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Suppose John and Kate must split a fixed income of $100.

Marginal Utility for John: MUj=400-2Ij
Marginal Utility for Kate: MUk=400-6Ik

Note: Ij and Ik are the amounts of income to John and Kate respectively.

a. What is the optimal distribution of income if social welfare function is additive.
What if the reverse is true. Comment on your answer.

b. What is the optimal distribution if society values only utility of Kate.

c. How will your answers change if MUc=400 and MUk=400.

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Public Finance - answers:

Given,
Marginal Utility for John: MUj=400-2Ij
Marginal Utility for Kate: MUk=400-6Ik

a) If the social welfare function is additive, the optimum distribution is attained when the MU functions of the two individuals are equated.

400-2Ij = 400-6Ik
6Ik - 2Ij = 0 , ...

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