$($O$\text{'}$Sullivan$,10\mathrm{.}2)$ Consider the following table:

Volume

Trip Time

Increase in Travel Time per Driver Increase in Total Travel Time

External Trip Cost

Private Trip Cost

Social Trip Cost

Marginal Benefit $($demand$)$

$20012\mathrm{.}000003\mathrm{.}203\mathrm{.}2022\mathrm{.}1240012\mathrm{.}000003\mathrm{.}203\mathrm{.}2019\mathrm{.}6460012\mathrm{.}600\mathrm{.}0053\mathrm{.}000\mathrm{.}303\mathrm{.}263\mathrm{.}5617\mathrm{.}1680014\mathrm{.}000\mathrm{.}0097\mathrm{.}200\mathrm{.}723\mathrm{.}404\mathrm{.}1214\mathrm{.}68100016\mathrm{.}200\mathrm{.}01313\mathrm{.}001\mathrm{.}303\mathrm{.}624\mathrm{.}9212\mathrm{.}20120019\mathrm{.}200\mathrm{.}01720\mathrm{.}402\mathrm{.}043\mathrm{.}925\mathrm{.}969\mathrm{.}72140023\mathrm{.}000\mathrm{.}02129\mathrm{.}402\mathrm{.}944\mathrm{.}307\mathrm{.}247\mathrm{.}24160027\mathrm{.}600\mathrm{.}02540\mathrm{.}004\mathrm{.}004\mathrm{.}768\mathrm{.}764\mathrm{.}76180033\mathrm{.}000\mathrm{.}02952\mathrm{.}205\mathrm{.}225\mathrm{.}3010\mathrm{.}522\mathrm{.}28200039\mathrm{.}200\mathrm{.}03366\mathrm{.}006\mathrm{.}605\mathrm{.}9212\mathrm{.}52$

$2\mathrm{.}1$ What is the equilibrium traffic volume? What is the equilibrium trip cost cost?

$2\mathrm{.}2$ What is the socially optimal traffic volume? What is the socially optimal trip cost cost?

$2\mathrm{.}3$ For a social planner to implement the optimum traffic volume using a congestion tax, what would that tax be$?$

$2\mathrm{.}4$ Why does the equilibrium volume exceed the optimum volume?