Question

Katherine is only made happy by eating portions of ice cream containing exactly four parts chocolate to three parts vanilla. She simply will not eat anything else and will not eat ice-cream in any other ratio. a) Write down a utility function for Katherine and sketch at least 2 indifference curves for her. b) If the price of chocolate ice cream is $3 per pint and price of vanilla is $2 per pint, what is Katherine’s utility-maximizing consumption of chocolate ice-cream when her income is $9? c) Suppose the price of chocolate ice cream now increases to $7.5, what is her new bundle? d) Sketch the demand curve for ice cream. (1 Mark) e) Decompose on a graph, the price increase of ice cream into the income and substitution effect. (You need to write the magnitude of both the effects) (

Answer 1

a) It is given that, Katherine is only happy when the icecream contains exactly 4 units of Chocolate and 3 units of Vanila.

Thus at optimal we must have -

4C=3V

Where C= Chocolate and V=Vanila .

The above can be written as -

(C/3) = (V/4)

Thus Katherine equilibrium choice must satisfy the above.

The Utility function of Katherine can be written as -

U(C,V) = Min { (C/3), (V/4) }

With this utility function we know that at equilibrium we have -

(C/3) = (V/4)

Now let us draw the indifference curve of Katherine -

We know that this type of utility functions are L-shaped shown as follows -

Where, C= Chocolate and V=Vanila.

Since IC2 contains more of both C&V than IC1, so IC2 represents higher utility level than IC1.

b)

Given, Income, M= $9

Price of Chocolate, Pc= $3

Price of Vanila, Pv= $2

The budget line of Katherine is -

M=(Pc.C) + (Pv.V)……........eq(1)

Now we have already found that at equilibrium we must have -

(C/3) = (V/4)

Or, C = (3V/4)….......eq(2)

Substituting eq(2) into eq(1) we get -

We have seen that Katherine has a Perfect Complement Utility function and we know that for Perfect Complement there is no Substitution Effect at all the total Price Effect is equals to the Income Effect.

Hence we have ,

Substitution Effect:

For Chocolate Icecream = 0

For Vanila Icecream = 0

Income Effect: (Final Choice - Initial Choice)

For Chocolate Icecream = { (108/30.5) - (108/26) } = - 0.613 (approx)

For Vanila Icecream = { (36/30.5) - (36/26) } = - 0.204 (approx)