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TCOM 546

Session 5

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Overview• Analyze access pricing

• Apply economic analyses to other telecom areas– International settlements– Spectrum

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Two-Way Access Pricing

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

A local B localA L-D

B L-D

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Two-Way Access Pricing (Continued)

• Assume customers of type H who are willing to pay H for LD, and of type L who are willing to pay L

• Let pi be the price of an LD call from region i (i = 1,2)

• Utility is then

UH = max{H - pi, 0}

UL = max{L - pi, 0}

Assume L < H < 2L

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Two-Way Access Pricing (Continued)

• Let aAB denote access charge levied by company B terminating company A traffic, etc.

• Then profits are

A = qA(pA – aAB) + qBaBA

B = qB(pB – aBA) + qAaAB

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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 = 2 if pi<L

= if L<pi<H

= 0 if pi>H

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The Access Pricing Game (Continued)

• So profits are

i = 2(L – aij) + qjaji if pi = L

= (H – aij) + qjaij if pi = H

= qjaji if pi > H

Note that setting pi = L gives a higher profit than H if

2(L – aij) > (H – aij) or

aij < 2L - H

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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 = L if aij < 2L – H

= H if 2L – H < aij < H

= aij if aij > H

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The Access Pricing Game (Continued)

• In Stage I, each carrier sets its value for a– Let *i be profit carrier i makes from

terminating carrier j calls, so

*i = ajiqj

– Then

*i = 2(2L – H) if aji < 2L – H

= H if 2L – H < aji < H

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The Access Pricing Game (Continued)

• Hence, carrier i will set access chargeaji = 2L – H if H < 4L/3

= H if H > 4L/3• Next, calculate profit with these prices:

If H < 4L/3, then aji = 2L – H andpi = L and qi = 2Then *i = 2(2L – H ) and revenue from LD is 2L- aij)But by symmetry aij = aji, so i = 2(2L – H ) + 2Laij)2L

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The Access Pricing Game (Continued)

• Similarly, if H > 4L/3, then

i = H

• Social welfare is calculated as

W = 2UH + 2UL +pA + pB

• If H < 4L/3 then aji = 2L – H

so pa = pb = L

and UL = 0 and UH = H - L

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The Access Pricing Game (Continued)

• In contrast, if H > 4L/3 we find aji = H

and UL = UH = 0

• Finally, social welfare is

W = 2(H – L) + 2*0 + 4L if H < 4L/3

= 2(H + L) and

W = 4*0 + 2H if H > 4L/3

= 2H

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Access Pricing Conclusion

• Low access pricing where aji = 2L – H yields higher social utility than high access pricing

• Market failure occurs when H > 4L/3

– That is, high valuation by high-income consumers

• Regulator should impose a ceiling of 2L – H on access prices

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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

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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

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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 N subscribers who wish to call country S, similarly for S

• Assume N > S

• Let pk be price of call from country k

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International Settlement Rates Model (Continued)

• Define consumer utility function

Uk = – pk if the consumer makes a call

= 0 otherwise• Let a be the settlement rate• Then ignoring production costs, profits are

N = (pN – a)N + aS and

S = (pS – a)S + aN

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International Settlement Rates Model (Continued)

• Note that

N = pNN + a(S – N) and

S = pSS + a(N – S)

• So increasing the settlement rate a decreases N’s profit and increases S’s profit

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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 = if a < , which yields qk = k

= a if a > , which yields qk = 0

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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

= /2, so

pN = pS = /2

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International Settlement Rates Model (Continued)

• This leads to

pN = pS = so that

N = S = (N + S)/2

• Which yields a cash flow from N to S of

a(N – S) = (N – S)/2

– Although N still makes a profit

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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 N = aS, S = aN

• So, increasing a increases profit for all companies– This is unlike the monopoly case (Chart 21)– Hence, a = , the profit-maximizing rate

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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

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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., A > B > 0– Assume government is ignorant of which is

better, but companies aren’t

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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

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Spectrum Auctions

• Open auction – each company openly announces the maximum it is prepared to pay

• Nash equilibrium exists at (B + , B), where is small

• Auction is efficient, but Government collects only B + not A

– Remaining possible A - B + goes to A as extra profit

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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

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Next Week

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

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Homework

• Read the Girard paper. List advantages and disadvantages of the FCC’s auction approach. Would you describe the outcome as successful?

• Shy, Chapter 5, exercise 5

• Read Benninga, Chapter 1