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
= stand-alone cost of subset T ⊆ N




services
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!!
4
Subsidy-free prices



The firm sells services in quantities xi ,i = 1,…,n
The charges ri = pi xi are subsidy free if they satisfy:
The stand-alone cost test
∑px
i i
≤ c(A), ∀A ⊆ N
i∈A

The incremental cost test
∑p x
i
i
≥ c(N) − c(N \ A), ∀A ⊆ N
i∈A

If these are violated, a new entrant can attract customers

Imply
∑p x
i
i
= c(N)
i∈N

The corresponding prices are subsidy free
5
Subsidy-free charge example
A1 x1 = 2
A2 x2 = 1
A12 = 10

In order to be subsidy-free, the revenues from product A1
and product A2 must satisfy
2 ≤ r1 (A1 x1 ) ≤ 12, 1 ≤ r2 (A2 x2 ) ≤ 11, r1 (A1 x1 ) + r2 (A2 x2 ) = 13

A possible set of charges are (6, 7)
6
7
8
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
9
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.
for some i, and

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




Cost is to be fairly shared amongst customers.
Charging algorithm: function φ (N) = (φ1 (N),..., φ n (N))
dividing c(N), N ⊆ {1,…,n}
Problem: find
that no customer can have a valid
argument against
If φ j (N) − φ j (N − {i}) > 0 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 :
φ i (N) − φ i (N − { j}) = φ j (N) − φ j (N − {i})


Same reasoning if customer
benefits from customer
φ j (N) − φ j (N − {i}) < 0
Unique φ : 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
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
16
Definitions related to the cost function
Variable cost (VC): cost of those factors whose
quantities depend on the amount of the service produced
marginal
cost (MC)
variable
cost

Fixed cost (FC): the sum of all factor costs that remain
constant when the quantity of the service changes
1
1
Fixed
cost

total volume
17
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 reoptimize its operation (in the long-run), forward looking
  includes the direct fixed cost of the service
LRIC(A) ≈
VC B
VC A
FC A
FC B
FCC AB
VC C
FC C
true fixed common cost
VC A
SRIC(A)
VC A
FC A
Note: cost(S-A) ≤ cost(S) – (VC(A)+FC(A))
hence LRIC(A) = cost(S)-cost(S-A) ≥ VC(A)+FC(A)
18
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
VC A
VC B
VC A
FC A
SAC(A) ≈
VC C
FC B
FCC AB
FC C
FCC(A,B,C)
FC A
FCC(A,B)
FCC(A,B,C)
In practice we use top-down models
19
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
direct costs
C
B
indirect common cost
from accounting records
A
VC B
VC A
FC A
FC B
FCC AB
VC C
FC C
true fixed common cost
20
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
21
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
22
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
23
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
24
The LRIC, LRIC+ approach


Two services A, B
LRAIC: Long-run average incremental cost
A : average variable cost if variable cost not linear

Costs are computed per unit of the service using a
bottom up model
var. cost A
fixed cost A
var. cost B
fixed cost B
common cost A,B
LRIC(A) + LRIC(B) < total cost
LRIC+(A) + LRIC+(B) = total cost
LRIC(A) = FC(A) + VC(A)
LRIC+(A) = LRIC(A) + CC(A,B) x LRIC(A)/(LRIC(A)+LRIC(B)
25
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
26
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
MC
Low
LRIC
LRIC+
LRIC+
FDC
LRIC+
SAC
High
27
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)
28
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
29
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
30
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
31
Εφαρµογή ABC, LRIC+ σε δίκτυα
Επιµέρους υπηρεσίες δικτύου
Α
Β
...........
N
Κοινό εντός του Δικτύου κόστος
(ISFC- Increment Specific
Fixed Cost)
Συνεργασία µε
Σάνδρα Κοέν
Επιµέρους υπηρεσίες πρόσβασης
a
...........
b
n
Κοινό εντός της Πρόσβασης
κόστος (ISFC- Increment
Specific Fixed Cost)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου
(FCC – Fixed Common Cost)
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
32
Εφαρµογή ABC, LRIC+ σε δίκτυα
LRIC+ υπηρεσίας
Incremental cost (σταθ. + µετβλ.) υπηρεσίας (IC) +
Αναλογία κοινού εντός του σχετικού increment
κόστους (ISFC) +
Αναλογία κοινού µεταξύ των Increments κόστους
(FCC)
ICΝι
...........
Κοινό εντός του Δικτύου κόστος
(ISFCΝ)
...........
Κοινό εντός της Πρόσβασης
κόστος (ISFCΑ)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου
(FCC)
33
Εφαρµογή ABC, LRIC+ σε δίκτυα

Αναλογία κοινού εντός του increment κόστους (ISFC)
ICNi
ISFCNi =
ISFCnetwork
∑ ICNj
n
ICΝι
...........
Κοινό εντός του Δικτύου κόστος
(ISFCΝ)
...........
Κοινό εντός της Πρόσβασης
κόστος (ISFCΑ)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου
(FCC)
34
Εφαρµογή ABC, LRIC+ σε δίκτυα

Αναλογίου κοινού µεταξύ των Increments κόστους (FCC)
FCCNi =
ICΝι
∑
n
ICNi + ISFCNi
FCC
ICNj + ISFCN + ∑ ICAj + ISFCA
...........
Κοινό εντός του Δικτύου κόστος
(ISFCN)
n
...........
Κοινό εντός της Πρόσβασης
κόστος (ISFCA)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου
(FCC)
35
Εφαρµογή ABC, LRIC+ σε δίκτυα



Σταθερό + µεταβλητό κόστος υπηρεσίας (IC)
Αναλογία κοινού εντός του increment κόστους (ISFC)
Αναλογίου κοινού µεταξύ των Increments κόστους (FCC)
ICΝι
...........
Κοινό εντός του Δικτύου κόστος
(ISFCΝ)
...........
Κοινό εντός της Πρόσβασης κόστος
(ISFCΑ)
Κοινό κόστος µεταξύ πρόσβασης και Δικτύου
(FCC)
LRICNi+ = ICNi + ISFCNi + FCCNi
36
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?
37
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
38
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
39
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
40
More on activity based costing and
FDC
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
42
FDC example (I)

Consider, as above, a facility that produces wooden and
bronze souvenirs, with the cost function
c(y w , y b ) = s f x f + sl (x 0l + α w y w + α b y b ) + swθ w y w +sb θ b y b ,
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
43
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 (y w ) = s θ w y w + γ w s x + s ( x + α w y w + α b y b )
w
f
[
f
l
l
0
] (1)
]
pb (y b ) = sbθ b y b + (1 − γ w ) s f x f + sl ( x 0l + α w y w + α b y b ) (2)
44
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)
45
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)
46
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
47
Observations (III)

Consider the price of wooden artifacts. The variable part
of the price in (3) is a better approximation of the longrun 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
48
models that are the basis of FDC pricing