10
parameter ranges (a) and (d), where sgn(#3) œ sgn("3), the model has finite “choke”"
prices and access values, similar to the linear demand system or the LES system with
negative subsistence quantities. For parameter range (b), it resembles the semilog
demand system and the AIDS or Constant Elasticity systems with own price-elastic
demands, in that the “choke” price is infinite but access value is always finite. For range
(c), the model resembles the LES system with positive subsistence quantities in that
demand converges to a positive quantity as own price goes infinite.#
Choke Prices
When finite [i.e., when sgn("3) œ sgn(#3)], the normalized Hicksian choke price sp38 is
defined implicitly as
8 8∏ , 4 8 ∕l'√ ∣√-1 1 #!+!#5p5 8 /ʌ8 , √∙l ι !"4p4 z4 , 4
x32(P3 β p—3,z,?) œ — #3e#3(p3 p3 )e 5 + "3>∕ep p3 )e4 ´ 0, (15)
where sgn("3) œ sgn(#3). The Hicksian demand now depends explicitly on the vector of
qualitiesz œ (zι,...,zn) at different sites since the price coefficients #4 œ #4! + #4D ■ z4
depend on quality. Using the indirect utility function (3) evaluated at initial prices p80
and M8 to identify the utility index ?, the choke price Pp3 can be written explicitly in
terms of observables as
p8 œ p + #ih.
Mn-x!/#3
M"-X!/"3
(16)
#!+!#4p48!
where x! œ ("3 — #3)e + "3M8 is the Marshallian demand at initial prices.
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