Suppose there are 3 potential users of a freeway: Mr. 1, Mr. 2, and Mr. 3. The cost of the best alternative route for each commuter is as follows:

Commuter Alternate Cost (ga)

Mr.1 $7

Mr.2 $5

Mr.3 $3

The average cost AC of using the freeway (i.e., the cost per car) as a function of traffic volume T is as follows:

T Average Cost (AC)

1 $2

2 $5

3 $9

Using this information, answer the following questions:

a) Find the equilibrium allocation of traffic between the freeway and alternate routes.

b) Compute the total commuting cost for all commuters for the following four allocations of traffic. Total cost is the cost incurred by freeway users plus the cost incurred by commuters who use their alternate routes. (Hint: Remember the definition of AC, while carrying out your calculations.)
On freeway Nobody On alternate routes nobody

Mr. 1, Mr. 2, Mr. 3

Mr. 1 Mr. 2, Mr. 3

Mr. 1, Mr. 2 Mr. 3

Mr. 1, Mr. 2, Mr. 3 nobody

c) Remember that the socially optimal allocation of traffic between the freeway and alternate routes is the one that minimizes total commuting cost for all commuters. Based on your answer to (b), which allocation is socially optimal? How does total cost at the optimum compare to total cost at the equilibrium? (Note that you don't need to use an MC curve to get the answer to this question.)