Gladys (who is careful with her money) is going to give her daughter, Beatrice, money for her birthday, and wants to minimise the amount she gives subject to Beatrice being able to attain a specified, fixed level of utility, uo. Beatrice’s utility function (which is known to Gladys) has indifference curves with the usual properties and she consumes two goods, x and y with pricespx, py respectively; Beatrice’s income consists entirely of Gladys’ cash gift to her, all of which she will spend on x and y.

(a) Use a diagram to illustrate Beatrice’s optimal choice. Explain carefully the nature of at Gladys’ choice problem in terms of this diagram? (5 marks)

(b) What will happen to the amount of x Beatrice consumes, and the amount of money Gladys will give her, if px rises? Answer by careful reference to a diagram only. Explain, briefly why you can be sure of the directions of these two effects of the rise in px by reference only to the diagram. (5 marks)