ilging crying babies on a plane 5. Consider a society with three individuals: Ri
ID: 1137022 • Letter: I
Question
ilging crying babies on a plane 5. Consider a society with three individuals: Rich, Middle and Poor. Market economy leads to a GDP of $100, which Rich earns $70, Middle earns $25 and Poor earns $5. Answer each of t different scen he following questions under two arios: first, redistribution has no cost. Second, redistribution s costly: for each dollar redistributed from one' person to another, the person whose dollar is taken loses half an extra dollar. (a) Suppose all three people in this economy have the following utility function: U V, where x is how many dollars you have. Consider the following policy: taking 20 dollars from Rich and giving them to Poor. i. Would a Utilitarian government approve this policy? ii. Would a Rawlsian government approve this policy? b) Suppose all three people in this economy have the following utility function U= " instead. i. Would a Utilitarian government approve the policy suggested in part a? ii. Would a Rawlsian government approve the policy suggested in part a? best policy in this scenario? policy? ii. As a Utilitarian government, what do you think would be the iv. If the government has a Rawlsian SWF, what is the optimalExplanation / Answer
a. i. When the income is transferred, the Rich will have $50, the poor will have $25 and the middle will have no change, and will remain to be $25. Thus, the total utility in this economy according to a utilitarian govt. would be:-
501/2 + 251/2 +251/2 = 7.07 + 5 + 5 = 17.7
In case there is no transfer, then the utility is 701/2 +251/2 + 51/2 = 8.36 + 5 + 2.23 = 15.59
Thus, the utilitarian govt. would approve this policy since the total utility is higher in that case.
Now, if we consider that half a dollar is lost for every dollar that is transferred, then the total utility will be, 401/2 + 251/2 + 251/2 = 6.32 + 5 + 5 = 16.32
Even in this case, the utilitarian govt. will approve the policy.
According to the Rawlsian welfare function, U(x,y) = min(x,y)
In both the cases(without half a dollar loss and with half a dollar loss), the minimum utility will be 5 when the money is transferred from the rich to the poor. And thus, the Rawlsian govt. will also approve of the policy.
2. a). When the dollars are transferred from rich to the poor, the total amount of income in the economy remains the same. And according to the given function U = x, the total utility will remain as 100. Thus, the utilitarian govt. will be indifferent between implementing and not implementing the policy. However, when there is half a dollar loss for every dollar that is transferred, the total utility will reduce to 90 utils, and thus the govt. would then not approve of the policy in that case.
b). Yes, the Rawlsian govt. will approve of the policy. This is because the minimum utility would then be 25 instead of 5 before the transfer. Thus, the Rawlsian govt. will approve the policy.
c). As a utilitarian govt. the best policy would be to increase the total utility, which would only be possible through increased total income. Transfers will not be of any use to a utilitarian govt.
d. The optimal policy for a Rawlsian govt. would be to maximize the min. utility level. This will be possible only when Ur = Um = Up; $33.33 should be the income for all the three individuals.
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