Question 1) Consider a society consisting of two individuals: A and B. The government is considering how to distribute $25 between A and B (that is MA + MB = 25). The utility functions of the two people are given as the following:
UA = 5 + √MA
UB = √MB
a. If society has a Utilitarian (or additive) Social Welfare Function (SWF), which of the following distributions is preferred by Society? Show and Explain.
i. MA= 16 and MB= 9
ii. MA= 9 and MB= 16
b. Consider the case of the Utilitarian SWF. What distribution of income maximizes social welfare? {Hint: note that while the two utility functions are different the marginal utility for both is the same: MUi= 1/(2√Mi)} Explain why this distribution maximizes social welfare in this case. Show that social welfare is higher with this distribution than either proposed in part a.
Question 2) Numerical answers are required. In the absence of any taxes, the supply and demand curves for gizmos are as follows:
Supply: P = 2Q
Demand: P = 50 - 3Q
a. Calculate the equilibrium price and quantity. Now, a $20 unit tax is imposed with the statutory incidence on the sellers:
b. Calculate the new equilibrium quantity, the new gross-of-tax price, and the new net-of-tax price.
c. Calculate the tax revenue generated for the government and tax burden for the buyers and sellers. Now, the statutory incidence is shifted to the buyers.
d. Calculate the new equilibrium quantity, the new gross-of-tax price, and the new net-of-tax price.
e. Calculate the tax revenue generated for the government and tax burden for the buyers and sellers.