Question

Find the utility maximizing demands for x and y, x* and y*, when U(x,y)=min(x,5y)

, the price of x is $1, the price of y is $15, and income (M) is $140. The demand for x is , and the demand for y is

Answer 1

Answer 6

U = min{x,5y}

In order to determine demand of x and y we have to :

Max : U = min{x,5y}
such that : x + 15y = 140 -------(1)

We can see that it considers x and y as perfect complements and optimal condition for this perfect complement function is that It chooses combination of goods at which Kink of an indifference curve will occur.

Here kink will occur when x = 5y

Using x = 5y in (1) we get :

5y + 15y = 140 => y* = 7 and thus x* = 35

Therefore, demand for x = 35 and demand for y = 7.