Suppose we have an economy with three individuals, each with the following utility functions and budget constraints:
Person 1: u(X1, X2) = X10.25 * X20.75 subject to 4X1 + 2X2 = 50
Person 2: u(X1, X2) = X10.5 * X20.5 subject to 4X1 + 2X2 = 75
Person 3: u(X1, X2) = X10.75 * X20.25 subject to 4X1 + 2X2 = 100
- For each individual, graphically depict the utility maximizing allocation of X1 and X2.
- What is the total social welfare in this economy using a Utilitarian social welfare function?
Who is the worst-off person in this society?
- Suppose the government wants to increase social welfare and taxes the most well-off person $25 and redistributes that income to the worst-off person.
- Depict how the utility maximizing decision changes for each person in the economy under this scenario.
- Discuss the relative magnitudes of the income and/or substitution effects due to the policy.
iii. How has social welfare changed as a result of the policy?