Cotton, an intelligent albino guinea pig consumes only two goods: greens and hay. Her preferences are represented by the utility function U(x,y)=x-x/2+y, where x is her consumption of greens, and y is her consumption of hay. Cotton always maximizes her utility subject to her budget constraint. Cotton has an income of Sm and she is allowed to spend as she wishes on greens and hay. The price of hay is always $1 and the price of greens is Px. a. What is Cotton's inverse demand function for greens? (2 marks) b. Suppose that Cotton's daily income is $3 and that the price of greens is $0.50. What is her optimal bundle? (1 mark) c. What bundle would she buy if the price of greens rose to $1? (1 mark) d. How much money would Cotton be willing to pay to avoid having the price of greens rise to $1? What is this called? (3 marks) e. Suppose the price of greens rose to $1. How much extra money would you have to pay Cotton to make her as well-off as she was at the old prices? What is this called? (3 marks) At the price of $0.50 and income of $3, how much (net) consumer's surplus is Cotton getting? (2 marks) f. g. What type of preference does Cotton have? (1 mark)