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.
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.
To find out Aneeta's pocket money, we need to first determine the relationship between the utility function, her consumption of chocolates and ice cream, and the prices of chocolates and ice cream.
The utility function U(x, y) represents Aneeta's satisfaction or happiness derived from consuming x chocolates and y ice creams. In this case, her utility function is U(x, y) = min(4x, 2x + y).
From the given information, Aneeta consumes 15 chocolates (x = 15) and 10 ice creams (y = 10). We can substitute these values into the utility function to find the utility she gets from these quantities:
U(15, 10) = min(4 * 15, 2 * 15 + 10)
= min(60, 40 + 10)
= min(60, 50)
= 50
Now, we need to consider the prices of chocolates and ice cream. It is given that the price of chocolates is Rs. 10.
Let's assume Aneeta's pocket money is P (in Rs.). Aneeta spends all her pocket money on chocolates and ice cream. So, the total amount she spends is equal to the cost of the chocolates she buys.
The cost of 15 chocolates is 15 * Rs.10 = Rs. 150.
Since the cost of chocolates she buys is equal to her total pocket money, we can set up the equation:
P = Rs. 150
Therefore, Aneeta's pocket money is Rs. 150.