Question

Problem 2A This problem is an example on peak load pricing. The basic premise is that the demand for many goods and services exhibits temporal variation—e.g., demand for transit services is greatest in the morning and evening hours. Since these temporal differences in demand are coupled with a capacity that does not change, firms facing these demand conditions should charge different prices in the demand peak and trough. Assume that an electric utility faces a demand curve of the form P = 50 – Q during off-peak hours and a demand curve of the form P = 110 - Q during peak hours. Its marginal costs are given by MC(Q) = 20+0.5Q. Derive the profit-maximizing peak-load monopoly prices. How do these prices compare compare with the competitive prices? Hint: Use period 1 (period 2) to refer to off-peak (peak) hours. You can find the peak-load prices using MR1(Q1) = MC(Qı) and MR2(Q2) = MC(Q2).

Answer 1

Under peak-load pricing, firm charge different prices during peak hours and off-peak hours. As demand is high at peak-hours, firm charge higher price at peak hours. Often marginal cost is higher at peak hours. Demand during off-peak hours is P1 = 50 - Q1 Demand during peak hours is P2 = 110-Q2 Marginal cost is MC (Q) = 20 +0.5Q (it is same in both periods) Profit-maximizing peak-load pricing using profit-maximizing monopoly condition, that is, MR = MC. For off-peak hours, The marginal revenue (MR1) is. TR =PxQ = (50-0.) = 500,-Q2 MR, DTR, dQ = 50-20 At profit-maximizing level, MR = MC 50-20 = 20 +0.50 9 = 30 Q =12 P1 = 50- = 50-12 P = 38 For peak hours, The marginal revenue (MR) is,

TR = P, XQ2 =(110-Q,)*Q2 =1100, -032 MR, = DIR dQ2 =110-20 At profit-maximizing level, MR = MC, 110-20, = 20 +0.502 090 02-2.5 02 = 36 Py=110-02 =110-36 P2 = 74 Hence, firm charge higher price during peak hours, that is P2 = 74 and lower price during off-peak hours, that is, Pa=38. In competitive markets, same price is charged in different periods and price is determined where P = MC. To determine competitive price, combine demand and solve as follows: Q=Q+Q2 Q = 50 - P+110-P Q=160-2P P = 80-0.50 At competitive equilibrium,

P=MC 80-0.5Q = 20+ 0.50 Q = 60 P= 80 -0.50 = 80 -0.5(60) P=50 Hence, firm charge same price in both periods, that is, P = 50. Comparing monopoly pricing with competitive pricing, it can be conclude that firm face loss for peak hours (as earlier price was 74 and now it is 50) and gain for off-peak hours (as earlier price was 38 and now it is 50).