The name is absent

13

Two-constraint demand systems have two expenditure functions dual to indirect
utility: one is the money expenditure function given the time budget and utility level, and
the other is the time expenditure function given money budget and utility. In the DS
system with two constraints on choice, the money expenditure function is

8 П ∖ Λ( M₁ Г    #! + !#зР0 .    !"4p⁰      ₈ r_r8"∣                ,ɔɔ,

/(p⁸,z,?) œ )(p,M) ∙ — e + ?e — 3 ∙ T⁸              (22)

which is similar to (5), with two major differences:

(a) the normalized prices p∏ in (5) are replaced by “full” prices p⁰ œ p∏ + 3⁸ ∙ t∏,
3⁸ is the normalized value of time,^$ and t₃⁸ ´ t3/<(t,T) and T⁸ ´ T/<(t,T) are time price
and time budget normalized by the deflator <(t,T), which is homogeneous of degree 1 in
(t,T);

(b) it has an additional term involving the normalized value of time and time
budget, — 3∏ ∙ T⁸.

The Hicksian and Marshallian demands are obtained from the two-constraint
money expenditure function (22) in the usual way, viz., by differentiating with respect to
money price and initializing the utility term in terms of full budget and full prices. The
functional form of the Marshallian demand system in (5) is unaffected, though the money
prices p₄^∏ and money budget M^∏ are replaced by full prices p₄⁰ and full budget M⁰.
Similarly, if the normalized shadow value of time is independent of budget arguments
(which satisfies the homogeneity requirements for it), the Hicksian and Marshallian
access values have the same functional form as (20) and (21), with M⁰ replacing M^∏.^%

Empirically, the marginal value of time can be treated in at least three ways. If
the individual is jointly choosing labor supply and recreation demands, the marginal
value of time is equated to an observable parameter (the marginal wage) which can be
used in its place (Becker; Bockstael et al.) The second is to identify it through auxiliary

<<   11   12   13   14   15   16   17   >>

More intriguing information