Question $\backslash$#$2$

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

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Increase $\backslash \backslash$

in Travel

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Increase in $\backslash \backslash$

Time per $\backslash \backslash$

Total Travel $\backslash \backslash$

Driver

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Time $\backslash \backslash$

External $\backslash \backslash$

Trip $\backslash \backslash$

Cost

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Private $\backslash \backslash$

Trip $\backslash \backslash$

Cost

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Social $\backslash \backslash$

Trip $\backslash \backslash$

Cost

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Marginal $\backslash \backslash$

Benefit $\backslash \backslash$

$($demand$)$

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Volume $\backslash \backslash$

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Time

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$\backslash$hline $200$ & $12\mathrm{.}00$ & $0$ & $0$ & $0$ & $3\mathrm{.}20$ & $3\mathrm{.}20$ & $22\mathrm{.}12\backslash \backslash$

$400$ & $12\mathrm{.}00$ & $0$ & $0$ & $0$ & $3\mathrm{.}20$ & $3\mathrm{.}20$ & $19\mathrm{.}64\backslash \backslash$

$600$ & $12\mathrm{.}60$ & $0\mathrm{.}005$ & $3\mathrm{.}00$ & $0\mathrm{.}30$ & $3\mathrm{.}26$ & $3\mathrm{.}56$ & $17\mathrm{.}16\backslash \backslash$

$800$ & $14\mathrm{.}00$ & $0\mathrm{.}009$ & $7\mathrm{.}20$ & $0\mathrm{.}72$ & $3\mathrm{.}40$ & $4\mathrm{.}12$ & $14\mathrm{.}68\backslash \backslash$

$1000$ & $16\mathrm{.}20$ & $0\mathrm{.}013$ & $13\mathrm{.}00$ & $1\mathrm{.}30$ & $3\mathrm{.}62$ & $4\mathrm{.}92$ & $12\mathrm{.}20\backslash \backslash$

$1200$ & $19\mathrm{.}20$ & $0\mathrm{.}017$ & $20\mathrm{.}40$ & $2\mathrm{.}04$ & $3\mathrm{.}92$ & $5\mathrm{.}96$ & $9\mathrm{.}72\backslash \backslash$

$1400$ & $23\mathrm{.}00$ & $0\mathrm{.}021$ & $29\mathrm{.}40$ & $2\mathrm{.}94$ & $4\mathrm{.}30$ & $7\mathrm{.}24$ & $7\mathrm{.}24\backslash \backslash$

$1600$ & $27\mathrm{.}60$ & $0\mathrm{.}025$ & $40\mathrm{.}00$ & $4\mathrm{.}00$ & $4\mathrm{.}76$ & $8\mathrm{.}76$ & $4\mathrm{.}76\backslash \backslash$

$1800$ & $33\mathrm{.}00$ & $0\mathrm{.}029$ & $52\mathrm{.}20$ & $5\mathrm{.}22$ & $5\mathrm{.}30$ & $10\mathrm{.}52$ & $2\mathrm{.}28\backslash \backslash$

$2000$ & $39\mathrm{.}20$ & $0\mathrm{.}033$ & $66\mathrm{.}00$ & $6\mathrm{.}60$ & $5\mathrm{.}92$ & $12\mathrm{.}52$ & $\backslash \backslash$

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$2\mathrm{.}1$ 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?