Exercise: Total marks 50

Four siblings share a house. The utility function of each sibling is( ) = 2 , where

isincomeofsibling,andfourincomelevelsare{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.[5 marks]

(b) Compute the household Gini coefficient using the formula: =2 ( ),

2=1 whereindividuals from poorest to richest,denotes mean andis the"rank" in the

income distribution( = 1,2,3, ... . ),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) Whatassumptionsaboututilityarerequiredfortheparentstodothis?[2marks]

(ii) ExplaintherationaleforredistributioniftheparentsareUtilitarian.Howwillthey redistribute income? What isafter the redistribution?[ 8 marks]

(iii) Explain the rationale for redistribution if the parents are Rawlsian. How will they redistribute income? What isafter the redistribution?[8 marks]

(d) Suppose the utility function of the two siblings with income9is now( ) = 6 .

How does this alter theparents' willingness toredistribute 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( ) = 2 . The siblings

express a preference for income distribution ={4,4,6,6}. What might explain this?[10 marks]

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