Question

3. If Sasha is indifferent between a piece of cake (c) and two fruits (f) (sees as substitutes), pc =8 - price of a piece of cake , p_f = 5 -price of fruit and her income is I , then her indirect utility is given by:

4. (a) V = I/8

(b) V = I/4

(c) V = I/5

(d) V =2I/5

Answer 1

The correct answer is (b) I/4

First lets derive her utility function.

It is given that she sees cake and fruits as substitutes.

Thus her Utility(U) = af + bc

It is given that Sasha is indifferent between a piece of cake (c) and two fruits (f). This means that she prefers cake 2 times over fruit implies that a = 1 and b = 2.

Hence U = f + 2c.

Indirect utility function shows the maximum utility she can derive with the given prices and Income.

Now, U = f + 2c.

As fruits and cake are perfect substitutes and she valus cake 2 times over fruit. Thus If price of cake > 2 * price of fruits, then she will consume only fruits and If price of cake < 2 * price of fruits, then she will consume only cake.

Here price of cake = 8 and price of fruits = 5 => price of cake < 2 * price of fruits, thus she will consume only cake.with all her income..

Let income be I and hence budget is given by: p_cc + p_ff = I => 8c + 5f = I and as discussed above she will consume cake only => f = 0

=> 8c = I

=> c = I/8 and f = 0.

Putting these value in above Utility function we get Indirect utility function(V).

=> V = 0 + 2(I/8)

=> V = I/4 ---------------------Indirect utility function.

Hence, the correct answer is (b) I/4