JPEG format plz A local charity has collected winter clothing to give away. Assu
ID: 1181725 • Letter: J
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JPEG format plz
A local charity has collected winter clothing to give away. Assume there are two people, one rich and one poor. The utility from winter clothing for each type is given by the following utility functions: where Cp is the amount of winter clothing the poor person receives and Cr the amount of winter clothing the rich person receives, w is the number of minutes spent waiting in line for the clothing. The charity wants to do the most good it can with the 16 pieces of clothing it has gathered. The charity defines "doing good" as maximizing a utilitarian social welfare function (i.e. maximizing the sum of the utilities of everyone in society). Write down the charity's social welfare function and its budget constraint. What is social welfare if the clothing is split evenly between rich and poor without any time spent waiting? What allocation of clothing maximizes social welfare? (i.e. how much of the clothing should be given to the rich and how much to the poor). Why? The charity would like to implement the division you found in part c, however, it does not have access to individuals' tax returns and cannot tell the rich and the poor apart. Propose a value of t such that the charity can simply give clothes to whomever shows up and waits for them and still end up with the allocation you found in part c. Do the same analysis as in point (d) but assume that: What is social welfare in point (e)? How does it compare to social welfare in point (d)? How does it compare to social welfare in point (b)? Explain the intuition behind these differences.Explanation / Answer
A)
social welfare function = U(poor) + U(rich)
= 2Cp -t + Cr - t^2/2
budget constraint =>
Cp + Cr - 16 = 0
B)
if the clothing is split evenly into rich and poor then
Cp = Cr = 8
social welfare function = 2 * 8 + 8 = 24 (if zero time is spent in waiting in line)
C)
if all the clothes is distributed to poors then it maximizes the social welfare function
Cp = 16 , Cr = 0
social welfare function = 2*16
=32
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