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Case 1:02-cv-01977-RPM

Document 92-8

Filed 03/09/2006

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Appendix D: A Dominant-Fringe Model of Favored and Disfavored CLECs
Consider a model with a dominant incumbent (Qwest) and a fringe supply (CLECs). The fringe supply consists of favored and disfavored competitors. Favored competitors pay a lower price to the incumbent than do disfavored competitors. The "residual demand" facing Qwest is given by
Y ( p ) = D( p) - Z ( p )

where D is the market demand curve and Z is the fringe supply curve. Suppose that Qwest faces a constant marginal cost equal to c . Qwest's profits are given by

Q = ( p - c)( D( p ) - Z ( p )) .
Denote by pQ the profit-maximizing price for Qwest, and by xQ the corresponding Qwest sales. Total sales are given by D = xQ + Z . Suppose further that demand and fringe supply are linear:
D = F - bp, Z = L + w ( p - m ) .

The parameter m represents the per-unit interconnection fee that Qwest charges CLECs. Substituting into Qwest's residual demand gives
x = ( F - L ) - ( b + w ) p + wm .

The standard profit maximization calculations ( MR = MC ) imply that

pQ =

( F - L ) + wm + c , 2 ( b + w) 2

xQ =

( F - L ) + wm - ( b + w) c .
2

FAVORED AND DISFAVORED CLECs

Suppose Qwest favors some competitors with better interconnection rates and the remaining competitors purchase at the standard rates. We can model this as an additional cost per unit faced by the disfavored CLECs:
m = m f + (1 - ) md

where 0 < 1 is the proportion of favored CLECs and m f < md .

Expert Report of John B. Hayes Appendix D

Case 1:02-cv-01977-RPM

Document 92-8

Filed 03/09/2006

Page 2 of 2

If the disfavored CLECs are charged a percentage markup 0 over the favored rate, this expression can be rewritten
m = u + (1 - )(1 + ) u ,

which simplifies to
m = u (1 + - )

where u denotes the per-unit interconnection fee for the favored CLECs. The term (1 + - ) scales unit cost in proportion to the percentage markup at the disfavored CLECs and the proportion of favored CLECs. Substituting this expression for m into Qwest's solutions for price and quantity we have: pQ =

( F - L ) + wu (1 + - ) + c , 2 ( b + w) 2
2

xQ =

( F - L ) + wu (1 + - ) - c ( b + w ) .

We are interested in how the equilibrium price and quantity sold by Qwest vary with and . The derivatives of xQ and pQ with respect to , are: dxQ d dpQ d
= =

wu (1 - ) , 2 wu (1 - ) . 2 (b + w)

Both of these expressions are non-negative because 0 < 1 . Thus xQ and pQ are increasing in

. An implication of this result is that Qwest's price and share of sales decline as is reduced.
The derivatives of xQ and pQ with respect to , are: dxQ d
dpQ d

=

- wu , 2

=

- wu . 2 ( b + w)

Both of these expressions are negative. Thus pQ and xQ are decreasing in the proportion of favored CLECs.

Expert Report of John B. Hayes Appendix D