(13 marks) 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 /2ty, 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 $m 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) f. At the price of $0.50 and income of $3, how much (net) consumer's surplus is Cotton getting? (2 marks) g . What type of preference does Cotton have? (1 mark)