Question #$5$

$(Brueckner,5\mathrm{.}1)$ Suppose there are three potential users $of$ a freeway: Person $1,$ Person $2,$ and Person

Each individual has the following costs for their best alternative routes $to$ the freeway:

$a_1=$$$7$

$a_2=$$$5$

$a_3=$$$3$

The average cost $of$ using the freeway $as$ a function $of$ traffic volume $isas$ follows:

$AC(V=1)=$$$2$

$AC(V=2)=$$$5$

$AC(V=3)=$$$9$

$5\mathrm{.}1$ Find the equilibrium allocation $of$ traffic between the freeway and alternate routes.

$5\mathrm{.}2$ Compute the total commuting cost for all consumers for the following four allocations $of$ traffic.

Total cost $is$ the cost incurred $by$ the freeway users plus the cost incurred $by$ commuters who use

their alternate routes. $(Hint$: Remember the definition $of$ average cost.$)$

$5\mathrm{.}3$ Remember that the socially optimal allocation $of$ traffic between the freeway and alternate routes

$is$ the one that minimizes total commuting costs for all commuters. $On$ the basis $of$ your answer

for $5\mathrm{.}2,$ which allocation $is$ socially optimal? How does total cost $at$ the optimum compare with

total cost $at$ the equilibrium? $(Note$ that you don't need a marginal cost curve $to$ answer this

question.$)$