Four siblings share a house. The utility function of each sibling is u(m;) = 2m;, where...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Four siblings share a house. The utility function of each sibling is u(m;) = 2m;, where m; is income of sibling j, and four income levels are {1,1,9,9}. (a) Draw the Lorenz curve associated with this income distribution of the household and illustrate a measure of inequality using your graph. (b) Compute the household Gini coefficient using the formula: [5 marks] 2 G = Mm i=1 1 i(m - m), where M individuals from poorest to richest, m denotes mean and i is the "rank" in the income distribution (i = 1,2,3, ... . M), from poorest to richest. [5 marks] (c) The parents can intervene to redistribute income between siblings with the objective of maximising a social welfare function of the household. (i) What assumptions about utility are required for the parents to do this? [2 marks] (ii) Explain the rationale for redistribution if the parents are Utilitarian. How will they redistribute income? What is G after the redistribution? [8 marks] (iii) Explain the rationale for redistribution if the parents are Rawlsian. How will they redistribute income? What is G after the redistribution? [8 marks] (d) Suppose the utility function of the two siblings with income 9 is now u(m;) = 6m;. How does this alter the parents' willingness to redistribute income in the case of (i) Utilitarianism, and (ii) Rawlsianism? Comment on household inequality in either case. [12 marks] (e) Assume once more that all siblings have utility function u(m;) = 2.m;. The siblings express a preference for income distribution m = {4,4,6,6}. What might explain this? [10 marks] Four siblings share a house. The utility function of each sibling is u(m;) = 2m;, where m; is income of sibling j, and four income levels are {1,1,9,9}. (a) Draw the Lorenz curve associated with this income distribution of the household and illustrate a measure of inequality using your graph. (b) Compute the household Gini coefficient using the formula: [5 marks] 2 G = Mm i=1 1 i(m - m), where M individuals from poorest to richest, m denotes mean and i is the "rank" in the income distribution (i = 1,2,3, ... . M), from poorest to richest. [5 marks] (c) The parents can intervene to redistribute income between siblings with the objective of maximising a social welfare function of the household. (i) What assumptions about utility are required for the parents to do this? [2 marks] (ii) Explain the rationale for redistribution if the parents are Utilitarian. How will they redistribute income? What is G after the redistribution? [8 marks] (iii) Explain the rationale for redistribution if the parents are Rawlsian. How will they redistribute income? What is G after the redistribution? [8 marks] (d) Suppose the utility function of the two siblings with income 9 is now u(m;) = 6m;. How does this alter the parents' willingness to redistribute income in the case of (i) Utilitarianism, and (ii) Rawlsianism? Comment on household inequality in either case. [12 marks] (e) Assume once more that all siblings have utility function u(m;) = 2.m;. The siblings express a preference for income distribution m = {4,4,6,6}. What might explain this? [10 marks]
Expert Answer:
Related Book For
Managerial Economics Theory Applications and Cases
ISBN: 978-0393912777
8th edition
Authors: Bruce Allen, Keith Weigelt, Neil A. Doherty, Edwin Mansfield
Posted Date:
Students also viewed these economics questions
-
Dictator game giving: altruism or artefact? Nicholas Bardsley What is the egotistical choice in the Revelation Game? How would you interpret the 0 choiceneither giving nor takingin the Revelation...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
If a particular glucose fermentation process is 87.0% efficient, how many grams of glucose would be required for the production of 51.0 g of ethyl alcohol (C 2 H 5 OH)? C 6 H 12 O 6 2C 2 H 5 OH +...
-
Dad gives Son a 20% capital and profits interest in the Family Partnership. Dad holds a 70% interest, and Fred, an unrelated individual, holds a 10% interest. Dad and Fred work in the partnership,...
-
. The input-output (Leontief) matrix A = [aj] for an economy based on tourism and mineral products is A [0.2 0.4 0.5 0.2 where tourism corresponds to subscript 1 and minerals corresponds to subscript...
-
Which of the following events most likely indicates the existence of related parties? a. Borrowing a large sum of money at a variable rate of interest. b. Making a loan without scheduled terms for...
-
To: [Your name] From: Supervising Attorney Re: Commonwealth v.Jones; assault by means of a dangerous weaponlightning This is a bizarre case to say the least. We have been appointed by the court to...
-
A strain gauge transducer uses a Wheatstone bridge circuit to measure strain using resistance as shown in Figure Q4. The maximum permissible instrument gauge current is 0.25 A. (a) (b) R Figure Q4...
-
in c++ please help 1. Analyze the following problems: Carrano, 2012, Programming Problems 6. Chapter 13, pp.395. 6. Implement the event-driven simulation of a bank that this chapter described. A...
-
Assume that Darrell randomly selected a sample of 7 5 credit memo packages, each of which contains a credit memo with a matching receiving report and inventory warehouse receipt, and has reviewed all...
-
Select a topic for research as it relates to health, culture, or society. How would you research that topic in the field of communication studies? Please use examples from other sources in addition...
-
A company that uses job order costing purchases $ 5 8 , 0 0 0 in raw materials for cash. It then uses $ 1 9 , 0 0 0 of raw materials as indirect materials and uses $ 3 0 , 6 0 0 of raw materials as...
-
What are the Market Efficient Hypothesis Theory and Behaviour Finance respectively? Explain Why do duration match have better immunization effect on interest rate risk than that of maturity match?...
-
A college administrator claims that the proportion of students that are nursing majors is less than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 149...
-
Infrastructure assets are accounted for similarly to other capital assets, it allows for a major exception with regard to depreciation. What is that exception?
-
14. In testing the existence assertion, an auditor ordinarily works from the a. Financial statements to the accounting records. b. General journal to the general ledger. c. Supporting evidence to the...
-
The total monthly sick leave time of employees of a small company has a normal distribution with mean 100 hours and standard deviation 20 hours. (1) What is the probability that the total monthly...
-
Let \(X\) have a geometric distribution with \[P(X=i)=(1-p) p^{i} ; \quad i=0,1, \ldots ; 0
-
A random variable \(X\) has distribution function \[F_{\alpha}(x)=e^{-\alpha / x} ; \alpha>0, x>0\] (Frecht distribution). What distribution type arises when mixing this distribution with regard to...
Study smarter with the SolutionInn App