TCOM 546

1
TCOM 546

• Session 5

2
Overview

• Analyze access pricing
• Apply economic analyses to other telecom areas
• International settlements
• Spectrum

3
Two-Way Access Pricing

• Consider a duopoly of two regional monopoly
  companies A and B
• 2h customers subscribed to each company

A local
B local
A L-D
B L-D
4
Two-Way Access Pricing (Continued)

• Assume h customers of type H who are willing to
  pay bH for LD, and h of type L who are willing to
  pay bL
• Let pi be the price of an LD call from region i
  (i 1,2)
• Utility is then
• UH maxbH - pi, 0
• UL maxbL - pi, 0
• Assume bL lt bH lt 2bL

5
Two-Way Access Pricing (Continued)

• Let aAB denote access charge levied by company B
  terminating company A traffic, etc.
• Then profits are
• pA qA(pA aAB) qBaBA
• pB qB(pB aBA) qAaAB

6
The Access Pricing Game

• Interaction takes the form of a 2-stage extensive
  game
• Stage I Both companies set access prices
• Stage II Both companies take access prices as
  given and set LD prices
• Now qi 2h if piltbL
• h if bLltpiltbH
• 0 if pigtbH

7
The Access Pricing Game (Continued)

• So profits are
• pi 2h(bL aij) qjaji if pi bL
• h(bH aij) qjaij if pi bH
• qjaji if pi gt bH
• Note that setting pi bL gives a higher profit
  than bH if
• 2h(bL aij) gt h(bH aij) or
• aij lt 2bL - bH

8
The Access Pricing Game (Continued)

• Solve the game backwards
• In stage II, the access charges are taken as
  given, and pi is chosen to maximize profit
• pi bL if aij lt 2bL bH
• bH if 2bL bH lt aij lt bH
• aij if aij gt bH

9
The Access Pricing Game (Continued)

• In Stage I, each carrier sets its value for a
• Let pi be profit carrier i makes from
  terminating carrier j calls, so
• pi ajiqj
• Then
• pi 2h(2bL bH) if aji lt 2bL bH
• hbH if 2bL bH lt aji lt bH

10
The Access Pricing Game (Continued)

• Hence, carrier i will set access charge
• aji 2bL bH if bH lt 4bL/3
• bH if bH gt 4bL/3
• Next, calculate profit with these prices
• If bH lt 4bL/3, then aji 2bL bH and
• pi bL and qi 2h
• Then pi 2h(2bL bH ) and revenue from LD is
• 2h(bL- aij)
• But by symmetry aij aji, so
• pi 2h(2bL bH ) 2h(bL - aij) 2hbL

11
The Access Pricing Game (Continued)

• Similarly, if bH gt 4bL/3, then
• pi hbH
• Social welfare is calculated as
• W 2hUH 2hUL pA pB
• If bH lt 4bL/3 then aji 2bL bH
• so pa pb bL
• and UL 0 and UH bH - bL

12
The Access Pricing Game (Continued)

• In contrast, if bH gt 4bL/3 we find aji bH
• and UL UH 0
• Finally, social welfare is
• W 2h(bH bL) 2h0 4bL if bH lt 4bL/3
• 2h(bH bL) and
• W 4h0 2hbH if bH gt 4bL/3
• 2hbH

13
Access Pricing Conclusion

• Low access pricing where aji 2bL bH yields
  higher social utility than high access pricing
• Market failure occurs when bH gt 4bL/3
• That is, high valuation by high-income consumers
• Regulator should impose a ceiling of 2bL bH on
  access prices

14
Access Pricing Conclusion (Continued)

• Illustrates problem with partial regulation
  providers overcharge each other for access
• Artificially increases costs
• Induces carriers to raise consumer prices
• Not socially optimal

15
International Settlement Rates

• Revenues generated from international calls are
  collected in the country where the calls
  originate
• Generally, the richer country originates more
  calls than the poorer
• E.g, 1997 US to Brazil 495 million minutes,
  Brazil to US 159 million minutes
• Carriers use a negotiated settlement rate to
  balance accounts when there is an imbalance of
  calls

16
International Settlement Rates Model

• Simple models to compare situation where each
  country has a monopoly provider with the
  fully-competitive situation
• Assume two countries, N and S
• Country N has hN subscribers who wish to call
  country S, similarly for S
• Assume hN gt hS
• Let pk be price of call from country k

17
International Settlement Rates Model (Continued)

• Define consumer utility function
• Uk b pk if the consumer makes a call
• 0 otherwise
• Let a be the settlement rate
• Then ignoring production costs, profits are
• pN (pN a)hN ahS and
• pS (pS a)hS ahN

18
International Settlement Rates Model (Continued)

• Note that
• pN pNhN a(hS hN) and
• pS pShS a(hN hS)
• So increasing the settlement rate a decreases Ns
  profit and increases Ss profit

19
International Settlement Rates Model (Continued)

• Again we solve the model backwards
• First, the settlement rate is negotiated
• Then the companies take the settlement rate as
  given and set pN and pS independently, giving
• pk b if a lt b, which yields qk hk
• a if a gt b, which yields qk 0

20
International Settlement Rates Model (Continued)

• How is the settlement negotiated?
• If ak is the profit-maximizing rate for company
  k, assume companies agree to average the charges
• a (aN aS)/2
• b/2, so
• pN pS b/2

21
International Settlement Rates Model (Continued)

• This leads to
• pN pS b so that
• pN pS b(hN hS)/2
• Which yields a cash flow from N to S of
• a(hN hS) b(hN hS)/2
• Although N still makes a profit

22
International Settlement Rates with Competition

• Suppose internal markets are competitive
• Companies in both countries charge prices equal
  to marginal costs
• Then pN pS a, and pN ahS, pS ahN
• So, increasing a increases profit for all
  companies
• This is unlike the monopoly case (Chart 21)
• Hence, a b, the profit-maximizing rate

23
Spectrum Allocation

• Allocation of spectrum by means other than
  auctions is socially inefficient
• Consider lotteries, introduced in 1981 for
  cellular spectrum
• Previous method of determining by public
  interest was slow and unwieldy

24
Spectrum Lottery

• Assume one frequency to be allotted to one
  company
• Assume two competitors, A and B, with differing
  technologies
• Assume A has more advanced technology and can
  raise greater revenue
• I.e., rA gt rB gt 0
• Assume government is ignorant of which is better,
  but companies arent

25
Spectrum Lottery (Continued)

• Lottery is clearly inefficient, because the
  less-efficient company has even chance of
  winning, which is socially inefficient
• However, if winner can sell its rights, system
  becomes socially efficient
• However, rents are distributed to private sector,
  not government

26
Spectrum Auctions

• Open auction each company openly announces the
  maximum it is prepared to pay
• Nash equilibrium exists at (rB e, rB), where e
  is small
• Auction is efficient, but Government collects
  only rB e, not rA
• Remaining possible rA - rB e goes to A as extra
  profit

27
Other Forms of Auction

• Read Girard Simultaneous Ascending Auctions and
  the Federal Communications Commission Spectrum
  Auction 35 for a detailed discussion of more
  sophisticated forms of auction as used by the FCC

28
Next Week

• We will look quickly at the Internet and
  broadcasting, then move on to start discussing
  financial statement and cost models

29
Homework

• Read the Girard paper. List advantages and
  disadvantages of the FCCs auction approach.
  Would you describe the outcome as successful?
• Shy, Chapter 5, exercise 5
• Read Benninga, Chapter 1