Theory of Regulation PhD, DFA M. Victor M. Martins Semester 2 2008/2009
2. 1 Natural monopoly regulation 2. 1 Natural monopoly regulation: efficient pricing, linear, non linear pricing and Ramsey pricing. Bibliography: ( VVH) Chap 11 Baumol W. J. and D. F. Bradford, 1970, "Optimal Departures from Marginal Cost Pricing," American Economic Review, Vol. 60, No. 3, pp. 265-83. Ramsey, 1927, "A Contribution to the Theory of Taxation," Economic Journal, Vol. 37, No. 1, pp. 47-61. Slide 2
2. 1 Natural monopoly regulation: definitions The natural monopoly problem An industry is a natural monopoly if the production of a particular good or service ( or all combinations of outputs in the multiple output case ) by a single firm minimizes cost It used to be that natural monopoly was simply defined as existing when the AC curve is everywhere downwardsloping relative to market demand ( economies of scale ) ( Baumol et al., 1970 ) introduced formally the notion of subadditive costs as a characteristic of natural monopoly Slide 3
2. 1 Natural monopoly regulation Economies of scale: definition Economies of scale are said to be present in production when unit (average) cost decreases as output increases. There are various explanations for the presence of economies of scale, such as: The existence of substantial fixed costs; Opportunities for specialization in the deployment of resources and A strong market position of factor inputs Slide 4
2. 1 Natural monopoly regulation: definitions Subadditivity: definition Consider a market for a homogeneous product where each of k firms produces output q i and total output is given by Q = qi k Each firm has an identical cost function C(q i ) Acording to technological or cost based definition, a natural monopoly will exist when: C(Q) < C(q 1) + C(q 2) +... + C(q k) Since it is less costly to supply output with a single firm. Firm cost functions that have this attribute are said to be subadditive at output level Q When firm cost functions for all values of Q, consistent with demand Q=D(q), then the cost function is said to be globally subadditive Slide 5
2. 1 Natural monopoly regulation: definitions According to this definition assume that firms i s cost function is defined as C i =F+cq i Than the firm s average cost of production AC i = (F/ q i )+c declines continuosly as its output expands. Price Cost P=D(Q) Q=q 1 +...+q n AC i =(F/ q i )+c c Quantity Slide 6
2. 1 Natural monopoly regulation: definitions Economies of scale: definition When a firm s average cost of production declines as its output expands its production technology is characterized by economies of scale In a single product case, economies of scale up to q i =Q is a sufficient condition but not a necessary condition for subadditivity over this range or, by technological definition, for natural monopoly It may still be less costly for output to be produced in a single firm rather than multiple firms even if output of a single firm has expanded beyond the point where there are economies of scale Slide 7
2. 1 Natural monopoly regulation: definitions Subadditivity and economies of scale One firm Two firms Price Cost P=D(Q) AC Price Cost Fig. 11.4 VVH AC 1 AC 2 MC q 1 q 2 Quantity Q 1 Q* Q 2 Q Slide 8
2. 1 Natural monopoly regulation: definitions Economies of scale and subadditivity There is a range of output ( Q<q 1 ) where there are economies of sale. After Q>q 1 the function flattens out and then enters a range of decreasing returns to scale However this cost function is still subadditive for some values of Q>q 1, despite there is decreasing returns to scale. This is the case because the market demand P=D(Q) is not large enough to support efficient production by two firms Slide 9
2. 1 Natural monopoly regulation: Definitions Economies of scope and subadditivity As figure 11.4 in the Viscusi et al. text illustrates, natural monopoly based on the subadditivity definition can occur even in a range of outputs for which there are diseconomies of scale in production (i.e., on the upwardsloping portion of the individual-firm AC curve). Thus the presence of economies of scale is sufficient (in the singleproduct case) but not necessary for the existence of natural monopoly. In the case of multiple products, the existence of economies of scale in the production of any one product is neither necessary nor sufficient (because of economies of scope in the production of multiple products). Slide 10
2. 1 Natural monopoly regulation: Definitions Multiproduct natural monopoly Most NM ( public utilities) produce more than one product and the interdependence among outputs becomes very important Economies of scope: definition Economies of scope are comparable to economies of scale but imply efficiency gains resulting from expansion of scope, or number of different output types, rather than from an increase in the volume of total output. Economies of scope exist when it is cheaper to produce two products together (joint production) than to produce them separately. Slide 11
2. 1 Natural monopoly regulation: Definitions Economies of scope When a firm produces two outputs, Q 1 and Q 2, economies of scope exist if the total cost function has the following structure C(Q 1,0)+C(Q 2,0)>C(Q 1,Q 2 ) Sources of economies of scope shared inputs shared advertising creating a brand name cost complementarities (producing one good reduces the cost of producing another) Slide 12
2. 1 Natural monopoly regulation: Definitions Economies of scope and subadditivity In the multiproduct case, product-specific scale economies is not a sufficient condition. Economies of scope is a necessary but not sufficient condition for subadditivity. One set of sufficient conditions for subadditivity of a multiproduct cost functions that it exhibit both economies of scope and declining average incremental cost for all products.. Slide 13
2. 1 Natural monopoly regulation: Natural monopoly: Fundamental conflict between productive and allocative efficiency Is natural monopoly productive efficient? Yes: Productive efficiency requires cost to be minimized Is natural monopoly allocative efficient No: A monopolist generates a deadweight loss by restricting output below the competitive level, since P M> MC Slide 14
2. 1 Natural monopoly regulation The natural monopoly regulation Solutions: Doing nothing Pricing solutions Linear pricing Marginal cost pricing Average cost pricing Non linear pricing or multipart tariff Ramsey pricing Slide 15
2. 1 Natural monopoly regulation : Pricing solutions with symmetric information Marginal cost pricing Efficient Marginal Cost Pricing: P 0 =C ( Q(P 0 )) Price Cost D P 0 Losses AC MC Firm ( NM ) is not able to break-even under the presence of fixed costs or economies of scale Q 0 Slide 16
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Problems with linear pricing Marginal cost pricing Outcome has allocative efficiency Weak incentive to reduce costs Firm does not cover costs and makes losses Use tax revenues or direct subsidy to firm to cover revenue shortfall? Govt need to raise new taxes to fund the subsidy The producer knows that revenue gap would always be funded Slide 17
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Average cost pricing Efficient Average Cost Pricing: P 0 =C( Q(P 0 ))/Q(P 0 ) Price Cost D P 0 AC MC The rule maximizes total welfare subject to the break-even constraint. Q 0 Slide 18
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Problems with linear pricing Average cost pricing Firm covers costs and earns economic profits Failure of allocative efficiency: less quantity and higher price than in MC pricing case ( but lower P and high quantity than profit maximization by NM) Weak incentives to reduce costs Deadweight loss Slide 19
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Non linear pricing Two-Part Tariff (1) A fixed fee, regardless of consumption, plus a marginal cost price per unit T(q)= A+Pq Non linear pricing than linear tariffs are more efficient Often used in the utility industries ( Telecom., Gas, Water, Electricity ) If the firm cost function is of the form: C(q)= K+cQ and consumers are homogeneous, then it would be optimal to set the two-part tariff with A*=K/N and P*=c Slide 20
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Non linear pricing Two-Part Tariff :T(q)= A+Pq T(q) P A 0 q Slide 21
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Two-Part Tariff (2) This argument breaks down when consumers are heterogeneous Consumers with low willingness to pay drop out of the market if K/N>CS(c ) When consumers are hetereogeneous, welfare maximizing nonlinear tariffs will most likely involving the firm offering consumers discriminatory two-part tariffs: Quantity discounts Multipart tariffs Self selecting tariffs Slide 22
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Increasing and declining block tariffs 0.50 0.40 0.30 0.20 0.50 0.40 0.30 0.20 100 200 300 100 200 300 kwh Increasing block rate Decreasing block rate Slide 23
2. 1 Natural monopoly regulation Multi-part tariff or self-selecting two part tariffs Total Expenditure 20 C D 10 B 5 A 100 200 Calls/month Slide 24
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Two-part tariff (3) What is the optimal two-part tariff? Trade-off: Efficiency losses because of exclusion of additional consumers when A raises Consumption losses as P increases marginal cost Optimal two-part tariffs generally involve a P that exceeds marginal cost and a fixed fee that excludes some consumers from the market The socially optimal (and discriminatory) two-part tariff will usually have an A" that excludes some consumers (failure of universal service) and a P" > MC (failure of allocative efficiency). Slide 25
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Pricing the multiproduct NM For multiproduct natural monopolist, MC pricing leads to negative profits. But if price for each product exceeds MC it can cover this shortfall, By how much? In the context of a multi-product monopolist, each product would have a linear price, and the set of prices would minimize deadweight social losses subject to the zero profit constraint. Slide 26
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information The Ramsey rule The Ramsey problem or Ramsey- Boiteux pricing is a policy rule concerning what price a monopolist should set in order to maximize social welfare subject to a constraint on profit. Ramsey found the result before ( 1927) in the context of the theory of taxation. The rule was later applied by M. Boiteux( 1956 ) to natural monopolies. Hence the Ramsey-Boiteux pricing consists into maximizing the total welfare under the condition of non-negative profit, that is, zero profit. In the Ramsey-Boiteux pricing, the markup of each commodity is also inversely proportional to the elasticities of demand but it is smaller as the inverse elasticity of demand is multiplied by a constant lower than 1. Slide 27
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information X X Y Y P 1 P 0 A B C D F P x P y P 0 G H I J 0 Q Q Q y Q x 0 0 Q 1 Q 0 Q Proportionate price increase Ramsey prices Slide 28
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information Ramsey Pricing Linear prices that satisfy the total revenues Equal total cost constraint and minimize the deadweight welfare losses P M C i i λ = P ε i i Factors limiting the use of Ramsey Pricing Redistributive concerns Regulatory capture Utility opportunism and non discriminatory rules Single cost recovery problem Slide 29