Problem $2[16$ points total$]$ Imagine a suburb called Tusville that is connected to the nearby city

of Irving by $2$ roads: route $1$ and route $2.$ Route $1$ is shorter but it gets congested. If the number

of cars on a road is relatively low, drivers can drive at free flow speed $($speed limit$),$ but as traffic

builds up$,$ speed goes down and it takes longer to reach Irving from Tusville as shown on Fig. $1$:

Figure $1.$ Time per commuter on Route $1.$

Route $2$ is newer, wider so it does not get congested, but without congestion on Route $1$ it takes

longer to drive between Tusville and Irving on Route $2(30$ minutes$).$

For simplicity, we assume that every commuter on route $1$ spends the same amount of time

commuting. It is useful to express the time cost in monetary terms $($as shown on Figure $1).$ This

dollar cost per commuter is like an average cost function where the output is the number $N_1$ of

trips from Tusville to Irving. Total cost $TC{C}_1$ is then $N_1$ times the average cost of one commuter

as given by Figure $1.$

Conversely, the commuting cost for each commuter on Route $2$ is $$5\mathrm{.}00.$ If $N_2$ commuters select

Route $2,$ the total cost of the $30$ minutes commute is $TC{C}_2=$$${5\mathrm{.}00}^{**}{N}_2$ and the marginal cost is

$$5\mathrm{.}00.$

$2\mathrm{.}1[4$ points$]$ Let us suppose that every weekday morning $5000$ residents of Tusville hop into

their cars and drive to work in Irving. In equilibrium, how many commuters will choose each

route?

$2\mathrm{.}2[6$ points$]$ On a graph with $2$ vertical axes, one at $0($for $TC{C}_1)$ where $N_1$ increases from left

to right, and another at $5000($for $TC{C}_2)$ where $N_2$ increases from right to left, graph $TC{C}_1,$

$TC{C}_2,$ and $TCC=TC{C}_1+TC{C}_2.$ Make sure to nicely label each axis. Show your answer to $2\mathrm{.}1$ and

briefly explain.

$2\mathrm{.}3[6$ points$]$ Find the equilibrium if instead of $5000$ commuters there are $3000.$ Then redo for

$4000,$ and finally for $6000.$Problem $2[16$ points total$]$ Imagine a suburb called Tusville that is connected to the nearby city

of Irving by $2$ roads: route $1$ and route $2.$ Route $1$ is shorter but it gets congested. If the number

of cars on a road is relatively low, drivers can drive at free flow speed $($speed limit$),$ but as traffic

builds up$,$ speed goes down and it takes longer to reach Irving from Tusville as shown on Fig. $1$:

F$1$gure $1.$ Iime per commuter on Koute $1.$

Route $2$ is newer, wider so it does not get congested, but without congestion on Route $1$ it takes

longer to drive between Tusville and Irving on Route $2(30$ minutes$).$

For simplicity, we assume that every commuter on route $1$ spends the same amount of time

commuting. It is useful to express the time cost in monetary terms $($as shown on Figure $1).$ This

dollar cost per commuter is like an average cost function where the output is the number $N_1$ of

trips from Tusville to Irving. Total cost $TC{C}_1$ is then $N_1$ times the average cost of one commuter

as given by Figure $1.$

Conversely, the commuting cost for each commuter on Route $2$ is $$5\mathrm{.}00.$ If $N_2$ commuters select

Route $2,$ the total cost of the $30$ minutes commute is $TC{C}_2=$$${5\mathrm{.}00}^{**}{N}_2$ and the marginal cost is

$$5\mathrm{.}00.$

$2\mathrm{.}1[4$ points$]$ Let us suppose that every weekday morning $5000$ residents of Tusville hop into

their cars and drive to work in Irving. In equilibrium, how many commuters will choose each

route?

$2\mathrm{.}2[6$ points$]$ On a graph with $2$ vertical axes, one at $0($for $TC{C}_1)$ where $N_1$ increases from left

to right, and another at $5000($for $TC{C}_2)$ where $N_2$ increases from right to left, graph $TC{C}_1,$

$TC{C}_2,$ and $TCC=TC{C}_1+TC{C}_2.$ Make sure to nicely label each axis. Show your answer to $2\mathrm{.}1$ and

briefly explain.

$2\mathrm{.}3[6$ points$]$ Find the equilibrium if instead of $5000$ commuters there are $3000.$ Then redo for

$4000,$ and finally for $6000.$