Fig. 5.18 shows the way budget line is drawn. Suppose, a consumer has Rs. 20 to be spent on two commodities ‘X’ and ‘Y’ If the price of commodity ‘X’ is Rs. 2 per unit and that of commodity ‘Y’ is Rs 1 per unit, he can buy 10 units of commodity ‘X’ (given by OA in the figure), when the entire income is spent to purchase commodity ‘X’. On the other hand, if the consumer spends his entire income to purchase commodity ‘Y’, he can purchase 20 units of commodity ‘Y’ (OB in the figure).
The consumer can also choose any other combination on the line joining points ‘A’ and ‘B’, when he partly spends his income on one commodity (say, Rs. 5 to purchase 10 units of commodity ‘X’) and partly on the other (say, Rs. 5 to purchase 5 units commodity ‘Y’).
Straight line AB is called the budget line. This line suggests that the consumer cannot choose any combination of commodities beyond this line (say, point ‘C’ in the figure), as his income does not permit him to do so. Any point, say, ‘D’ below this line indicates that his income is not fully spent.
The budget line is also called as the consumption possibility line, as it represents the different possibilities of the two goods, the consumer can purchase with his given income. Sometimes, it is referred to as opportunity line, since it provides an opportunity of buying one combination rather than the other.
Leftwich calls it the line of attainable combinations. Friedman has also used the same term in his book, ‘Price Theory’. The budget line can also be known as the menu of choices open to the consumer, given his money income and the prices of the goods.
To understand the properties of the budget line, budget equation of the consumer needs to be explained. Money income of the consumer together with the prices of goods would define the budget equation, consumer’s budget set or the feasible consumption choice set.
If there are ‘N’ commodities X1 X2, X3………………, XN in the market with their respective prices Pp P2, P3,…………………… PN and consumer’s money income is ‘M’, then the budget equation is given by
M = P1X1 + P2X2 + P2X3 +…………….. + PN XN
Where X1, X2, X3,…………. XN are the quantities of commodities X1 X2, X3,………………. , XN respectively.
The various terms on the right hand side of the above equation represent the expenditure (price x quantity) on commodities X1, X2, X3,………. XN respectively.
For two-dimensional graphical representation, we consider only two commodities ‘X’ and ‘Y’ to be shown on horizontal and vertical axis respectively. Alternatively, expenditure on all the commodities other than the one shown on the X-axis may be taken together, for which Y-axis may be used. Now, for two commodities ‘X’ and ‘Y’ with respective prices Px and Py, the budget equation is given by M = XPx + YPy …(5.1)
The above equation implies that the money income must be spent on either commodity ‘X’ or commodity ‘Y’ or both. Further, income must equal expenditure. In other words, the entire income must be completely exhausted in purchasing the two goods. In this equation, M, Px and Py are constants, while ‘X’ and ‘Y’ are variables.