Question

Mary considers spoonfuls of sugar (S) and spoonfuls of medicine (M) to be perfect substitutes and always requires 4 spoonfuls of sugar to be willing to give up 2 spoonfuls of medicine (Notice that it means the spoonful of medicine is more valuable for Mary than the spoonful of sugar). Suppose sugar costs $2 per spoonful and medicine costs $3 per spoonful. Mary's income is $18. Which of the following expresses Mary's utility function and optimal consumption bundle?

A. U(S,M) = 4S + 2M; 9 spoonfuls of sugar and 0 spoonfuls of medicine

B. U(S,M) = 2S + 4M; 9 spoonfuls of sugar and 0 spoonfuls of medicine

C. U(S,M) = 4S + 2M; 0 spoonfuls of sugar and 6 spoonfuls of medicine

D. U(S,M) = 2S + 4M; 0 spoonfuls of sugar and 6 spoonfuls of medicine

Answer 1

For Mary, sugar and medicines are substitutes.

She is ready to give up 4 spoonful sugar for 2 spoonful medicine.

Hence her utility function will be U(S,M) = 4S+2M.

Her budget is $18. She can have either 9 spoonfuls of sugar or 6 spoonfuls of medicine.

If sugar is twice or more than medicine, Mary will go for sugar.

Here it is clearly visible that this is not the case.

Hence she will go for 6 spoonfuls of medicine.

The correct option is therefore (C).