Pricing according to cost Cost-based pricing Cost of a service = - - PowerPoint PPT Presentation
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
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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
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= set of services = stand-alone cost of subset Economies of scale, scope: 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!!
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The firm sells to customers The charges are subsidy free if they satisfy: The stand-alone cost test The incremental cost test If these are violated, a new entrant can attract customers Imply
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In order to be subsidy-free, the revenues from product A1
and product A2 must satisfy A possible set of charges are (6, 7)
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= cost of producing quantities
is a support price for at if it satisfies: Price are subsidy-free for all sub-quantities of x Note that these imply economies of scale, Consumers have no incentives for bypass We also need
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Potential competition:
incumbent sets prices to cover costs, competitor tries to take part of the incumbent’s market by posting prices which are lower for at least one service
We say are sustainable prices if there is no and s.t.
Necessary conditions for sustainable prices
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Cost is to be fairly shared amongst customers. Charging algorithm: function
dividing
Problem: find that no customer can have a valid
argument against
If then customer is paying
more than he would if customer were not being served
He might argue this is unfair, unless customer can
argue that he’s just as disadvantaged because of :
Same reasoning if customer benefits from customer Unique : charge average incremental cost
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Three airplanes share a runway, require 1,2 and 3 km to
Problem: How to share the cost?
Order Adds cost 1 2 3 1,2,3 1 1 1 1,3,2 1 2 2,1,3 2 1 2,3,1 2 1 3,1,2 3 3,2,1 3 avg 2/6 5/6 11/6
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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
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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
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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
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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
cost of providing ONLY this service
fixed common cost A,B fixed cost A fixed cost B
IC(A)
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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
true fixed common cost FC A FC B
VC A
VC B
IC(A) common cost from accounting records A
B
C
FCC AB
FC C
VC C
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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
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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
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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
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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
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Two services A, B MC: Marginal cost IC: Incremental cost (short run) LRAIC: Long-run incremental cost, in general LRIC ≥ IC
common cost A,B fixed cost A fixed cost B
LRIC(A) ≈ IC(A) = FC(A) + VC(A) MC(A) = VC(A) LRIC+(A) = LRIC(A) + CC(A,B) x LRIC(A)/(LRIC(A)+LRIC(B) LRIC(A)+LRIC(B) < total cost Costs are computed per unit of the service A : average LRIC+(A)+LRIC+(B) = total cost
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MC AIC LRAIC+ FDC LRAIC+ SAC Low High LRAIC+
Which cost definition to use for regulation? In a competitive market MC, IC make more sense Low prices (LRIC) in wholesale of the incumbent help
competitors
High prices in retail (FDC) promote entry by competitors
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How do we compute incremental costs, variable costs? We need the cost function of the firm Usually directly attributable cost is a very small
percentage of the total cost
Need better understanding of the operation of the firm
and the causation of costs
=> the activity based model helps in “constructing” the
cost function and answering questions about the incremental cost of a service, the fixed costs associated with subsets of services, etc.
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Activity-Based Costing approach defines intermediate
activities that contribute to the production of end products
Each activity cost can be computed from accounting
information about the amounts of input factors that are consumed by each activity A large part of the common cost is attributed to the activities and so be subtracted from common cost
Refinement of the FDC approach: By reducing the
unaccounted-for common cost, it reduces the inaccuracy that stems from the ad-hoc cost splitting
Useful for LRIC+ approximations since it allows the
calculation of the incremental and fixed costs
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Bottom level: the input factors
consumed by the net operator, such as labor, power, cost of infrastructure and bandwidth
Activity level: processes that
must run in order for the network to operate and produce services. An activity has a well-defined purpose, such as the maintenance
management, the links’ operation
Next level defines the allocation of
the activity costs to the network elements such as routers, links
Service level: Services such as
calls, IP connectivity
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Bottom level: the input factors consumed by the net operator, such as labor, power, cost of infrastructure and bandwidth Activity level: processes that run in order for the network to operate. An activity has a well-defined purpose, such as the maintenance
management, the links’ operation Next level defines the allocation of the activity costs to the network elements such as routers, links Service level: e.g. phone calls
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Hides inefficiencies of the network provider (e.g. if a
network element is underutilized)
No incentive for the provider to improve his efficiency
unless he were only allowed to recover the cost of a network element in proportion to its actual utilization
Activity-based pricing is not really suitable for
determining the long run incremental cost of a service
If a service is not produced, the facility can be
reorganized to provide the remaining services at a lesser cost (long-run IC)
Nevertheless it provides some lower approximation
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Σςνεπγαζία με Σάνδπα Κοέν
Β N a n
........... ...........
Κοινό ενηόρ ηηρ Ππόζβαζηρ κόζηορ (ISFC- Increment Specific Fixed Cost)
Κοινό κόζηορ μεηαξύ ππόζβαζηρ και Γικηύος (FCC – Fixed Common Cost)
Κοινό ενηόρ ηος Γικηύος κόζηορ (ISFC- Increment Specific Fixed Cost) Δπιμέποςρ ςπηπεζίερ δικηύος Δπιμέποςρ ςπηπεζίερ ππόζβαζηρ b Α
Η κάθε ςπηπεζία είναι ένα Increment To Γίκηςο και η Ππόζβαζη είναι εςπύηεπα increments Μεηαξύ ηων ςπηπεζιών ηος δικηύος ςπάπσοςν κοινά κόζηη Μεηαξύ ηων ςπηπεζιών ηηρ ππόζβαζηρ ςπάπσοςν κοινά κόζηη Μεηαξύ ηων Increments ηος δικηύος και ηηρ ππόζβαζηρ ςπάπσοςν κοινά κόζηη
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Μεηαβληηό κόζηορ (IC) + Αναλογία κοινού ενηόρ ηος ζσεηικού increment κόζηοςρ (ISFC) + Αναλογία κοινού μεηαξύ ηων Increments κόζηοςρ (FCC)
ICΝι
........... ...........
Κοινό εντόρ τηρ Ππόσβασηρ κόστορ (ISFCΑ)
Κοινό κόστορ μεταξύ ππόσβασηρ και Δικτύος (FCC)
Κοινό εντόρ τος Δικτύος κόστορ (ISFCΝ) LRAIC+ σπηρεσίας
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Αναλογία κοινού ενηόρ ηος increment κόζηοςρ (ISFC)
ICΝι ........... ...........
Κοινό εντόρ τηρ Ππόσβασηρ κόστορ (ISFCΑ)
Κοινό κόστορ μεταξύ ππόσβασηρ και Δικτύος (FCC)
Κοινό εντόρ τος Δικτύος κόστορ (ISFCΝ)
ISFCNi ICNi ICNj
n
ISFCnetwork
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Αναλογίος κοινού μεηαξύ ηων Increments κόζηοςρ (FCC)
ICΝι
........... ...........
Κοινό εντόρ τηρ Ππόσβασηρ κόστορ (ISFCA)
Κοινό κόστορ μεταξύ ππόσβασηρ και Δικτύος (FCC)
Κοινό εντόρ τος Δικτύος κόστορ (ISFCN)
FCCNi ICNi ISFCNi ICNj ISFCN ICAj ISFCA
n
n
FCC
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Μεηαβληηό κόζηορ (IC) Αναλογία κοινού ενηόρ ηος increment κόζηοςρ (ISFC) Αναλογίος κοινού μεηαξύ ηων Increments κόζηοςρ (FCC)
........... ...........
Κοινό εντόρ τηρ Ππόσβασηρ κόστορ (ISFCΑ)
Κοινό κόστορ μεταξύ ππόσβασηρ και Δικτύος (FCC)
Κοινό εντόρ τος Δικτύος κόστορ (ISFCΝ)
LRAIC Ni ICNi ISFCNi FCCNi
ICΝι
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A factory produces souvenirs from wood and bronze The only factors directly attributed to the souvenirs
production are the amounts of wood and bronze and
Common cost: Other factors used in producing
souvenirs, such as the labor and electricity
A single accounting record for each, no info on how to
attribute these costs to the souvenirs production
Problem: How to define the cost of each product?
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FDC: We must find a way to split the common cost This approach can give prices that are far from being
subsidy-free
For instance, suppose we take
The bronze souvenirs cost that must be recovered is that is probably greater than the stand-alone cost for producing the same quantity
e l
e l FDC w
e l FDC b
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Incremental cost approach: computes the difference of
the cost of the facility that produces both types from the cost of the facility that produces a single type
Problems: accounting records hold only the actual cost
and must be evaluated
is greater than
inaccurate computation of
,
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scratch, by building models of fictitious facilities that specialize in the production of a given product
and tries to allocate the cost to the various products but attempt to reduce the unaccounted-for common costs
How? Refine the accounting information, by keeping more information on how common cost is generated
Use the activity-based model
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Formally, suppose service is produced in quantity and
has a variable cost that is directly attributable to that service. There is a shared cost that is attributable to all services. The price for the quantity
The price per unit is defined as
The s may be chosen in various ways: as proportions of revenue, variable costs, quantities supplied, or revenue, i.e., proportional to
Clearly, once the coefficients are defined, then the
construction of the prices is rather trivial and can be done automatically using accounting data
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Consider, as above, a facility that produces wooden and
bronze souvenirs, with the cost function where is the per unit cost of the fixed factor , is the per unit cost of the labor factor, are the per unit costs of wood and bronze respectively, the fixed amount of labor that is consumed independently of the production, and are coefficients that relate the levels of production of the artifacts to the amount of consumed labor that is directly attributed to the production, and and relate these levels
Note that
are fixed costs, whereas is the variable part of the cost
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Consider first the case of simple FDC pricing without
activity definitions and no explicit accounting info on how labor effort is spent
In this case
the common cost is the remaining part
and the FDC prices are of the form
b b b b w w w w
b b w w l l f f b w
l wyw byb
l wyw byb
(1) (2)
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Now suppose two activities defined, related to the
production of the artifacts. In each activity, there is exact accounting of the labor effort required for the production
and the common cost is reduced to The resulting FDC prices are
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l l f f b w
l l f f w w w w w l w w
l l f f w b b b b l b b
(3) (4)
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The prices in the simple FDC approach less accurately
relate prices to actual costs
Suppose,
i.e., wooden artifacts are extremely easy to construct and the greater part of labor effort is spent on bronze artifacts. Let there be equal sharing of the common cost, so Then the price of wooden artifacts in (1) subsidizes the production of bronze artifacts as it pays for a substantial part of the labor for making them This cross-subsidization disappears in (3)
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Suppose that the facility is built inefficiently and that the
amount of building space is larger than would be required if new technologies were used
This fact is hidden in both (1) and (3). However, if one
develops a bottom-up model for the facility, the corresponding factor in this model will be less, say This will reduce the corresponding prices in (3)
Thus with the activity-based approach one can trace the
reason for the price discrepancy between the top-down and the bottom-up model, as being due to the second term, and hence one can trace the inefficiency in the existing system
f
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Consider the price of wooden artifacts. The variable part
run incremental cost of producing the amount of wooden artifacts than the variable part in (1)
The reason that it may not be equal to the long-run
incremental cost is that if only one artifact is produced, then the common cost could be reduced (perhaps a smaller facility is needed, or one secretary will suffice rather than two). Unfortunately this reduction can’t be extracted from the accounting data
One must construct a `virtual' model of the facility
specialized in constructing only bronze artifacts, to subtract the corresponding total production costs
This again shows the weakness of the top-down
models that are the basis of FDC pricing
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