Pricing according to cost
Cost-based pricing Cost of a service = value of economic means used in order to provide the service Cost is a relative notion! Tariffs must cover some notion of cost related to service provisioning Cost definition different incentives Replacement of equipment, introduction of new technologies, encourage or deter entry, invest in sunk costs We investigate Theoretical aspects of cost-sharing Cost-based pricing in practice 2
Theories of cost-sharing
Prices based on cost N 1,2,..., n = set of services n T N c ( T ) = stand-alone cost of subset Economies of scale, scope: c ( T U ) c ( T ) c ( U ) The service provider must share the total cost of the services amongst the customers in a fair manner prices based on costs Stable under competition No incentives for bypass and self-production Solutions of bargaining games Not unique!! 4
Subsidy-free prices { x i } The firm sells to customers { p i } The charges are subsidy free if they satisfy: The stand-alone cost test p i x i c ( A ), A N i A The incremental cost test p i x i c ( N ) c ( N \ A ), A N i A If these are violated, a new entrant can attract customers p i x i c ( N ) Imply i N 5
Subsidy-free charge example A 1 = 2 A 2 = 1 c ( x , x ) 1 2 A A x A x A 12 = 10 12 1 1 2 2 In order to be subsidy-free, the revenues from product A 1 and product A 2 must satisfy 2 r ( A ) 12 , 1 r ( A ) 11 , r ( A ) r ( A ) 13 1 1 2 2 1 1 2 2 A possible set of charges are ( 6, 7) 6
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Support prices c ( x ) ( x , x ,..., x ) = cost of producing quantities 1 2 n p c ( x ) x is a support price for at if it satisfies: p y c ( y ), for all y x i i i N p z c ( x ) c ( x z ), for all z x i i i N Price are subsidy-free for all sub-quantities of x p x c ( x ) Note that these imply economies of scale, i i i N Consumers have no incentives for bypass D ( p ) x We also need 9
Sustainable Prices Potential competition : p incumbent sets prices to cover costs, competitor tries to p take part of the incumbent’s market by posting prices which are lower for at least one service p x p We say are sustainable prices if there is no and s.t. ' ' E p x c ( x ), and p p x x ( p , p ) for some i , and i i i i i N Necessary conditions for sustainable prices 1. must operate with zero profits 2. must produce at minimum cost 3. prices for all subsets of output must be subsidy free 10
Axiomatic cost sharing: Shapley value n Cost is to be fairly shared amongst customers. ( N ) ( 1 ( N ),..., n ( N )) Charging algorithm: function c ( N ) dividing Problem: find that no customer can have a valid argument against j ( N ) j ( N { i }) 0 j If then customer is paying more than he would if customer were not being served i i He might argue this is unfair, unless customer can j argue that he’s just as disadvantaged because of : i ( N ) i ( N { j }) j ( N ) j ( N { i }) j Same reasoning if customer benefits from customer i j ( N ) j ( N { i }) 0 Unique : charge average incremental cost 11
Sharing the Cost of a Runway Three airplanes share a runway, require 1,2 and 3 km to land. Cost = 1$/km. Problem: How to share the cost? Adds cost Order 1 2 3 1,2,3 1 1 1 1,3,2 1 0 2 2,1,3 0 2 1 2,3,1 0 2 1 3,1,2 0 0 3 3,2,1 0 0 3 avg 2/6 5/6 11/6 12
Pricing in Practice
The key principles for pricing In practice, we can identify some key principles Cost causation: service cost should be closely related to the cost of the factors consumed by the service Objectivity: the cost of the service should be related to the right cost factors in an objective way Transparency: the relation of the cost of the service to the cost factors should be clear and analytical Danger of leaving the biggest part of the cost, i.e., the common cost , unrecovered 14
Historic and current costs Historic cost: the actual amount paid to purchase the various factors (equipment, etc) Top-down models, such as FDC, use the historic costs found in the accounting records Current cost: the equipment cost if it were bought today Bottom-up models are naturally combined with current costs (the network model is built from scratch) The use of historic or current costs provides very different incentives to network service providers Examples: access service and interconnection prices 15
Definitions related to the cost function Direct cost: the part of the cost attributed solely to the particular service, ceases to exist if service is not produced Indirect cost: other cost related to the service provision Indirectly attributable cost: arises from the provision of a group of services and there is a logical way to specify the percentage of the cost that is related to the provision of each service Unattributable cost: cannot be divided straightforwardly amongst the services, -> common cost 16
Definitions related to the cost function Fixed cost: the sum of all factor costs that remain constant when the quantity of the service changes Variable cost: cost of those factors whose quantities depend on the amount of the service produced Is the cost of the building really a fixed cost? Depends on the time frame over which the firm is allowed to re-optimize its production capabilities Definition of the short-run incremental cost and the long-run incremental cost var. cost A • Stand alone cost (SAC) var. cost B IC(A) fixed cost A fixed cost B cost of providing ONLY this service fixed common cost A,B 17
Pricing in practice In practice , we lack a function that can tell us the cost of producing or not any given bundle of services. All we know is the current cost of various factors involved in production Common cost cannot be directly attributed to any particular service, so far as the accounting records show. Only a small part of the total cost concerns factors that can be are uniquely related to a single service This is a major problem when trying to construct cost-related prices A VC B C IC(A) B VC A common cost VC C FC B FC A from accounting records FC C FCC AB true fixed common cost 18
Methodologies for constructing prices The Fully Distributed Cost (FDC) approach: make each service pay for part of the common cost Problem: ad-hoc division of the common cost since the common cost is large, prices can be ``cooked’’ LRIC (or IC) (Subsidy-free prices): construct prices by calculating the long-run incremental cost of a service in a network designed to be forward looking Hard to compute the true long run incremental cost Needs bottom-up models of the network, current costs, modern equivalent assets Problem: The sum of the incremental costs of the services leaves some common cost unaccounted for 19
Methodologies for constructing prices (2) LRIC+ : add common cost to the LRIC prices in a proportional fashion Problem: prices not necessarily subsidy-free Better approximation of subsidy-free prices than FDC 20
The Fully Distributed Cost approach FDC divides the total cost that the firm incurs amongst the services that it sells All the cost of factors that are not uniquely identified with a single service go to a common cost pool (directly attributable costs) Next, one defines a way to split the common cost among the services 21
Various FDC Problems I. There is no reason that the prices constructed are in any sense optimal or have any stability property II. These prices hide potential inefficiencies of the network such as excess capacity, out-of-date equipment, bad routing, inefficient operation and resource allocation Here is where the refinement of the activity model helps. The definition of activities helps to link a larger part of the common cost to particular services, so improves the subsidy-free properties of the resulting pricing scheme 22
The LRIC, LRIC+ approach Two services A, B MC: Marginal cost IC: Incremental cost (short run) LRAIC: Long-run incremental cost, in general LRIC ≥ IC A : average Costs are computed per unit of the service var. cost A var. cost B fixed cost A fixed cost B common cost A,B LRIC(A)+LRIC(B) < total cost MC(A) = VC(A) LRIC+(A)+LRIC+(B) = total cost LRIC(A) ≈ IC(A) = FC(A) + VC(A) LRIC+(A) = LRIC(A) + CC(A,B) x LRIC(A)/(LRIC(A)+LRIC(B) 23
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