Why slope of Budget line is represented by Price Ratio - Economics - Theory of Consumer Behaviour

Question

Why slope of Budget line is represented by Price Ratio?

Ritika Chauhan · Accepted Answer

Budget line represents the different combinations of two goods that can purchased by the consumer given a fixed level of income and market prices for the two goods.

The budget line is therefore,

$P_{1} X_{1} + P_{2} X_{2} = M$

where,

$P_{1} : \Pr i c e o f g o o d 1 P_{2} : \Pr i c e o f g o o d 2 X_{1} : Q u a n t i t y o f g o o d 1 p u r c h a s e d X_{2} : Q u a n i t y o f g o o d 2 p u r c h a s e d$

On the other hand, the slope of a budget line measures the amount of good 2 that must be sacrifices in order to obtain additional amount of good1, with income fixed.

i.e

$P_{1} △ X_{1} + P_{2} △ X_{2} = △ M w h e r e, △ X_{1} : C h a n g e i n q u a n t i t y o f g o o d 1 p u r c h a s e d △ X_{2} : C h a n g e i n q u a n t i t y o f g o o d 2 p u r c h a s e d △ M : C h a n g e i n i n c o m e = 0, \sin c e i n c o m e i s f i x e d .$

this can be written as ,

$P_{1} △ X_{1} + P_{2} △ X_{2} = 0 P_{1} △ X_{1} = - P_{2} △ X_{2} \frac{△ X_{2}}{△ X_{1}} = - \frac{P_{1}}{P_{2}}$

This, is why the slope of a budget line is represented by a price ratio.