Max is a utility-maximizer consumer with a utility function U (x , y )=x+ y and the usual budget

constraint M=px x+ p y y , where M is his income, px and py is the price of good x and y,

respectively

Write down Max's optimization problem as a constrained optimization problem.

Write down the first order conditions for Max's constrained optimization problem.

Use the implicit functions procedure on the first order conditions to calculate the derivatives of Max's demand for good y with respect to M, px and py. Note: you have to calculate those partial derivatives without finding the demand for x or y!

Write down the second order condition(s) and check whether it/they is/are satisfied.

Find Max's demand for good x and y