Question: A consumer has a utility function U(x1, x2) = x1x2 + x1 + x2. Her income is m dollars, while prices of goods 1 and 2 are p1 and p2, respectively.
(a) Find the demand functions for goods 1 and 2.
(b) Find the indirect utility function, that is, find the maximum level of utility in terms of prices and income.
(c) Find the function that expresses the marginal utility of money income as a function of prices and income. Show that this function is equal to the Lagrange multiplier.