(i) Since budget line is derived from a linear budget equation M = XPx + YPy, so it is a straight line. The intercepts of this line with the axes show the maximum amount of one commodity that can be purchased, if none of the other is bought.
(ii) Budget line has a negative slope, i.e., slopes downward from left to right. The negative slope of the budget line is mathematically established by noticing coefficient of ‘X’, i.e., – PX/PY when the budget equation is rearranged as
(iii) Mathematically, the slope of the budget line is derivative ∂Y/∂X or coefficient of ‘X’ in the above equation. Thus, the slope of the budget line is negative of the price ratio, i.e., – Px/ Py. If prices of commodity ‘X’ and commodity ‘Y’ are equal, then, the budget line would have a 45° angle with both the axis.
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A flatter budget line means that the relative price of the commodity on the X-axis is lower. The slope of budget line can be known geometrically as the ratio of OB/OA in Fig. 5.18, i.e., Perpendicular/Base or tan 8. OB indicates the units of commodity ‘Y’ that the consumer can purchase, when he spends his entire income on ‘Y’.
It is equal to consumer’s income divided by the price of commodity ‘Y’ or M/Py. Similarly, OA indicates the units of ‘X’ that the consumer can purchase, when he spends his whole income on commodity ‘X’. It is equal to M/Px Now, the slope of the budget line AB is OB/ OA = (M/Py)/(M/Px) = Px/Py. The value of OB and OA can also be worked out by putting X = 0 and Y = 0 in budget equation (5.2) in the two cases respectively so as to get OB or Y = M/Py and OA or X = M/Px.
These are Y-intercept and X-intercept respectively. Now, slope of the budget line = OB/OA = Px/Py Its economic interpretation is that if the individual purchases one unit less of ‘X’, he saves an amount of money equivalent to Px.
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He can use this money to purchase PX/PY units of ‘Y’ Therefore, Px/Py or slope of the budget line represents the rate at which commodity ‘Y’ is substituted for commodity ‘X’ or the number of units of ‘Y’ that the consumer has to sacrifice to get an additional unit of ‘X’. If PX/PY or slope of the budget line is 2, this implies that price of commodity ‘X’ is twice the price of commodity ‘Y’.
(iv) So long as the price ratio remains the same, the slope of the budget line will be the same. If for the same budget for the consumer, prices of both the commodities rise and fall by the same proportion, the budget line will have an outward and inward parallel shift in the two cases respectively (Fig. 5.19).
However, if prices of the two commodities don’t change proportionately, there will be non-parallel shift in the budget line. However, if the prices of the two goods as well as budget of the consumer change in the same proportion, the budget line will remain unchanged.
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In this case, change in the prices of the two goods is offset by the corresponding change in the income of the consumer. Further, if prices of the two goods remaining the same, only the income of the consumer increases (or decreases), the budget line will have a parallel outward (or inward), shift (Fig. 5.19), as the consumer can buy more (or less) with increased (or reduced) income. This will increase (or decrease) both ‘X’ and ‘Y’ intercepts, in the two cases respectively. In all these cases, the slope of the budget line will remain the same.
(v) The budget line shows only the combinations of the two commodities that an individual can afford to purchase. It only specifies the real income or the real purchasing power available to the consumer.
That is why; it is also termed as real income line. Since monetary units are not shown on the diagram of budget line, it is not possible to know the money price of any commodity from it. However, it is possible to know the price ratio of the two commodities from the slope of the budget line.
(vi) Budget line depicts the boundary line (or dividing line), below which lies the region containing attainable combinations of the two commodities. This right angled triangle formed between the budget line and the axes is called the feasible consumption choice set or budget set (shaded portion in Fig. 5.18).
The portion above the boundary line is beyond the reach of the consumer with given income and prices of the two commodities. Thus, the budget line reinforces the concept of scarcity, i.e., the consumer cannot have unlimited amounts of anything or everything.
(vii) Position as well as slope of the budget line will change, if the price of any one commodity changes with the same income. This is explained below.
Suppose income of the consumer and price of commodity ‘X’ remain constant and price of commodity ‘Y’ falls. Then, the consumer is able to purchase more units of commodity ‘Y’ and same number of units of commodity ‘X’.
As a result, the budget line will shift only at its end touching Y-axis. This will increase Y – intercept. In Fig. 5.20(a), the budget line shifts outward from BA to BA, and becomes more steep. The slope of the budget line (given by price ratio of the two commodities) increases from OA/OB to OA/OB.
In case of rise in the price of commodity ‘Y’ the consumer will be able to purchase lesser units of this commodity. As a result, the budget line will shift inward to BA2. This will decrease Y-intercept. The slope of the budget line in this case decreases to OA2/OB.
Now, when the price of commodity ‘X’ changes (income of the consumer and price of other good remains constant), the budget line will shift only at its end touching the X-axis (Fig. 5.20 (b)). In case price of commodity ‘X’ decreases, the consumer can buy more of commodity ‘X’.
Here, the budget line shifts outward, increasing the intercept on X-axis. In the figure, the budget line shifts from AB to AB1 On the other hand, when the price of commodity ‘X’ rises, the consumer can purchase less of commodity ‘X’. Therefore, the budget line shifts inward to AB1. The new budget line becomes relatively flatter and steeper in these two cases respectively.
(viii) To show more than two commodities on a budget line, the most important commodity is isolated, which is shown on the X-axis. The other commodities may be grouped together as ‘composite commodity’ or money income, to be shown on the Y-axis. The slope of the budget line in such situation will be equal to the price of the commodity on the X-axis, i.e., money income divided by the available number of units of commodity ‘X’.