Suppose that an economy consists of two people: Ted and Jane. Their marginal utility functions are given by: MUT = 600 - 3IT and MUJ = 600 - 2IJ, where IT is Ted’s income and IJ is Jane’s income. There is a total income of I = 500 generated by the economy.
a. Compute the optimal income distribution for the two people, assuming that society values each person’s utility equally, i.e. W = UT + UJ. Explain why this income distribution is optimal.
b. Draw a graph and identify the welfare loss to society of an egalitarian income distribution where Ted and Jane are each allocated income of 250. Explain why an egalitarian income distribution is typically non-optimal.
c. Explain the assumption made in this type of analysis regarding the relationship between the income distribution and the total income in the economy.