Question 3 A consumer has the following utility function: U(x,y=x+y i) ii) iii) Suppose that prices and income are Px=2, P =1 and I 10. How many units will the consumer buy of product x, and how many of product y? Explain your reasoning. [20%] Draw a graph clearly indicating the constraints and at least two indifference curves, indicating the optimal point (the solution you have found). [20%] Suppose that, instead, the utility function is: U(x,y)=xy Prices and income are the same as before. How many units will the consumer buy for each product? Provide the analytical solution and the reasoning behind it. [20%] iv) Again, draw a graph clearly indicating the constraints and at least two indifference curves, indicating the optimal point (the solution you have found in part iii). [20%] v) Suppose that the utility function is: U(x,y)=2xy Prices and income are the same as before. How many units will the consumer buy for each product? Provide the analytical solution and the reasoning behind it. [20%]