Car Ownership? Evidence from the Copenhagen Metropolitan Area

The extension of the metro network implies that the values of two variables change: and
. If the house price adjusts to a new equilibrium , will also change. We will denote these
changes as ∆ , ∆ and ∆ , , respectively. All other characteristics of the alternatives
remain constant.
We will first look at the compensating variation conditional upon the choice of a
particular alternative. That is, we want to compute the change in income that is necessary to
maintain a given level of utility after the extension of the metro network has been realized. To be
able to do this, we recall that all the coefficients in (A1) are linear functions of the logarithm of
income as specified for the ’s in (10), which we repeat here as:
ln ∑
(A2)
While similar equations hold for the other coefficients. Substitution of these equations in (A1)
and rearranging terms allows us to rewrite (A1) as:
,, , , , , , , ; ,
ln ln ln ,
(A3)
, ln
The second line of (A3) gives the cross terms of log income and the variables that change due to
the extension of the metro network; the third line collects the terms that are linear in these
variables or in log income and the terms in which neither of these variables occur.
The change in log income, ∆ln ,, that keeps the utility of a household in , ,
constant after the extension of the metro network can now be determined as:
∆ln ,, ∆ ∆ ∆ ,
,
(A4)
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