A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) = a + bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on others

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