7. (Shephard's Lemma and Roy's Identity) Suppose the utility function is u(1, $2) = rix and the budget constraint is pit1 + p242 = m. (a) Solve utility maximization problem for Mashallian demand and indirect utility function. (b) Solve Expenditure Minimization problem for Hicks demand and Expenditure function. (c) Use this example to verify Shephard's Lemma. (d) Use this example to verify Roy's Identity