Question

Problem 3: Natural Monopoly Regulation. A natural monopolist faces a demand curve P = 100-Q. The monopolist a constant marginal cost MC = 20 and an average cost AC = 20 + 800 a) In an unregulated market, what price will the monopolist charge? What is the DWL associated with this allocation? b) Suppose that a regulator imposes marginal cost regulation by setting P = 20. How many units will the monopoly sell? What is the DWL associated with this allocation? What are the monopolist profits? c) Suppose that there are N = 80 consumers and the regulator wants to implement the optimal two-part tariff. What per-unit price P should they choose? What fixed fee F should they choose? d) Briefly describe why the regulator prefers the outcome in c) to the outcome in b)?

Answer 1

Problem 3 . a) In a morvopoly market structure; profit is. maxinuired at a point where, conta - Marginal Revenue (MR) & Marginal lost (MC)... Here, we have a P=100-8 . io Total Revenue (TR) = p 9 = (100-9) 9 : = 1009 -g2 .. in Marginal Revenue (MR): ♡ TR = 100 – 29. Heme, at, MR = Me, 100- 29 = 20 (since, Me = 20), ; -) 29 = 80 ...) = 40=3 Cing:2.10 wir In an engi3.01. Mis At 8-40, P=10038-100 - 40*2;60: p rin ay p605 Pines . In an in regulated market, the monopolist will change," Pon=:60; Had this been a perfectly competitine market stovetine, the profit maximisation point would be given by a N fit maximisation puisqvi 2,!11 pa me v d es infections Deo ., op=MC = 20.= Ppc.. or, 100 – Q = 20 m or. Q = 80 = OPC jö; :-::

- MYD Now, let us imorporate the findings in the following diagram PMR, me ,AR (Pec ) 20 by MC I D MRLE BPC) = Quantity, 40 l 80 The loss in welfare (or surplus), or efficiency, due to a certain market structure in or restrictions, is known as the Deadweight Loss (Dwl). In a perfectly competitive market, welfare, or efficiency is maximised. Heme, deviation from the competitive market, structure to monopoly, gines rise to certain amount of Deadweight loss. (Note: Here, we have referred Total surplus as welfare, where, Total. Surplus = consumer Supples. it Producer scoplus). % In this case, the DWL is given by a DWL = *(60-20) « (80 – 40) .

-) DWL = x 40 x 40 = 800 ir the DWL will be : 800 units : (In the above diagram, the, area. A is referred represents the DWL). b) At p=20, we have the perfeetly conipetiline market structure. óc quantity sold by the monopolist will be: Spé = 80. Sime, perfectly competitive market structure yields the maximwni welfare, there is no DWL'associatesti Hence, in this case, DWL = 0 O nda wor we in this case, T have (A Ċ x.) o s? giuris >> To = (Pex Bpe) (ciuni: We have a Profit ; 7) = TR = (AĆ xg) = TR - TO => 77 = (2x Spe) - (AC x 8pc), It is given that a AC = 20+ 360 . CE 20+ Tobie já Sen ons ! 80 At g = gpc = 80, A.C. = 20+ - h 800 - 20+ 10 = BO JAC = 30 LE A Cpc). LES i. Tpc = (Ppc x Ope) - (AC pc. X TACX Open PO = (20 x 80) – (30 x 800); -800-

8. In the perfectly competitive market structure, the monopolist's profits are negative, lie, he or she faces loss which equals 800 units . . Note: Under the monopoly market, structure without regulations we have i T = (Pm x 3mi) = (A CM X.Qm) Ipm x Qai) " .seun so we have ... 800. 208 + 8 D3 1 800 . At f = 9 m = 40, AC = 204 .. 40. E A Cimi . Im = (.PMX & gi) (A CM X 9M) .. = 16040) - (40x40), = 800 is thregulated Monopoly yields a profit of i TIM. = .800 units.

price that buyers pay. It is given a in the two part pricing strategy, there are two. components involued : fixed fee () and per-unit Price (0) To find the fixed fee, i. e, f, we have to find the consernier surplus (cs) associated with the unregulated monopoly fice, the perfectly competitive) market structure. consumer surplus is the difference between the maximum price that buyers are willing to pay and the price they actually have to pay. It is given by the area between the demand wrie (6) and the actual price (Pre)... In our diagram, the triangle XYZ gives us the es. is (S = Area of ex y2 = 4 x (100 – 20) (80–0) 1 x 80 x 80 – 3200, i, CS = 3200 units. There are N= 80 consumers. . Fixed fee each have to pay will be: es al - 3200 =40: - or, F = 40 8. The per-unit price will be the competitive price, nie, pappc = rounits and Fixed fee will be :f = 40 units (per consumer). (Note : In this case, the monopolist extracts the entire cs),

d). In the outionie in (b), the monopolist faces a loss, but in the outconce in (c) that loss is compensated by the total extraction of the consumer surghis, and hence, it becomes feasible for the monopolist to operate ...