Distributional goals as a rationale for public policy intervention and government failure Suppose we have a society consisting of four individuals (A. B. C. and D). The government of this society is considering a series of alternative policies (1. 2.3. and 4) aimed at addressing some social problem. Although the analysts in the legislature are able to estimate the utilities for each of the four individuals under each of the four policy alternatives. they are unsure as to which social welfare function the legislature would be most likely to apply. The utilities for each of the individuals under each of the four policies is presented in the table below.
Individual utilities from alternative policies
A
Policy 1 110 100 30 160 Policy 2 SO 150 90 60 Policy 3 85 140 25 180 Policy 4 100 70 50 190
- (30 pts) Based on this information. compute the social welfare that would result if the social welfare function used in prescribing policy was (0 utilitarian. (is) Rawlsian, or (in) multiplicative (divide by 100.000). Under each of these social welfare functions. which policy would be preferred? 2. (25 pts) Suppose the legislature was unable to determine which social welfare function to use in making a policy determination. Instead, they decided to put these four policy options on a referendum to let the citizens decide on their preferred option. Suppose each citizen is allowed to cast one vote for the policy of their choice, and assume that citizens are rational, utility maximizing individuals who prefer the policy that optimizes their individual utility. If we assume that each vote carries the same weight, which policy would win this referendum? Is this choice consistent with the choice that would be made under one of the three social welfare functions considered in question 1? (This voting system is referred to as 'plurality' voting, since it rewards the policy or candidate that receives the plurality — or largest number — of votes). 3. (25 pts) Now, instead of each citizen casting a single vote for their preferred policy. the legislature instead allows citizens to rank their policy preferences from most preferred to least preferred, again assuming that the citizens are rational, utility maximizing individuals whose preference rankings mirror the ranking of utility that would result from these different policies. In computing the votes. the election board awards 4 points for the policy that an individual selects as his or her most preferred policy. 3 points for the policy that the individual selects as his or her second most preferred policy, 2 points for the policy that the individual selects as his or her third most preferred policy, and 1 point for the policy that the individual selects as his or her least preferred policy. Under this voting system, which policy would win the referendum? Is this choice consistent with the choice that would be made under one of the three social welfare functions considered in question I? (This voting system has some of the characteristics of rank-choice voting, but is not entirely the same.)
- (25 pts) Under these two competing voting systems, what do we observe about the ability of referenda to achieve both a social optimum (i.e., maximizing social welfare according to some social welfare function) and maintain an equitable distribution of costs? In considering the costs of different policies, consider the opportunity cost of a particular policy relative to the policy that would yield the maximum utility for a specific individual
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