There are two routes for driving from A to B. One is a freeway, and the other consists of local…

There are two routes for driving from A to B. One is a
freeway, and the other consists of local roads. The benefit of using the
freeway is constant and equal to 1.8, irrespective of the number of people
using it. Local roads get congested when too many people use this alternative,
but if not enough people use it, the few isolated drivers run the risk of
becoming victims of crimes. Suppose that when a fraction x of the population is
using the local roads, the benefit of this mode to each driver is given by

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(a) Draw a graph showing the benefits of the two driving
routes as functions of x, regarding x as a continuous variable that can range
from 0 to 1.

(b) Identify all possible equilibrium traffic patterns
from your graph in part (a). Which equilibria are stable? Which ones are
unstable? Why?

(c) What value of x maximizes the total benefit to the
whole population?

 

 

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