Suppose that it people use m3 to commute to london by car

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Reference no: EM13371136

Suppose that it people use M3 to commute to London by car. Each drivers chooses how many times to travel a year, s. The total number of trips of all drivers except i in a year is x_i = ∑_j≠isj. Let the total annual benefit that an individual i derives from getting to London be v (so = 2√7. Assume that there is a cost of travelling of c per trip (petrol, car depreciation etc) (this is not an annual cost, but a cost per trip). Finally, assume also that there is a congestion cost per trip equal to ax i where a is a positive parameter (that is, the more drivers other than i use the M3, the more it costs driver i to travel).

(a) Formulate this situation as a normal-form game. In paticular, write what is the utility/payoff fuction for commuter i.

(b) Find the best response functions and characterize the Nash Equilibrium. (Hint: you may obtain an equation that is difficult to solve. In this case do not solve it, but in any case explain).

(d) Now suppose that the authorities introduce a fee/toll for using the M3, equal to t per trip. Formulate this game and characterize the equilibrium (decentralized) outcome with such a toll. Explain how the authorities should choose the toll to bring the equilibrium number of trips to the efficient level.

Reference no: EM13371136

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