"The Army pays soldiers a salary of $2000 per month. Suppose that all soldiers have the same utility function U=HY, where H is the quantity of housing services demanded per month (i.e., the number of square feet of space) and Y is a composite of all other goods. The price of housing is PH and the price of Y is PY. The Marshallian demand functions are H*=I/2PH and Y*=I/2PY. Soldiers have no income other than their Army salary.
In addition to pay, the government provides a housing allowance that reimburses each soldier for 75 percent of their housing expenditures. How does the housing allowance affect the soldier's budget constraint? What is the utility level with the allowance? How much housing does the soldier purchase? How much does a soldier receive in housing subsidy?