Consider two groups of citizens, each group can either choose to drive x = d or to take public transport x = p. The first group, group 1, enjoys driving and has the following benefit from using their car within the ULEZ area: B1(x1 = d) = 18. The second group, group 2, does not enjoy driving and has a benefit of B2(x2 = d) = 0 from driving their car. If they don’t drive, citizens can use public transport to get around. The benefit of doing so is the same for both groups: B1(x1 = p) = B2(x2 = p) = 10. Both groups drive cars that do not meet the ULEZ requirements and therefore create excessive pollution. For simplicity, we consider that pollution, and the health problems it induces, are the main cost of driving. This cost is imposed on both groups and is equal to Ci(x1 = d, x2 = d) = 10 if both groups drive, Ci(x1 = p, x2 = d) = Ci(x1 = d, x2 = p) = 5 if only one group drives and Ci(x1 = p, x2 = p) = 0 if neither group drives, where i represents either group 1 or group 2. The utility of each group from choosing action xi is equal to the benefits minus the costs: Ui(xi , xj ) = Bi(xi) − Ci(xi , xj ), where i ∈ {1, 2}. 4. Suppose now that ULEZ is introduced so that citizens have to pay a fee equal to τ = 12.50 to drive. The benefit of driving is therefore now reduced to B1(x1 = d) = 18 − 12.50 = 5.5 for group 1 and B2(x2 = d) = 0 − τ = −12.50 for group 2. Does group 1 prefer to drive or take public transport? Does group 2 prefer to drive or take public transport? Calculate the social welfare after ULEZ has been implemented, that is compute S = U1(x1, x2)+U2(x1, x2) given the optimal choice of transportation of each group when τ = 12.50.
Consider two groups of citizens, each group can either choose to drive x = d or to take public transport x = p. The first group, group 1, enjoys driving and has the following benefit from using their car within the ULEZ area: B1(x1 = d) = 18. The second group, group 2, does not enjoy driving and has a benefit of B2(x2 = d) = 0 from driving their car. If they don’t drive, citizens can use public transport to get around. The benefit of doing so is the same for both groups: B1(x1 = p) = B2(x2 = p) = 10. Both groups drive cars that do not meet the ULEZ requirements and therefore create excessive pollution. For simplicity, we consider that pollution, and the health problems it induces, are the main cost of driving. This cost is imposed on both groups and is equal to Ci(x1 = d, x2 = d) = 10 if both groups drive, Ci(x1 = p, x2 = d) = Ci(x1 = d, x2 = p) = 5 if only one group drives and Ci(x1 = p, x2 = p) = 0 if neither group drives, where i represents either group 1 or group 2. The utility of each group from choosing action xi is equal to the benefits minus the costs: Ui(xi , xj ) = Bi(xi) − Ci(xi , xj ), where i ∈ {1, 2}. 4. Suppose now that ULEZ is introduced so that citizens have to pay a fee equal to τ = 12.50 to drive. The benefit of driving is therefore now reduced to B1(x1 = d) = 18 − 12.50 = 5.5 for group 1 and B2(x2 = d) = 0 − τ = −12.50 for group 2. Does group 1 prefer to drive or take public transport? Does group 2 prefer to drive or take public transport? Calculate the social welfare after ULEZ has been implemented, that is compute S = U1(x1, x2)+U2(x1, x2) given the optimal choice of transportation of each group when τ = 12.50.
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