The Peakload Pricing Power Company (PPPC) faces different demands for its electricity during the day and night-which each last for 12 hours. The demand functions are Qd = 1000 - 10 Pd and Qn = 500 - 30 Pn . The cost function for generating power is C(Qd , Qn) = 4Qd + 4Qn + 6K, where K = max[Qd , Qn ].
(a) What is the socially optimal capacity?
(b) What would be the optimal prices at this capacity? Why does Pd > Pn ?
(c) A clever scientist develops and patents a process that can store energy for up to 24 hours with zero loss and at zero cost. If PPPC had access to this technology, but still had the capacity of part (a), what would be the socially optimal prices?
(d) In the long run, PPPC can change its capacity choice. What capacity should it choose to maximize total surplus, given that it has access to the new storage technology?