wo common specifications of the social welfare function (SWF) are the Utilitarian SWF and the Rawlsian SWF. Compare the two specifications and outline which specification would generally lead to a higher level of redistribution. Explain your answer.
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Two common specifications of the social welfare function (SWF) are the Utilitarian SWF
and the Rawlsian SWF. Compare the two specifications and outline which specification
would generally lead to a higher level of redistribution. Explain your answer.
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- The Utilitarian specification of the social welfare function (SWF) generally leads to a higher level of redistribution than the Rawlsian specification of the SWF. True or false? Explain your answerThe Second Welfare Theorem implies that it is possible to achieve another Pareto optimal outcome with a more equal distribution of wealth but changing the initial endowments. Analyze how realistic this conclusion is given a) incentive distortions and b) the knowledge problem.The most general form of a social welfare function (SWF ) can be written as W = W(U1; ... ; UH). a. Explain the following properties that a SWF may satisfy: non paternalism, Pareto principle, anonymity (the names of the agents do not matter), and concavity (aversion to inequality). b. Consider two agents h = 1; 2 with utilities U1 and U2. Depict the social indifference curve of the utilitarian SWF in (U1; U2)-space. Which of the properties in part a does it satisfy? c. Depict the social indifference curves of the maxim in or Rawlins SWF. Contrast to the utilitarian SWF with respect to the aversion to inequality. Which properties does the Rawlins SWF satisfy? d. The Bernoulli-Nash social welfare function is given by the product of individual utilities. Discuss the distributional properties of the Bernoulli-Nash SWF.
- Redistribution of income occurs through the federal income tax and government antipoverty programs. Explain whether or not this level of redistribution is appropriate and whether more redistribution should occur.Consider a society consisting of two people. Jacques earns an income of $100,000 per year and Kyoko earns an income of $30,000 per year. The government is considering a redistribution plan that would impose a 25% tax on Jacques's income and give the revenue to Kyoko. Without any incentive distortion, Jacques would retain $75,000 and Kyoko would end up with $55,000. However, let us assume that since Jacques will not receive all the income he earns, he decides to work less and earn an income of only $90,000, of which 25%×$90,000=$22,50025%×$90,000=$22,500 will be owed in taxes. With the redistribution plan, Jacques will take home an income of . The $22,500 that Jacques pays in taxes will be transferred by the government to Kyoko. Let us assume that since Kyoko now receives payment from the government, she will not work as many hours and will earn an income from work of only $29,000 instead of her initial $30,000. With the redistribution plan, Kyoko's total income…Suppose there are two possible income distributionsin a society of ten people. In the first distribution,nine people have incomes of $60,000 and one personhas an income of $20,000. In the second distribution,all ten people have incomes of $50,000.a. If the society had the first income distribution,what would be the utilitarian argument forredistributing income?b. Which income distribution would Rawls considermore equitable? Explain.c. Which income distribution would Nozick considermore equitable? Explain.
- The Betropolis University Investment Club of 5 have investment incomes of $5,000, $10,000, $15,000, $20,000, and $50,000. A.Using the Trapezoidal Rule with 5 trapezoids find the area under the Lorenz Curve. Your answer should be correct to 3 places after the decimal point. _____________ B. Using the result of Part A find the Gini Index. Your answer should be correct to 3 places after the decimal point. _______________The net welfare effects rate is a. area b + d b. area b + d + e c. area e d. area e - b - dWhat are three policy solutions to lessen the economic consequences of inequality. Explain in detail.
- Suppose that the last dollar that Victoria receives as income brings her a marginal utility of 10 utils while the last dollar that Fredrick receives as income brings him a marginal utility of 15 utils. If our goal is to maximize the combined total utility of Victoria and Fredrick, we should: a. Redistribute income from Victoria to Fredrick. b. Redistribute income from Fredrick to Victoria. c. Not engage in any redistribution because the current situation already maximizes total utility. d. None of the above.4.4 Using diagrams, discuss and explain the three conditions for optimal social welfare.For a social welfare function W = W(U1(M1); ... ; UH (MH )), where Mh is income the ‘‘social marginal utility of income’’ is defined by for all h, show that the social marginal utility of income is decreasing in Mh for a utilitarian social welfare function. Use this to argue that a fixed stock of income will be distributed equally. Show that the argument extends to any anonymous and concave social welfare function when all consumers have the same utility function.
