Question

5_._ _Minimum Efficient Scale and Natural Monopolies

Pandora is a small island with just one power plant, which is a monopolist in the island’s electricity market. The plant’s cost function is ?(?)=0.5?3−20?2 + 282.5 ?, where ? is the number of MW-h of electricity produced per day. This implies the marginal cost curve ?C(?) =1.5 ?2 –40? + 282.50. Daily demand for electricity in Pandora is given by ??(?) = 16 −(1/20)?, where ? is the price of a MW-h of electricity.

a) Find the power plant’s minimum efficient scale. Is this a natural monopoly? Why? [Hint: Can the firm exhaust its economies of scale and still find customers at that output level? You may want to graph the demand curve before you answer that question.]

b) Suppose a private firm built and operates this power plant. In the absence of any government intervention, will the monopolist be maximizing its profit if it charges $220 per MW-h of electricity? Why or why not?

[Hint: Check whether the optimal mark-up formula ([(?−?C)⁄p] = 1/|??|) is satisfied]

Answer 1

a) CC®) = 0.503- 200°+28Q5 Q At minimum efficient scale : MCCQ) = ACCO) av, OC 1502-400 +288.5 = 0.52- 200 +2865 :ar, Q? - 200 ::Q2 = 20 The maximum demand for the firm in at poo Qe (P) = 16 Now Q (P) < Qe i then the firm's demand lie on the falling part of the average cost curve. Hence, the firm in a natural monopoly b) At p = 220; Qd (p) = 16- X 228 -5 :: Ed Soupes et = x -22 At Q = 5, MC = 1.5(5)2 - 40(5) + 282.5 = 120 þ - M 1C 220-120 220 © 220 22 22 - 22 Teal As the mark up formula is satisfied þ= 220, the monopolist maximizes at this price . at profit