derivative of profit with respect to each output (Qd and Qc) and set each equal to zero to find the profit maximizing (“first-order”) conditions for each type of electricity. Denote marginal costs of each type of electricity as MCd and MCc. Write down and interpret these first-order conditions. (Hint: Are these expressions consistent with the behavior of a profit-maximizing firm?)
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