Question

Suppose you only consume two goods food (f) and water (w). Both cost $1. At your current income, you spend some money on food and some on water. You find an extra $20. How much of it do you spend on food if your utility function is given by :
A) U(w,f)= 6(√w) + f
B) U(w,f) = min(2w, 3f)

Answer 1

a)  U(w,f)= 6(√w) + f

MU_w = 6*(1/2√w) = 3 /√w

MU_f = 1

MU_w / MU_f = 3 /√w / 1 = 3/ √w

at equilibrium,

MU_w / MU_f = Pw / Pf

Both cost $1, so

3 /√w = 1

√w = 3

w = 9

So from the extra $20, he will buy 9 unit of water and the remaining will be spent on food.

It means we should spend 20 - 9 = $11 on food.

b) U(w,f) = min(2w, 3f)

At equilibrium,

2w = 3f

w = 3f/2

put this value of w in budget constraint,

I = $20

20 = Pw*w + Pf* f

20 = 1*3f/2 + f

20 = 5f/2

40/5 = f

8 = f

As price of both good is $1.

We should spend $8 on food.