4. What is the optimal income distribution between two citizens under these three assumptions: -The Social Welfare Function is Utilitarian. - The total income is fixed. - The two citizens have the same individual utility function, which exhibits decreasing but positive marginal utility of income.
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- 1. Second Fundamental Theorem of Welfare Economicsa. Describe the theorem, making sure that you define clearly the terms used in thedescription (e.g. if you use the term “efficient” you have to describe what this means).b. Explain why the theorem implies that there is no intrinsic trade-off between efficiencyand interpersonal equity. c. Demonstrate your argument using an Edgeworth box, making sure that you describe allthe elements of the box appropriately.2. Consider a society with only two people one rich and one poor-who have the same util- ity functions. These utility functions exhibit diminishing marginal utility. Suppose that taxes are set such that the total amount of utility that each person loses is the same. Does it follow that the tax will be progressive? Explain.2. The standard model of consumer behavior assumes that income is exogenous. Of course, a person's income usually depends upon the number of hours the individual works. Suppose that an individual has T hours each day which can be allocated toward working time, H, or leisure time, L-that is, T = H + L. The individual earns w dollars for each hour worked. Then the individual's income is M + wH where M denotes any non-labor income. The individual has preferences over leisure time, L, and a consumption good, X, which can be represented by a quasi-concave utility function, U(X, L). The consumption good, X, can be purchased at the price Px. The individual seeks to maximize the utility subject to the constraints on time and money. (1) Formulate the individual's problem as an optimization problem with two constraints a time constraint and a money constraint. Derive the first-order conditions. Give an economic interpretation of the Lagrange multipliers. (2) The two-constraints problem can be…
- 1. Write down an exchange economy model with two individuals and two goods, in whichthere is no consumption externality. State and explain the key assumptions of the model.Using the model, answer the following questions:(a) Explain carefully how the concept of Pareto efficiency differs from that of socialwelfare.(b) State the Second Theorem of Welfare Economics and explain carefully why it holds.What is the importance of the assumption of convex preferences to this theorem?3. First and Second Welfare Theorems There are two goods A and B and two inputs K and L. The production functions are Ya AK,L 1-8 The production functions display the standard properties, including constant returns to scale. A representative household has utility U(Ca, Ch) where is the consumption of good i. The total supply of each factor is fixed Ci K Ka + K, La + L,1. Write down an exchange economy model with two individuals and two goods, in whichthere is no consumption externality. State and explain the key assumptions of the model.Using the model, answer the following questions:(a) Explain carefully how the concept of Pareto efficiency differs from that of socialwelfare.(b) State the Second Theorem of Welfare Economics and explain carefully why it holds.What is the importance of the assumption of convex preferences to this theorem?(c) Explain the concept of the utility possibility frontier. What is the role of the utilitypossibility frontier in the social welfare maximization problem of a welfarist society?
- What is the difference between a Social Welfare Function and Social Choice Rule? Explain whether requiring a Social Choice Rule rather than a Social Welfare Func- tion successfully resolves the paradoxical results in social choice theory.7. An economy consists of two individuals, Lynne and Jonathan, whose utility levels are given by U₁ and U₁, respectively. a. Suppose that the social welfare function is W = U₁ + U₁ True or false: Society is indifferent between giv- ing a dollar to Lynne and a dollar to Jonathan. b. Now suppose that, instead, the social welfare function is W = U₁ + 8U, True or false: Society values Jonathan's hap- piness more than Lynne's. c. Now suppose that, instead, the social welfare function is W = min[U₂, U₁] True or false: In this society, the optimal dis- tribution of income is complete equality.The figure below show the initial optimal point of a family who has to decide how much kids (K) to have in 5 years and at the same time how much of all other goods to consumer (measured as composite good in dollars). Now assuming that kids are inferior goods/services, show the new optimal point as e2 if the income of the family increases. IC₁ to K
- 3 b. State and explain the Second Theorem of Welfare Economics and discuss its economicimplications and significance.a. Using a production possibility frontier, an arbitrary price line that does not equate supply and demand in the goods market, and a mapping of homothetic indifference curves (you only need to show one indifference curve), indicate the point of production and the point of consumption in the final goods market that this economy will choose if in addition to seeking to maximize incomes from production it also wishes to maximize utility from the consumption of goods. In your depiction, is there a shortage of A or M?6. Provide a detailed analysis of the Second Welfare Theorem of Economics