Question

Aneeta spends all her pocket money on chocolates(x)and icecream(y). Her utility function is U(x,y)= min(4x,2x+y). Aneeta consumes 15 chocolates and 10 icecreams. The price of chocolates is Rs.10. Find out her pocket money.

Answer 1

First, lets break apart the Utility function. We know Aneeta consumes 15 x and 10 y. Her utility is therefore min(4*15, 2*15+10) = min(60, 40) = 40. So, for here relevant consumption pattern, her utility function is simply U=2x+y.

Utility will be maximized when MUx/MUy = Px/Py
MUx is the first derivitive of U with respect to x. So, MUx=2, MUy=1. So MUx/MUy = 2. You are given Px=10. Ergo, Py must be 2.

Take it from here to find amount of pocket money.