Optimal Point on a Budget Line

The optimal point on a budget line is derived by the intersection of the budget line and indifference curve. In order to understand about the “Optimal point on the budget line”, it is therefore very important to know about a budget line, indifference curve and their characteristics.

An indifference curve is a curve that shows combination of two products from which the same amount of satisfaction can be derived. This makes the consumer indifferent in nature and hence the name of the curve is given. The characteristics of the indifference curve can be stated as below:

1. Same level of satisfaction is obtained throughout every point in the curve and hence consumer does not have any preferences for either of the combinations.
2. The indifference curve slopes from left to right and is convex to the origin. The reason for this property is that when the consumption of one product increases the consumption of the other decreases and as a result the Marginal Rate of Substitution also keeps on reducing.
3. Higher indifference curve means higher satisfaction.  
4. Two indifference curves can never intersect each other because if it does it will contradict the third characteristic that has been mentioned above.
5. Indifference curves are therefore parallel to each other.

The budget line shows the combination of two commodities that a consumer can buy with his given income at a particular market price. The properties of a budget line are as follows:

It is a negatively sloped straight line. The slope of the budget line is the negative of the price ratio, which is .

1. It functions on the income and the spending of the consumers.
2. The budget line can shift both parallel and non-parallel wise depending upon the change in the slope that occurs because of the change in either of the commodities.

The optimal point on the budget line is the combination of these curves, where the budget line is tangent to the indifference curve and where MRS is equal to opportunity cost, which can be explained with the help of the following diagram.

The above diagram shows the interaction of the indifference curve with the budget line. It can be seen that there are three indifference curves IC 1, IC 2 and IC 3. The IC 1 and 2 curves intersect at point A, B and C. We know that lower indifference curve means lower satisfaction and hence we will not consider the points A and C. Anything on the budget line can be afforded, anything below the budget line can be improved and anything above the budget line is not affordable. The IC 3 curve will not be considered therefore. Point B therefore is considered as the optimal point as it provides a higher satisfaction than point A and C. At point B, the slope of budget line and the slope of indifference curve is same, which means MRS is equal to (- ).