Transcript Fully Distributed Cost Pricing, Ramsey Pricing, & Shapley

By:
Presented by:
D. Mark Kennet
Fadhila Al Faraj
David J. Gabel
Demonstrates how:
-
Fully Distributed Cost (FDC) prices,
- Ramsey-optimal prices,
Shapely prices,
- Standalone prices
Can be computed for a variety of baseline output levels using LECOM
(Local Exchange Cost Optimization Model)
Compares the properties of various public utility pricing schemes
in terms of their:
- Ability to prevent cross-subsidies
- Lead to price structures that are in the core
- Minimize welfare losses arising from departures from marginal cost
pricing
There are three primary types of facilities found in the local
exchange carrier's network:
a.
Local Loop: facilities that provide signaling and voice transmission path
between a central office and the customer station.
b.
Switch: connects a customer’s line to either another customer who is served
by the same switch or to an interface trunk.
c.
Trunk: carries the calls between central offices.
How LECOM operates:
a.
Determine a city dimension and a customer usage level from user data
b.
LECOM search for technological mix, capacity, & location of switches that
minimize the annual cost of production.
Ramsey requirement:
a.
b.
Demand elasticity
Marginal & stand-alone costs of different services
Hard to implement:
- The Interstate Commerce Commission reject it because it requires both
marginal cost and elasticity of demand to be quantified which is
overwhelming
-
Fairness issue in allocating prices e.g; multiproduct firm operates in a
competitive & non-competitive market, subscribes to the monopoly service art
not subsidizing other product
-
The revenue from the service must be less than its stand-alone cost
- Flat rate: residential customers are connected to the network and are
able to make an unlimited number of local calls within their local calling
area.
- The demand elasticity value is telling us how both demand for access to
the network and usage during the peak period declines when the price of
flat-rate residential service is increased.
FDC
- Objective: to account for principle of recovering cost from the various
products that use the input
- The relative output approach is to attribute to each output product those
costs which can be unambiguously attributed, as well as the percentage of
the common and joint cost according to the percentage of the common or
joint facility that each service uses
Ramsey Pricing to satisfy
𝜀𝑖
𝑃𝑗 − 𝑀𝐶𝑗
𝑃𝑖 − 𝑀𝐶𝑖
= 𝜀𝑗
,𝑖 ≠ 𝑗
𝑃𝑖
𝑃𝑗
𝑖
𝑃𝑖 𝑄𝑖 𝑃𝑖 − 𝐶 𝑄 𝑃
=0
Where;
𝑃𝑖 is the product price, 𝑄𝑖 is the quantity
𝑀𝐶𝑖 is the marginal cost, 𝜀𝑖 is I’s own price elasticity
Q is the vector of output, 𝐶 𝑄 𝑃
vector P
is the total cost at the price
For simplicity
𝑀𝐶𝑖 = [𝐶 𝑖, 𝐼 − 𝐶(0, 𝐼)]/𝑖
where I represents all products except i
Shapley Pricing
Objective: "fairness" in the sense that the price is a weighted average of
different measures of the incremental value of the service.
Shapley prices are computed by:
-
Arranging all possible orderings of the products of the firm
-
All orderings are assumed to be equally likely, so the average of all the
increments is taken to be the Shapley price.
and then, for the product in question, determine the incremental cost of
adding that product to the output vector in that order.
Shapley Pricing
𝑆 1
1
1
1
1
= 𝐶 1 +
[𝐶 12 − 𝐶 2 ] +
[𝐶 13 − 𝐶 3 ] +
[𝐶 14
4
12
12
12
1
1
1
−𝐶 4 ]+
[𝐶 123 − 𝐶 23 ] +
[𝐶 134 − 𝐶 34 ] +
[𝐶 124
12
12
12
1
− 𝐶 24 ] +
[𝐶 1234 − 𝐶 234 ]
12
Since marginal cost pricing is the economic "ideal" in that it maximizes
the sum of consumer and producer surplus, the approach is used as a basis
for welfare analysis of the other schemes.
There are two allocation rules
studied here:
*
a refers to allocating
switched access costs
to local and exchange
services according to
relative usage in the
FDC case and
allowing the Ramsey
rule to determine the
allocation in the
Ramsey case
*
b refers to allocating
the entire access cost
to local exchange in
the FDC case and
treating it as part of
the marginal cost of
local exchange in the
Ramsey case
Summarizing tables I-III data:
-
How many of the subsidy constraints (including the breakeven
constraint)
-
Each scheme violates in a given city
Adding the ranks across cities to come up with a list of schemes from
best to worst according to this notion of weak sustainability
The list ranking:
1.
2.
3.
4.
Shapley Pricing & Marginal Cost (tied)
FDC a
Ramsey b & FDC B (tied)
Ramsey a
Q: What are the welfare consequences in each of the cities simulated by each
pricing scheme?
A:
a.
Estimate a model of demand for toll exchange service, and uses the
estimates of price elasticity of demand for toll service along with
outside estimates of price elasticity of demand for local service to
analyze departures from optimal pricing.
b.
Simplifying assumption to answer:
1.
No cross-elasticity terms in the demand system for the four
telephone services
2.
𝑄𝑖 𝑃𝑖 =∝𝑖 𝑃𝑖 −𝜀
Where ∝𝑖 is a parameter which we compute by inverting the demand function
when price is equal to marginal cost
3.
The change in welfare:
𝜀𝑖
𝑄2 𝑖
∆𝑊𝑖 = 1/[∝ (𝜀𝑖 − 1)𝜀𝑖 ] [(
𝛼
(𝜀𝑖 −1)/𝜀𝑖
)
𝑄1 𝑖
− [(
𝛼
)(𝜀𝑖−1)/𝜀𝑖 − 𝐶𝑖 (𝑄2 𝑖 -𝑄1 𝑖 )
Where,
𝑄1 𝑖 is the baseline quantity of service t when price is equal to marginal cost
𝑄 2 𝑖 is quantity of service t when price is equal to the alternative price
By ranking pricing schemes within a city:
-
From least welfare loss to most
Sum those ranks
Results:
1.
2.
3.
Ramsey b
Ramsey a
Shapley, and FDC (tied)
* Analysis of
consumer surplus change relative to the marginal cost baseline
shows that while Ramsey pricing maximizes social welfare over the set of
schemes considered, only the Shapley approach results in subsidy-free
prices.
* The welfare loss minimizers are the predicted Ramsey pricing schemes.
* Overall best performer in terms of
subsidy-free pricing is the Shapley
approach where the Ramsey were poor.
* FDC pricing is more consistent with the outcome that would be observed
were entrants permitted to compete in competitive markets which one of
the primary goals of regulation is to emulate the outcome of competitive
markets.
* As the elasticity of
demand was constant, if the model were modified to
reflect elasticity increasing with prices, fewer violations would be observed.
(lack of information)
* Few of
the FDC prices were below the marginal cost of service. This
suggests that if regulators are to use FDC studies for providing guidance
on pricing, they should simultaneously evaluate if the prices exceed the
marginal cost of service