October 1 st 2009, SoCal NEGT Symposium Welfare Effects of Spectrum - - PowerPoint PPT Presentation

October 1st 2009, SoCal NEGT Symposium

Welfare Effects of Spectrum Management Regimes

Ergin Bayrak

Scholar in Residence, Annenberg School for Communication Ph.D. Candidate, Department of Economics University of Southern California

BACKGROUND What is electromagnetic spectrum?

BACKGROUND What is electromagnetic spectrum? ..Colors of light Those we can see and those we can not ..can be utilized to carry information in the absence of physical wired connections by the use of modulation ..can be monetized

BACKGROUND What is electromagnetic spectrum? ..Colors of light Those we can see and those we can not ..can be utilized to carry information in the absence of physical wired connections by the use of modulation ..can be monetized

BACKGROUND What is electromagnetic spectrum? ..Colors of light Those we can see and those we can not Why is its management so important?

BACKGROUND What is electromagnetic spectrum? ..Colors of light Those we can see and those we can not Why is its management so important? You

20-20000Hz

Me

100-1000Hz

KCRW, KPFK, Clear Channel 88-107MHz

FOX, CNN, NBC

54-698Mhz

Cell Phone

850-1800-1900Mhz

Garage door opener

300-400Mhz

Wi-Fi/Bluetooth/Microwave 2.4-2.5GHz Baby monitor

49Mhz

Police radar

30GHz

BACKGROUND

BACKGROUND

BACKGROUND What to do with these white spaces ? Licensing Commons Exclusive Licenses Unlicensed Common Access ISSUES: Interference Incentives Competition Diversity Consumer Welfare

BACKGROUND Simple economics of resource allocation:

20 40 60 80 100

% allocated to Licensed Marginal Social Value MSV of Unlicensed Allocation Case1 MSV UL Allocation Case2 MSV of Licensed Allocation X

QUESTIONS What is the social value of incremental allocations? Is it commensurate under alternative management regimes? Is it sensitive to non-market considerations, particularly interference?

CHALLENGES Estimating welfare derived from unlicensed spectrum is challenging

• Used by numerous devices and services (NPV of use)
• Not traded in the usual sense

(expenditure) Estimating welfare derived from time intensive goods is challenging

• Market expenditure is miniscule compared to time use
• Time use and opportunity cost of time hard to observe

Incorporating interference and endogenous quality is challenging

• Aligning physics and economics of communication devices
• Spanning the ever increasing parameter space

CONTRIBUTIONS

A first back of the envelope estimate of welfare from unlicensed spectrum A first model of communications market incorporating interference

PART ONE

Estimate the welfare derived from the Internet by wired network owners Estimate the welfare derived from the Internet by wireless network owners

Difference can be attributed to unlicensed spectrum (lower bound)

PART ONE The time intensive nature of internet consumption: Market Exp. Time Wireless network owners 0.33% of Income 9.4% Wired network owners 0.33% of Income 9.7%

PART ONE

Home Network Composition

0.00% 5.00% 10.00% 15.00% 20.00% 25.00%

2004 2005 2006 2007 2008 2009 Year Home Networks Wireless Home Networks Wired/Wireless Mix Home Networks

MODEL Consumers

σ σ β β σ σ α α

θ θ

1 1 1 1

) )( 1 ( ) ( max

− − − −

− + =

• i

i

L C L C U s.t. Pi Ci + F + Po Co = W ( 1 – Li – Lo ) Let ) ( ) (

1 1 β β α α − −

= =

• i

i i

L C Y L C Y

β β α α

β β ρ α α ρ

− −

        −         =       −       =

1 1

1 1 W P W P

• i

i

MODEL Optimal Choices: ) / 1 1 ( ) 1 ( ∆ + − = ∆ + − =

• i

i

F W Y F W Y ρ ρ where

σ σ

θ θ ρ ρ       −         = ∆

− 1 1

• i

Breaking down the bundles

( ) ( )

W Y L W Y L P Y C P Y C

• i

i i

• i

i i i

ρ β ρ α ρ β ρ α − = − = = = 1 1

MODEL From

( )

) 1 ( 1 ∆ + − = − =

i i i i i

F W Y and W Y L ρ ρ α we have

i i

L L W F − − − = ∆ ) / 1 ( ) 1 ( α using the bundle prices and rearranging

σ σ α β σ α β β α

θ θ α β β α       −         − − = ∆

− − − − −

1 ) 1 ( ) / ( ) 1 ( ) / (

) 1 )( ( 1 1 1

W P P

• i

ESTIMATION

σ σ α β

θ θ α       − = − − −

− −

1 ) / 1 ( ) 1 (

) 1 )( (

W A L L W F

i i

Assuming small flat fixed fee for internet and taking logs       − + − − + =         − θ θ σ σ α β 1 ln ) ln( ) 1 ( ) ( ) ln( 1 ln W A L L

i i

ESTIMATION Time intensities ) 1 ( 1 ) 1 ( ) 1 ( 1 ) 1 (

• i
• i

i i i

L L L E E L L L E E − − + − = − − − + − = − β α

ESTIMATION

WELFARE Consumer Surplus measured as Equivalent Variation 1 1 1 1

1 1

−               −       ∆ + =

−

W F W EV

σ

Revoking the small flat fee assumption

( )

1 1

1 1

− − =

− − σ i

L W EV With linearized demand )) / 1 ( 1 ( 2 W F L L CS

i i

− − = σ

WELFARE Unlicensed spectrum does create considerable welfare

• n the order of $18billion (824*20% of Households)

PART TWO Given that the unlicensed allocations do result in considerable welfare, lets address the interference concern. Do unlicensed allocations lead to a tragedy of commons because of excessive interference?

MODEL There are M consumers with the utility function defined over the n varieties of devices as

2 2 1

) ( q T q T q T q q U

j j i i i j i i i i n i

+ − − =

∑ ∑ ∑

< =

γ qi Quantity Ti Quality 0 <γ < 2 Substitutability q0 Homogenous numeraire Following standard utility maximization leads to inverse demand:

j j i j i i i i

T q T T q p

∑

≠

− − = γ

2

2 1

MODEL Quality:

C e T

i

d i

) 1 (

−

− =

di Design / robustness of devices C Shannon’s Law (Shannon-Hartley Theorem)

Considering all possible multi-level and multi-phase encoding techniques, the Shannon–Hartley theorem states that the theoretical maximum rate of clean (or arbitrarily low bit error rate) data that can be sent with a given average signal power S through a communication channel of bandwidth W subject to additive white Gaussian noise of power N, is:

      + ⋅ = N S W C 1 log2

MODEL Quality:

      + − =

− ε

Nm S W e n N S w W d T

i

d i i

1 log ) 1 ( ) , , , , | (

2

W Bandwidth of a white space (6Mhz) S Base signal power N Base noise power m Number of firms per channel ε Interference elasticity di Design K(di) Cost of design

) 1 ( − −

i d

d e

i

MODEL Timing: Given the number and bandwidth of white spaces and the management regime First stage: Firms choose device design di Second stage: Firms compete in device market a la Cournot

MODEL Working backwards: Last stage:

F d K q T q T T q M

i i j j i j i i i i q i

− −         − − =

∑

≠

) ( 2 1 max

2

γ π

implies the equilibrium quantities and prices

b a T aT T q

j n j i i c i

      ∑ − =

=1

γ

b a T T aT p

i j n j i c i

      ∑ − =

=1

2 γ

Where

)] 1 ( 4 [ − + = n a γ

and

) 4 ( γ − = b

MODEL First stage profit in terms of qualities (design)

( )

F d K b a T T a M d d

i j n j i j i i di

− −       ∑ − =

=

) ( 2 ) | ( max

2 2 1

γ π

where

      + − =

− ε

Nm S W e T

i

d i

1 log ) 1 (

2

MODEL Substituting quality and taking the FOC:

i e e e b a a MC e e b a a MC

i j i i i

d d i j d d d

∀ − = − − + − −

− ≠ − − −

∑

1 ) 1 ( ) ( 4 ) 1 ( ) ( 4

2 2 2 2 2 2 2

γ γ γ

Solving the fixed point of the BR correspondence gives optimal design:

        − − + − + = ) 4 ( )] 1 ( 4 [ )] 2 ( 4 [ 4 ln 2 1

2 2

γ γ γ n n MC dc

CHARACTERIZATION

      + − =

− ε

Nm S W e T

c

d c

1 log ) 1 (

2

)] 1 ( 4 [

2

− + = n T q

c c

γ )] 1 ( 4 [ 2 − + = n pc γ F d e n MT

i d c c

i

− − − − − + = ) 1 ( )] 1 ( 4 [ 2

2 2

γ π         −         − −         − =

c c c c c c c c

q p T q n T q q M n n CS

2 * 2 * *

2 ) 1 ( ) ( γ

SIMULATION Licensing regime: n = w Commons regime: n ⇐ zero profit

{ }

90 , 80 , 70 , 60 , 50 , 40 , 30 , 20 , 10 , ) ( = dB N S

{ }

9 . 1 , 7 . 1 ,..., 5 . , 3 . , 1 . = γ

{ }

2 , 8 . 1 ,..., 6 . , 4 . , 2 . = ε

w = 10 W = 6 x 106 Hz (6MHz) M = 1

SIMULATION Simulation algorithm in pseudo-code

RESULTS

Consumer Surplus at 0dB Native SNR

RESULTS

Consumer Surplus at 10dB Native SNR

RESULTS

Consumer Surplus at 20dB Native SNR

RESULTS

Consumer Surplus at 30dB Native SNR

RESULTS

Consumer Surplus at 40dB Native SNR

RESULTS

Consumer Surplus at 50dB Native SNR

RESULTS

Consumer Surplus at 60dB Native SNR

RESULTS

Consumer Surplus at 70dB Native SNR

RESULTS

Consumer Surplus at 80dB Native SNR

RESULTS

Consumer Surplus at 90dB Native SNR

RESULTS

Boundary of Consumer Surplus Dominance

CONCLUSION We have shown that unlicensed allocations do create welfare and can not be disregarded as has been done in the earlier debates on spectrum management. We have shown that although interference degrades quality, it can lead to higher consumer surplus if the degradation is a result of differentiation. Tragedy of commons is not particularly suitable to justify licensed allocations. All future allocations should be guided by marginal social value criterion and should be informed by consumer preferences and technological environment.

Thank You! Ergin Bayrak ebayrak@usc.edu