The function that relates the inverse of speed (1/S) to traffic volume on a highway is 1=S ¼ (1=60) þ 0:0005V;

where the inverse of speed is measured in hours per mile. What would this equation be if expressed in minutes per mile? The demand for traffic volume on this road is V ¼ 6;880  80 (travel time per mile):

Travel time per mile is measured in minutes.

a. Find the equilibrium traffic volume in the absence of any congestion toll.

b. Find the marginal cost function for traffic volume, where cost is expressed as travel time per mile in minutes.

c. Find the optimal level of traffic volume.

d. Find the optimal congestion toll, expressed in minutes. (Imagine that the congestion toll consists of sitting in the ‘‘penalty box’’ for this period of time. The toll can also be assessed in money terms, of course.)