Given the utility expression

$U_k=A_k-0\mathrm{.}05T_a-0\mathrm{.}04T_w-0\mathrm{.}02T_r-0\mathrm{.}01C$

where $T_a$ is the access time, $T_w$ is the waiting time, $T_r$ is the riding time, and $C$ is the out$-$

of$-$pocket cost.

a$)$ Apply the logit model to calculate the shares of the automobile mode $(A_k=\}$

$0\mathrm{.}005$ and a mass$-$transit mode $(A_k=-0\mathrm{.}05)$ if

b$)$ Estimate the patronage shift that would result from the doubling the bus out$-$

of$-$pocket cost.