Consider a public bridge that drivers can use for free. For each individual driver, the benefit...

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Consider a public bridge that drivers can use for free. For each individual driver, the benefit from using the bridge is b. With n drivers using the bridge, the cost (in terms of delay) to each driver is c(n), so when there are n drivers in total crossing the bridge the net benefit or utility to each of those drivers is bc(n). A driver who does not cross the bridge does not pay the cost or get any benefit and has a utility of 0. Assume that c(0) = 0, c'(n) > 0 and c" (n) > 0 for all n 0. So that there is little delay with few drivers on the bridge, but delay increases with the number of drivers, getting progressively worse as the congestion increases. (Although in reality n must be an integer, assume for the calculations than n is a real number. If c' (n) > 0 is small until n is very large, rounding to the nearest integer will not be a significant issue.) 1. Find the equilibrium outcome and the socially optimal outcome (in terms of the number of bridge users). To do this, you need to find the social benefit and social cost. 2. Identify a toll that would lead to usage equal to the optimal level. 3. Illustrate with c(n) = an, where a > 0. Consider a public bridge that drivers can use for free. For each individual driver, the benefit from using the bridge is b. With n drivers using the bridge, the cost (in terms of delay) to each driver is c(n), so when there are n drivers in total crossing the bridge the net benefit or utility to each of those drivers is bc(n). A driver who does not cross the bridge does not pay the cost or get any benefit and has a utility of 0. Assume that c(0) = 0, c'(n) > 0 and c" (n) > 0 for all n 0. So that there is little delay with few drivers on the bridge, but delay increases with the number of drivers, getting progressively worse as the congestion increases. (Although in reality n must be an integer, assume for the calculations than n is a real number. If c' (n) > 0 is small until n is very large, rounding to the nearest integer will not be a significant issue.) 1. Find the equilibrium outcome and the socially optimal outcome (in terms of the number of bridge users). To do this, you need to find the social benefit and social cost. 2. Identify a toll that would lead to usage equal to the optimal level. 3. Illustrate with c(n) = an, where a > 0.