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?

(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.

Answer 1

a.) Beatrice's optimal choice will be at the point where the slope of her indifference curve is equal to the slope of her budget line. In this case, her budget line is the amount of money that Gladys gives her. The intercept on the x-axis shows the number of units of good x that Beatrice can afford if she spends all her money on good x and the intercept on the y axis is the number of units of good y that Beatrice can buy if she spends all her money on good y. The budget line shows all the various combinations of goods x and y that Beatrice can afford, and the indifference curve shows all the various combinations of good x and y that yeild the same level of satisfaction for Beatrice.

Hence, the problem for Gladys is that she has to decide which indifference curve Beatrice should be placed on, as higher the indifference curve, more will be the money that Beatrice will need.

b.) If the price of good x rises, then the budget line rotates to the left, i.e. inwards. In such a case, it is seen that Beatrice is brought to a lower indifference curve, as her utility will now reduce because she has to pay more for x. There will be two kinds of effects here -

Income effect: the consumption of x and y will reduce as now the price of x is increased which will reduce the real income of Beatrice.

Substitution effect: the consumption of y will increase as Beatrice will substitute some x for y, because the price of x has increased.

In the diagram, we can see that the initial budget line is MM1, where Beatrice consumes bundle A at utility level U0. When the price of good x rises, the budget line rotates to MN1, and the bundle Beatrice now consumes is C. If we want to capture the income and the substitution effects separately, we take away equivalent amount of real income while Beatrice is still at budget line MM1, to reach budget line NM2. The bundle she now consumes is B.

We can see that income effect is the shift from bundle A to B, where the amount of good y and good x both reduce, and substitution effect is from A to C, where the amount of good y increases and x decreases as the price of x increases.