Why is the budget line negatively sloped?

Answer 1

The budget line is negatively sloped because :-

1. MATHEMATICALLY

* Given a budget line p1x1+ p2x2= M

* where (x1,x2) is the budget bundle of good 1 and good 2 resp. ( i.e quantity bought of good 1 & 2 respectively)

* p1 and p2 are the prevailing prices of good 1 and good 2;

* M is the total budget;

then,

x2 = (M/p2) - (p1/p2)x1

where M/p2 is the intercept along the axis of good 2 and

slope is -p1/p2 which is negative and thus there is a negative slope.

2. MEANING

The slope of the budget line -(p1/p2) signifies the rate by which the consumer is ready to substitute good 1 for good 2. Consider a situation with a budget bundle (x1,x2) such that x1>x2.There would always be a point where the consumer would decline substituting good 1 for good 2 because he/she has more of good 1 and less of good 2 thus the rate of substituting declines giving a negative slope.

Example:-

A young guy likes to keep a collection of high end sports cars. He plans to buy 5 Bentley Azures and 2 Convertible Corvettes (notice the price difference between the two). In such a situation, it is very obvious for the person not to compromise on Corvettes for an extra Bentley.

Note:- This phenomena can also be explained via Indifference Curves