Assume that a citizen’s utility curve is given by: U = 10YA + 10YB, where YA is income of the Rich, and YB is income of Poor (less rich). Plot the Indifference curves and equilibrium outcome on an ecnonomic inequality feasible frontier diagram.
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Assume that a citizen’s utility curve is given by: U = 10YA + 10YB, where YA is income of the Rich, and YB is income of Poor (less rich). Plot the Indifference curves and equilibrium outcome on an ecnonomic inequality feasible frontier diagram.
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- Person 1 and person 2 are the only two residents of an economy. Person i (where i is either 1 or 2) has the utility function Here, Yi is person i’s income and β is parameter between 0 and 1. Assume that the social welfare function is where α is a parameter between 0 and 1. Initially, person 1’s income is 1 and person 2’s income is 2. a) Express W in terms of Y1 and Y2. If a social indifference curve shows all the pairs (Y1, Y2) that yield the same value of W, what would a social indifference curve look like if it were drawn in the (Y1, Y2) quadrant? Find an algebraic expression for the slope of a social indifference curve. b) Imagine that income redistribution is costless, in the sense that the economy can reach any pair (Y1, Y2) that satisfies the condition Draw a graph of the attainable pairs in the (Y1, Y2) quadrant. This set is called the “utility possibility frontier.” Using this frontier and the social indifference curves,…9There are three popular types of social welfare functions. Benthamite Social Welfare Function - W (u,, uz, --- Un) = Eu Egalitarian Social Welfare Function - W(u,uz, Un) = E,u-1E(u- min(u)) Rawlsian Social Welfare Function - W(u,, u, .u) = min(u) Select two values of 2 in the Egalitarian Social Welfare Function such that it becomes equivalent to the Benthamite Function and Rawlsian Function respectively. (Note: Make sure that the first value in the option corresponds to Benthamite and second value corresponds to Rawlsian.) ON, 1/N O0, 1 01.0 O0.33, 0.67 O0.67,0.33We now focus on one country. Assume that the society is composed of two individuals A and B. The VIA total income available in the society is $550,000. The utility of individual A is given by UA= and individual B ones is given by UA = 0.5/IB. b) What should the income distribution be for the individuals to have the same utility level? c) Find the income distribution that maximizes social welfare in the case of an additive social welfare function. Now imagine that in reality, individual A has an income of $500,000 and individual B's income is $50,000. d) How far from the optimal income distribution defined in question c) are we? What redistri- bution should be chosen to reach the optimal social welfare calculated in c)?
- After a long public discussion about goods and services that should be provided to the population, the government decides that a certain scarce good should be provided to anyone who wants it at no cost. As part of this effort, the government sets a price of zero for that good and passes a law making it illegal to transact the good at any price. However, people can give the good away. Assuming that this good is highly desirable for segments of the population, what do you think the effect of this law will most likely have on the market? What would happen if this particular law was removed after being implemented?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 answerSuppose society consists of two individuals, A and B, who must split a fixed income of $150. Individual A's marginal utility of income is given by MUA=400-IA and individual B's marginal utility of income is given by MUB=600-6IB. Suppose the social welfare function is W=UA+UB. What if the social welfare function is, instead, W=min(UA,UB). 44. Then equity in the distribution of income would be synonymous with equality of What if the social welfare function is, instead, W=UA+2.6UB and individual B's marginal utility is, instead, MUB=200-IB. 45. What is the optimal distribution of income to individual A? $ 46. What is the optimal distribution of income to individual B? $ 47. Equity in the distribution of income would be synonymous with equality of
- Suppose there are two people, Selma and Burak, who must split a fixed income of 200. The marginal utilities of income for Selma and Burak are as follows: MUS = 600- 2*ls MUB = 600- 4*IB where IS and IB are incomes of Selma and Burak respectively. a) What is optimal distribution of income if social welfare function is additive? b) Draw the MUof Selma and Burak in the Edgeworth box and show part (a). c) What is the optimal distribution if society values only the utility of Selma? What is the optimal distribution if society values only the utility of Burak? d) This example refers to ... rationale for income redistribution and it is Pareto ...Let: U1 = x1 + z^.5, Y1 = x1 + pz1 %3| %3D U2 = x2 - .5z^.5, Y2 = x2 + pz2 %3D z = z1 + z2, Y is the income of the agent, and p is the price of z1 and z2. What is the social-optimal amount of z1 and z2? What is the optimal amount of z1 agent 1 would choose given z2, and vice versa? What can the social planner do so that the agents choose the socially optimal level of z1 and z2? How much is needed to achieve the social-optimal amount?Shen, who is currently unemployed, is a participant in four welfare programs that offer daily benefits of $10 each to people with no earned income. Each program then curtails its benefits by 50 cents for every dollar of income a recipient earns. Shen's identical twin brother, Sean, is enrolled in an experimental negative income tax program that gives him $40/day in benefits and then taxes him at the rate of 50 percent on each dollar of earned income. Now suppose Shen is offered a job that pays $4/hr, the same wage his brother earns. a. Draw the budget constraint for each twin. Instructions: To earn full credit for this graph you must plot all required points for each curve. 1. Use the line tool (Shen's budget constraint, plot 3 points) to draw the Shen's budget constraint. 2. Use the line tool (Sean's budget constraint, plot 2 points) to draw the Sean's budget constraint. After tax-income ($/day) 98 84 70 56 42 28 14 0 2 4 6 8 10 12 14 16 18 20 22 24 26 Leisure (hrs/day) Tools Shen's…
- While the Lindahl model (equilibrium) can be analogous to the market for private goods, they have interesting differences. How do we interpret Q1 in the diagram? What about S?Consider an inequality-averse player who must decide about allocations of money for him/herself and another player. Their preferences can be represented by: U(Town, Mother) = Town - 0.6*max(¹other - Town, 0) – 0.3*max(¹own - Mother, 0), with Town the amount of money for the player and other the amount of money for the other player. The player can always choose between two options. Which of the following statements is correct regarding this player's decisions: a. The player prefers (Town-5,other-5) over (Town =6,other-4). b. The player prefers (Town =21,Пother-18) over (Town =19,other =19). c. The player will be indifferent between (Town =12,Пother =16) and (Town 11,other =9). d. The player prefers (Town 8,¹other =16) over (Town =4,"other =4).Please explain how Jack and Cody can maxmise utility through living in the same household with a unitary and non-unitary models. Unitary models - Mutual altruism (or any unitary model) Non-unitary models - Copertive models - Collective + Bargaining model.(or any Non-unitary models)