[10 marks] Consider a consumer whose preferences are given by the utility function U(x,y) = (x +1)2 (y +1) where x and y are the quantities he consumes of goods x and y and the prices of good x and good y are px and p3; respectively and his income is m. (It is n_ot required to use the Lagrangian method to solve this question) 1. [2 marks] Show that the preferences satisfy the monotonicity and convexity assumptions. 2. [3 marks] Write down the maximization program of the consumer and determine the demand function of good x( pm) and good y (py,m) ifpx is twice of py (px = Zpy). 3. [2 marks] Now, assume thatpx = py = $2 and m = $14. Determine the optimal consumption of good x and good y . 4. (3 marks) Now assume that the consumer has endowments of ux = 10 units of good x and my = 5 units of good y (instead of monetary income m). Write down the maximization program of the consumer again and determine the net demand of good x and good y ifpx = $2 and py = $1