Lee has the following utility function: U(x, y) = x(y + 1), where x and y are quantities of two consumption goods whose prices are pr and py respectively. Lee has a budget of m. Therefore the Lee's maximization problem is x(y + 1) + X(m - Pxx - Pyy) 1. Write down the Lee's maximization problem and the Lagrangian function. 2. Write the first order conditions. 3. Using the first order conditions, find expressions for the demand functions x* = x(px, Py, m), y* = y(px, Py, m) = 4. Verify that Lee is at a maximum by checking the second order conditions. 5. The indirect utility function U U (Pa, Py, m) gives the consumer's maximal attainable utility given goods prices and income. By substituting r* and y* into the utility function, find an expressions for the indirect utility function. 6. The expenditure function m* = m (px, Py, Uā) reveals the minimum expenditure/income required to attain a specific level of utility, Uo, at given prices, px and py. Rearrange the indirect utility function from question 5 in terms of m to derive an expression for the expenditure function. 7. Find am/ap and am/apy. Interpret this expression.
