Question

# Suppose there are only two people, Simon and Casey, who must split a fixed income of...

1. Suppose there are only two people, Simon and Casey, who must split a fixed income of \$100. For Simon, the marginal utility of income is MUS = 400 - 2IS, while for Casey, marginal utility is MUC = 400 - 6IC, where IS and IC are the amounts of income to Simon and Casey, respectively.
1. What is the optimal distribution of income if the social welfare function is additive?
2. What is the optimal distribution of income if the social welfare function is W= IS + 8 IC?
3. What is the optimal distribution of income if the society only values the utility of Simon? Comment on your answers.
4. What is the optimal distribution of income if the society only values the utility of Casey? Comment on your answers.
5. Comment on how your answers change under question (a) if MUS = 400 and MUC = 400.

a) To maximize W, set marginal utilities equal; the constraint is  IS + IC = 100

So, 400 - 6IC = 400 - 2IS

Substituting IC = 100- IS gives us 2IS = 6(100-IS)

Therefore,  IC = \$25  IS = \$75

b) Society's overall welfare is the sum of the utility of each individual i.e. Simon and Casey in this case.

400 - 2IS +  400 - 6IC = IS + 8 IC

Substituting Is = 100- Icgives us 800=14 IC + 3(100- IC)

Therefore,  IC = \$45.45 IS = \$54.55

c) If only Simon matters, then give all the money to Simon until MUs = 0 (unless all the money in the economy is exhuasted first)

So,  400 - 2IS = 0 hence Is =\$200

Comment: Giving all the money to Simon is optimal. Infact, we would like to give him upto \$200.

d) If only Casey matters, then give all the money to Casey until MUC = 0 (unless all the money in the economy is exhuasted first)

So, 400 - 6IC = 0 hence, IC = \$66.67

Comment: Giving any more money to Casey will make her marginal utility negative, which is not optimal. We don't care whether the remaining money is given to Simon or not.

e) MUS = MUC = 400., for all levels of income. Hence the society is indifferent among all distributions of income.

#### Earn Coins

Coins can be redeemed for fabulous gifts.