Q. "The Army pays soldiers a salary of $2000 every month. Assume that all soldiers have the same utility function U=HY, where H is the quantity of housing services demanded every month (i.e., the number of square feet of space) also Y is a composite of all other goods. The price of housing is PH also the price of Y is PY. The Marshalling demand functions are H*=I/2PH also Y*=I/2PY. Soldiers have no income other than their Army salary.

a. Find out the indirect utility function also the expenditure function for the typical soldier.

b. In addition to pay, the government provides a housing allowance that reimburses each soldier for 75 percent of their housing expenditures. Elucidate how does the housing allowance affect the soldier's budget constraint? Illustrate what is the utility level with the allowance? Elucidate how much housing does the soldier purchase? Elucidate how much does a soldier receive in housing subsidy?

c. Assume that the Army abolishes the housing allowance in part c. Illustrate what salary would be required for the soldiers to be as well off as with the allowance?