BUDGET LINE

 

BUDGET LINE

The budget line can be defined as a set of combinations of two commodities that can be purchased if whole of income is ,spent on them and its slope is equal to the negative of the price ratio. The budget line shows all those combinations of two goods which the consumer can buy spending his given money income on the two goods at their given prices.

Suppose our consumer has got income of Rs. 50 to spend on goods X and Y. Let the price of the good X in the market be Rs. 10 per unit and that of Y Rs. 5 per unit. If the consumer spends his whole income of Rs. 50 on good X, he would buy 5 units of X; if he spends his whole income of Rs. 50 on good Y he would buy 10 units    of Y. If a straight line joining 5X and l0Y is drawn, we will get what is called the price line or the budget line. A look at Fig. 1 shows that with Rs. 50 and the prices of X and Y being Rs. 10 and Rs. 5 respectively the consumer can buy l0Y and OX; or 8 Y and 1X; or 6Y and 2X, or 4 Y and 3X etc.

 

 

FIG:1 The Budget Line

 

 In other words, he can buy any combination that lies on the budget line with his given money income and given prices of the goods. It should be carefully noted that any combination of goods as H (5Y and 4X) which lies above and outside the given budget line will be beyond the reach of the-consumer. But any combination lying within the budget line such as K (2X and 21) will be well within the reach of the consumer, but if he buys any such combination he will not be spending all his income of Rs. 50. Thus, with the assumption that whole of the given income is spent on the given goods and at given prices of them, the consumer has to choose from all those combinations which lie on the budget line.

 

 

It is clear from above that budget line graphically shows the budget constraint. The combi­nations of commodities lying to the right of the budget line are unattainable because income of the consumer is not sufficient to be able to buy those combinations. Given his income and the prices of goods, the combinations of goods lying to the left of the budget line are attainable, that is, the consumer can buy any one of them. 

 

The budget line can be written algebraically as follows :

 

Px.X + Py.Y = M

 

 Where Px and Py denote prices of goods X and Y respectively and

 

 M stands for money income

 

Solving the equation  for Y we have the following alternative form of the budget equation.

 

Y=  ─  . X

 

The first term on the right side of the budget equation , that is, M/Py, shows the amount of commodity Y that can bought if quantity purchased of X is zero. In Figure:1, this is represented by the distance OB on the Y-axis. Thus M/Px is the vertical intercept of the budget line equation. The second term on the right hand side of the equation  has the coefficient  which equals the slope of the budget line.

Budget Space

 

A budget space shows a set of all commodity combinations that can be purchased by spending the whole or a part of the given income. In other words, budget space represents all those combinations of the commodities which the consumer can afford to buy, given the budget constraint. Thus, the budget space implies the set of all combinations of two goods for which income spent on good X (i.e Px.X) and income spent on good Y(i.e Py.Y) must not exceed the given money income. Therefore, we can algebraically express the budget space in the following form of inequality.

 

 

PxX + Py.Y≤ M, or M ≥ Px. X + PY.Y

 

The budget space has been graphically shown in Figure 6.22 as the shaded area. The budget space is the entire area enclosed by the budget line BL and the two axes.

Fig. 2. Budget space

 

Changes in Price and Shift in Budget Line

 

Now, what happens to the price line if either the prices of goods change or the income changes. Let is first take the case of the changes in prices of the goods. This is illustrated in Fig. 3. Suppose the budget line in the beginning is BL, given certain prices of the goods X and Y and a certain income.

 

 

Fig.3 Changes in budget line as a result of

 

         Changes in price of good X

 

Suppose the price of X falls, the price of Y and income remaining unchanged. Now, with a lower price of X the consumer will be able to purchase more quantity of X than before with his given income. Let at the lower price of X, the given income purchases OL' of X which is greater than OL. Since the price of Y remains the same, there can be no change in the quantity purchased of good Y with the same given income and as a result there will be no shift in the point B. Thus, with the fall in the price of good X, the consumer's money income and the price of Y remaining constant, the price line will take the new position BL'.

 

Now, what will happen to the budget line (initial budget line BL) if the price of good X rises, the price of good Y and income remaining unaltered. With higher price of good X, the consumer can purchase smaller quantity of X, say OL", than before. Thus, with the rise in price of X the price line will assume the new position BL".

 

Fig.4 Changes in budget line as a result of

 

         Changes in price of good Y

 

Fig. 4 shows the changes in the price line when the price of good Y falls or rises, with the price of X and income remaining the same. In this the initial budget line is BL. With the fall in price of good Y, other things remaining unchanged, the consumer could buy more of Y with the given money income and therefore budget line will shift to LB'. Similarly, with the rise in price Y, other things being constant, the budget line will shift to LB".

 

Changes in Income and Shifts in Budget Line

Now, the question is what happens to the budget line if the income changes, while the prices of goods remain the same. The effect of changes in income on the budget line is shown in Fig. 5. Let BL be the initial budget line, given certain prices of goods and income. If the consumer's income increases while the prices of both goods X and Y remain unaltered, the price line shifts upward (say, to B'L') and is parallel to the original budget line BL. This is because with the increased income the consumer is able to purchase proportionately larger quantity of good X than before if whole of the income is spent on X, and proportionately greater quantity of good Y than before if whole of the income is spent on Y. On the other hand, if the income of the consumer decreases, the prices of both goods X and Y remaining unchanged, the budget line shifts downward (say, to B"L") but remains parallel to the original price line BL. This is because a lower income will purchase a proportionately smaller quantity of good X if whole of the income is spent on X and proportionately smaller quantity of good Y if whole of the income is spent on Y.

 

 

 

Fig. 5. Shifts in Budget Line as a result of Changes in income