48
Pricing according to cost
Pricing according to cost
2
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
Theories of cost-sharing
4
Prices based on cost
= 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
è prices based on costs
Stable under competition
No incentives for bypass and self-production
Solutions of bargaining games
Not unique!!
�
N = 1,2,...,n{ }
�
T ⊆ N
5
The firm sells services in quantities 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
The corresponding prices are subsidy free
Subsidy-free prices
pixi ≤ c(A),∀i∈A∑ A⊆ N
�
pixi ≥ c(N) − c(N \ A),i∈A∑ ∀A ⊆ N
xi ,i = 1,…,n
�
pixi = c(N)i∈N∑
ri = pixi
6
Subsidy-free charge example
In order to be subsidy-free, the revenues from product A1 and product A2 must satisfy
A possible set of charges are (6, 7)
r1(A1x1)+ r2 (A2x2 ) = 132 ≤ r1(A1x1) ≤12, 1≤ r2 (A2x2 ) ≤11,
A12 = 10
A1x1 = 2 A2x2 = 1
7
8
9
Support prices = 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
�
D(p) = x
10
Sustainable Prices Potential competition:
incumbent sets prices to cover costs, competitor (E) 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 1. must operate with zero profits 2. must produce at minimum cost 3. prices for all subsets of output must be subsidy free
for some i, and
11
Axiomatic cost sharing: Shapley value 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
�
c(N), N ⊆ {1,…,n}
�
φ(N) = (φ1(N),...,φn (N))
�
φ j (N) −φ j (N −{i}) > 0
�
φi(N) −φi(N −{ j}) = φ j (N) −φ j (N −{i})
�
φ j (N) −φ j (N −{i}) < 0
�
φ
12
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?
Order Adds cost
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
Pricing in Practice
14
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
15
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
16
Types of cost from accounting 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
Un-attributable cost: cannot be divided straightforwardly amongst the services, -> common cost
17
Definitions related to the cost function Fixed cost (FC): the sum of all factor costs that remain
constant when the quantity of the service changes Variable cost (VC): cost of those factors whose
quantities depend on the amount of the service produced
total volume
varia
ble
cost
Fi
xed
co
st
1
1
marginal cost (MC)
18
Incremental cost concepts Short-Run Incremental Cost (SRIC): cost of providing a
variable amount of the service in the short run assuming that all other services are provided at the same levels (=VC)
Long-Run Incremental Cost (LRIC): cost difference of not providing the given service assuming that the facility provides the other services at the same levels as before but can re-optimize its operation (in the long-run), forward looking includes the direct fixed cost of the service
true fixed common cost
FC A FC B VC A
VC B LRIC(A) ≈
FCC AB FC C
VC C FC A
VC A SRIC(A) VC A
Note: cost(S-A) ≤ cost(S) – (VC(A)+FC(A)) hence LRIC(A) = cost(S)-cost(S-A) ≥ VC(A)+FC(A)
19
Stand-alone cost Stand-alone cost (SAC): The cost of building a facility
from scratch that provides the single service at the given quantity higher because no economies of scale and scope lower because optimized to offer this service
LRIC, SAC need bottom-up models to be correctly estimated
FCC(A,B,C)
FC A
VC A
FCC(A,B)
SAC(A) ≈
FCC(A,B,C)
FC A FC B VC A
VC B
FCC AB FC C
VC C
In practice we use top-down models
20
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
true fixed common cost
FC A FC B VC A
VC B
FCC AB FC C
VC C
indirect common cost from accounting records
A B C direct costs
21
Methodologies for constructing prices The Fully Distributed Cost (FDC) approach: make each
service pay for part of the (historic) 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 IC
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
22
Methodologies for constructing prices (2) LRIC+ : add common cost (or the cost that is not covered)
to the LRIC prices in a proportional fashion Reasonable approximation of subsidy-free prices since
LRIC(A) ≤ LRIC+(A) ≤ SAC(A)
Problem: prices not necessarily truly subsidy-free according to theory since we don’t analyze each possible subset of services
Better approximation than FDC since incremental cost is better approximated than just direct cost
Uses current costs instead of historic, bottom-up models, approximates prices in a competitive market
23
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
24
Evaluation of FDC § Advantages:
§ Covers total cost, easy to compute (top-down model) and audit, practical, covers past investments, transparency.
§ Disadvantages: § There is no reason that the prices constructed are in any sense
optimal (competitive) or have any stability property. They 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
25
The LRIC, LRIC+ approach Two services A, B LRAIC: Long-run average incremental cost
Costs are computed per unit of the service using a bottom up model
common cost A,B
fixed cost A fixed cost B
var. cost A var. cost B
LRIC(A) = FC(A) + VC(A) LRIC+(A) = LRIC(A) + CC(A,B) x LRIC(A)/(LRIC(A)+LRIC(B)
LRIC(A) + LRIC(B) < total cost
A : average variable cost if variable cost not linear
LRIC+(A) + LRIC+(B) = total cost
26
Evaluation of LRIC+ Prices promote the correct economic signals to the
network operator for improving efficiency Approximate better a competitive market But need bottom-up models which are harder to
implement Don’t necessarily cover the actual cost of the network
27
MC LRIC LRIC+ FDC SAC
Low High
Ordering of the various cost definitions 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
LRIC+ LRIC+
28
Practical approximations How do we compute fixed costs, variable costs, etc? Easier to use top-down models than bottom-up: use the
existing cost accounting records 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 to allocate indirect 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.
Allows in practice an approximation for the LRIC of services (within ≈15% of the bottom up calculations)
29
Activity-Based Costing approach Activity-Based Costing (ABC) 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 Þ 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
30
Activity-Based Costs (I) 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 of certain equipment, the network 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
31
Activity-Based Costs (II) 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
32
Συνεργασία µε Σάνδρα Κοέν
Εφαρµογή ABC, LRIC+ σε δίκτυα
Β N a n ........... ...........
Κοινό εντός της Πρόσβασης κόστος (ISFC- Increment
Specific Fixed Cost)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου (FCC – Fixed Common Cost)
Κοινό εντός του Δικτύου κόστος (ISFC- Increment Specific
Fixed Cost)
Επιµέρους υπηρεσίες δικτύου Επιµέρους υπηρεσίες πρόσβασης
b Α
Η κάθε υπηρεσία είναι ένα Increment To Δίκτυο και η Πρόσβαση είναι ευρύτερα increments Μεταξύ των υπηρεσιών του δικτύου υπάρχουν κοινά κόστη Μεταξύ των υπηρεσιών της πρόσβασης υπάρχουν κοινά κόστη Μεταξύ των Increments του δικτύου και της πρόσβασης υπάρχουν κοινά κόστη
33
Incremental cost (σταθ. + µετβλ.) υπηρεσίας (IC) + Αναλογία κοινού εντός του σχετικού increment κόστους (ISFC) +
Αναλογία κοινού µεταξύ των Increments κόστους (FCC)
ICΝι ........... ...........
Κοινό εντός της Πρόσβασης κόστος (ISFCΑ)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου (FCC)
Κοινό εντός του Δικτύου κόστος (ISFCΝ)
LRIC
+ υπηρεσίας
Εφαρµογή ABC, LRIC+ σε δίκτυα
34
Αναλογία κοινού εντός του increment κόστους (ISFC)
ICΝι ........... ...........
Κοινό εντός της Πρόσβασης κόστος (ISFCΑ)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου (FCC)
Κοινό εντός του Δικτύου κόστος (ISFCΝ)
�
ISFCNi =ICNi
ICNjn∑ ISFCnetwork
Εφαρµογή ABC, LRIC+ σε δίκτυα
35
Αναλογίου κοινού µεταξύ των Increments κόστους (FCC)
ICΝι ........... ...........
Κοινό εντός της Πρόσβασης κόστος (ISFCA)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου (FCC)
Κοινό εντός του Δικτύου κόστος (ISFCN)
�
FCCNi =ICNi + ISFCNi
ICNj + ISFCN + ICAj + ISFCAn∑
n∑ FCC
Εφαρµογή ABC, LRIC+ σε δίκτυα
36
Εφαρµογή ABC, LRIC+ σε δίκτυα
Σταθερό + µεταβλητό κόστος υπηρεσίας (IC) Αναλογία κοινού εντός του increment κόστους (ISFC) Αναλογίου κοινού µεταξύ των Increments κόστους (FCC)
........... ...........
Κοινό εντός της Πρόσβασης κόστος (ISFCΑ)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου (FCC)
�
LRICNi+ = ICNi + ISFCNi + FCCNi
ICΝι
Κοινό εντός του Δικτύου κόστος (ISFCΝ)
37
An application (1)
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?
38
An application (2) 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 Þ The bronze souvenirs cost that must be recovered is
that is probably greater than the stand-alone cost for producing the same quantity
39
An application (3) 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 hence inaccurate
computation of
40
Two solutions 1. Bottom-up approach: Construct and from
scratch, by building models of fictitious facilities that specialize in the production of a given product
2. Top-down approach: starts from the given cost structure 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
More on activity based costing and FDC
42
The FDC approach revisited 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
of service is defined to be its cost, i.e.,
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 or
Clearly, once the coefficients are defined, then the construction of the prices is rather trivial and can be done automatically using accounting data
43
FDC example (I) 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 of production to the amount of raw materials consumed
ü Note that are fixed costs, whereas is the variable part of the cost
�
c(yw,yb ) = s f x f + sl (x0l + αwyw + αb yb ) + swθwyw +sbθb yb ,
44
FDC Example (II) 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
�
pw (yw ) = swθwyw + γ w s f x f + sl x0l + αwyw + αb yb( )[ ]
�
pb (yb ) = sbθb yb + (1− γ w ) sf x f + sl x0
l + αwyw + αb yb( )[ ](1)
(2)
45
FDC Example (III) 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 of each artifact Now
and the common cost is reduced to
The resulting FDC prices are
(3)
(4)
46
Observations (I) 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 Þ 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 ü This cross-subsidization disappears in (3)
47
Observations (II) 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
48
Observations (III) Consider the price of wooden artifacts. The variable part
of the price in (3) is a better approximation of the long-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
