Question 2 (22 marks). Sofia consumes only clothes (good a) and books (good y). Her utility unction is given by U(x, y) = 31 + 2y. The price of a is p, per unit and the price of y is py per unit. (a) Are Sofia's preferences monotone? Are they strictly monotone? Does this utility function satisfy diminishing MRS? (5 marks) (b) Find the expenditure-minimising bundle (r, y) as a function of the prices Pr, Py, and the target utility U. Find the corresponding expenditure-minimising function E*(Pr, Py; U). (5 marks) (c) Sofia's girlfriend, Jingshuang, shares her passion for fashion and reading; her utility function is V(x, y) = min{r, y}. (c.1) Find the expenditure-minimising bundle (x, y) as a function of the prices pr, Py, and the target utility V. Find the corresponding expenditure-minimising function E*(Pr, Py; V). (3 marks) (c.2) The owner of the store where Jingshuang buys clothes and books offers a special deal: customers who buy a pieces of clothing get the same number of books for free. Customers can buy additional books at py per book. Find Jingshuang's new expenditure minimising bundle and the corresponding expenditure-minimising function E*(Pr, Py; U). (2 marks) (d) Excited about this offer, Jingshuang calls Sofia to tell her. Find Sofia's expenditure-minimising function E*(Pr, Py; V) with the special deal of this store. (7 marks)