The budget line is defined as, “The locus of all combinations of commodities which cost some fixed amount of money while the prices are held as constant.” This line shows the various amounts of two or more commodities with a given amount of money a consumer can buy when the relative prices are held as constant. In drawing a budget line we require the income of the consumer and the prices of the commodities. On the basis of this information we can draw budget line.
The budget line is the locus of combination of X and Y which the consumer can buy by spending his entire income, given the prices of goods X and Y. The budget line is derived in the following way. Suppose the consumer spends all his money income on good X. whatever amount of X he can then buy is shown by point K on X-axis. On the other hand, if spends his entire income on Y, he can buy the amount of Y shown by point L on the Y-axis.
Suppose he spend his entire income to buy some combination of X as well as Y i.e. (P
(Px. X+PY, Y= Income). Those combinations represented by the straight line joining K and L can show the various combinations of goods X and Y, which the consumer buys by spending his entire income. The KL line is called budget line.
When the income of the consumer rises, the capacity to buy of the consumer rises. Since the prices of both goods are constant, therefore budget line shifts parallel towards right side. On the other hand, budget line shifts parallel towards left when the income of the consumer declines.
This can explained with the help of the following diagram.
The slope of budget line changes only when the price of one-commodity changes and the income of the consumer and the price of other commodity remain constant. This is shown in the following diagram.
At the given income and prices of the two goods budget line AB is drawn. When the price for good X declines, the consumer can buy more units of X than earlier. Now he can buy OC units of X at lower price of good X. Joint A to C we get new budget line AC.