When U= alnx+blny
(a) Solve for the utility-maximizing levels of x and y (the Marshallian demand functions)
(b) Solve for the indirect utility function.
(c) Solve for the expenditure function (either by inverting the indirect utility function or minimizing expenditure using the Lagrangian method).
(d) Show that the Marshallian demand functions can be obtained from the indirect utility function (Roy’s identity)
(e) Show that the first derivative of the Marshallian demand for x with respect to px can be obtained through the Slusky decomposition. Make sure to identify the income and the substitution effects separately.
(f) Show that the Hicksian (compensated demand) functions can be obtained from the expenditure function (Shephard’s lemma).