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 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 requirements and therefore create excessive pollution. 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}. 1. Compute the utility of group 1 from driving when group 2 takes public transport: U1(x1 = d, x2 = p). Compute the utility of group 1 from taking public transport when group 2 takes public transport: U1(x1 = p, x2 = p). Does group 1 prefer to drive or take public transport, given that group 2 takes public transport? 2. Compute the utility of group 2 from driving when group 1 drives: U2(x2 = d,x1 = d). Compute the utility of group 2 from taking public transport when group 1 drives: U2(x2 = p,x1 = d). Does group 2 prefer to drive or take public transport, given that group 1 drives? 3. Compute the social welfare given the optimal decision of each group: that is, calculate S = U1(x1, x2) + U2(x1, x2) given what group 1 prefers to do and what group 2 prefers to do, as derived in the two previous questions. 4. Suppose now that ULEZ is introduced so that citizens must 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 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 requirements and therefore create excessive pollution.
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}.
1. Compute the utility of group 1 from driving when group 2 takes public transport: U1(x1 = d, x2 = p). Compute the utility of group 1 from taking public transport when group 2 takes public transport: U1(x1 = p, x2 = p). Does group 1 prefer to drive or take public transport, given that group 2 takes public transport?
2. Compute the utility of group 2 from driving when group 1 drives: U2(x2 = d,x1 = d). Compute the utility of group 2 from taking public transport when group 1 drives: U2(x2 = p,x1 = d). Does group 2 prefer to drive or take public transport, given that group 1 drives?
3. Compute the social welfare given the optimal decision of each group: that is, calculate S = U1(x1, x2) + U2(x1, x2) given what group 1 prefers to do and what group 2 prefers to do, as derived in the two previous questions.
4. Suppose now that ULEZ is introduced so that citizens must 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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