Suppose that the utility of a consumer depends on the consumption of Goods X and Y, and U = U(x,y). The price of good x and y is respectively given by Px and Py, and the consumer has income = I. a) Using the method of Lagrange, set up the consumer’s utility maximization problem. b) Using (a) above, derive the first order conditions. c) Construct the bordered Hessian matrix of second derivatives. What conditions must the bordered Hessian matrix satisfy for the solution from (b) to be a maximum. d) Suppose there is an increase in Price of Good Y, Py. Derive how this increase in Py would affect the demand for Good x and Good y. e) Comment on the income and substitution effect of the price change.