Question

explain the derivation of slope of budget line?

Answer 1

The knowledge of the concept of budget line or what is also called budget constraint is essential for understanding the theory of consumer’s equilibrium.

A higher indifference curve shows a higher level of satisfaction than a lower one. Therefore, a consumer in his attempt to maximise his satisfaction will try to reach the highest possible indifference curve.

But in his pursuit of buying more and more goods and thus obtaining more and more satisfaction he has to work under two constraints: first, he has to pay the prices for the goods and, secondly, he has a limited money income with which to purchase the goods. Thus, how far he would go in for his purchases depends upon the prices of the goods and the money income which he has to spend on the goods.

Answer 2

Derivation of slope of budget line

Explanation:

The slope of the budget line measures the amount of change in good 2 required per unit of change in good 1 along the budget line. Now, let us derive the slope of the budget line as follows:

Take two points on the budget line.

$(x_1,x_2) and (x_1+\Delta x_1),(x_2,\Delta X_2)\\\\p_1x_1+p_2x_2=M...(1)\\\\p_1(x_1+\Delta x_1)+p_2(x_2,\Delta X_2)=M..(2)\\\\\text{subtract 1 from 2} \\\\p_1\Delta x_1+p_2\Delta x_2=0\\\\\frac{\Delta x_2}{\Delta x_1}= - \frac{p_1}{p_2}$

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