An electric utility is going to use a block-pricing schedule. They plan to charge P1 for the first Q1 units and P2 for the subsequent units. The units sold at P2 are the total units sold, Q2, minus the total units sold at P1. The inverse demand curve is P = $100 - Q, and the marginal and average cost is $40. Use calculus to solve for P1, P2, Q1, Q2
What will be an ideal response?
The profit equation for this utility is ? = P1(Q1 ) ? Q1 + P2(Q2 ) ? (Q2 - Q1 ) - 40Q2. The derivative of profit with respect to Q1 is 100 - 2 ? Q1 - 100 + Q2. The derivative of profit with respect to Q2 is 100 - 2 ? Q2 + Q1 - 40. By setting these two derivatives equal to zero and substituting, Q1 equals 20 and Q2 equals 40. Substituting the quantities into the inverse demand curve, P1 equals $80 and P2 equals $60.
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