ð
Þ
As the first step we construct the value associated with the actual
(observed) adjustment path (i.e., Wðx
0
Þ)representedbyEq.(3).The
first component of this equation (i.e.,
R
t ¼ t
t ¼ t
n
0
e
rt
gðxðtÞÞdt)calculates
the discounted payoff function (utility function) corresponding to the
actual (observed) development path fxðtÞ; t Aðt
Þg for which the
historical data is available. The utility function in our model represents
drivers' satisfaction and is defined as a function of the road
condition or the CCI. Since the CCI varies between 0 and 100, low
road quality represented by low CCI leads to low utility. However, our
interviews with highway engineers suggest that drivers' utility does
not scale linearly with the CCI (and thus the road quality) measure.
This is largely because CCI is defined so that it is most sensitive at its
upper range. In fact, the low values of CCI (quality slightly above 0.5)
are significantly lower than most drivers accept, and will result in
lower traffic. At very low levels, incremental improvements in CCI
will improve drivers’ utility at very small increments, while higher
values of CCI have larger marginal returns in improvement. We
therefore use a “utility multiplier” as a function of road quality (and
consequently of the CCI) so that we can capture this nonlinearity in
our model, using Eq. (8). Data on drivers' satisfaction with different
road qualities can help improve the qualitatively derived functional
form we use here.
0
; t
n