Question

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)

Answer 1

an Pg. No. level. Om yo MUX muy Muxa Margind utility of X; Mug = Mergine utility of y Glady would give money to Beatrice to atten At the utility maximizing point oo Py be the marginal utility derived per unit of dollar is equal in both the goods we margind utility for beth goods. Rearranging muy Py PX of money is equal o м" Pt MRJ = Pt. curul line slope of Indifference slope of budget and for the utility to The money I'M = px xt py y needed goody a А. Ei equilibinum point E X U=U Budgetfline good y $cannell with CamScanner B Teacher's Sign

b) MUX py So in need of the price of x rises then it will become < Px (for point El Muy order to equalise both sides we to decrease the consumption of good X and increase the consum onsumption goody by doing due to law of diminshing Marginal utility Mux will increase will fell increasing the left hand side the inequality till both sides become equal. goody a so in and м”, F: new equilibinum F. x E vo D. good X X? x consumption and ons a of x has reduced g y increased. maption CSScanned with CamScanner