Question

A consumer has $25 in budget to purchase goods X & Y. Assume Px = 3 and Py=1. What is the maximum amount of Y that she can buy?

Answer 1

Solution:

Derive the income function (budget line):

I = PxX + PyY

25 = 3X + Y

Y = 25 – 3X

The optimal consumption bundle is where the slope of the indifference curve$(\frac{MUx}{MUy} )$ is equal to the slope of the budget line $(\frac{Px}{Py} )$ in absolute value terms.

MUx = Y and MUy = X, therefore $(\frac{MUx}{MUy} )$ = $(\frac{Y}{X} )$

$(\frac{Px}{Py} )$ = $(\frac{3}{1} )$ = 3, Therefore, $(\frac{Y}{X} )$ = 3 or X = $(\frac{Y}{3} )$

Substitute this into the budget line to get:

Y = 25 – 3X

Y = 25 – 3 $(\frac{Y}{3} )$

Y = 25 – Y

Y + Y = 25

2Y = 25

Y = $(\frac{25}{2} )$ = 13

To get X:

X = $(\frac{Y}{3} )$ = $(\frac{13}{3} )$ = 4

Therefore, the optimum consumption bundle (x,y) = (4, 13)

The maximum amount of Y she can buy is 13 units