Budget line of the consumer:

Assume that the consumer has $ 20 to expend on tea and biscuits that cost 50 cent and 40 cent correspondingly. The consumer has three option possibilities before him.

(a) He might decide to purchase tea only, in which situation he can purchase 40 cups of tea.
(b) He might choose to purchase biscuits only, in which situation he can purchase 50 biscuits.
(c) He might decide to purchase some quantity of both the goods, say 20 cups of tea (i.e., $ 10) and 25 biscuits (i.e., $ 10) or 12 cups of tea (i.e., $ 6) and 35 biscuits (i.e., $ 14), and so forth. (Net amount = $ 20).

 Figure: Budget Line

The figure above shows the above three possibilities. The line LM symbolizes maximum amount of biscuits (i.e., 50) and to tea (i.e., 40 cups), that the consumer can purchase with his income of $ 20. The line LM represents that the consumer can’t select any combination beyond this line since his income does not allow him. Nor would he like to select a combination beneath this line; say, B, as it will not symbolize the maximum satisfaction.

Line LM is termed as the budget line as it represents the different amounts the consumer can purchase with his income; it is also termed as the price-ratio line or merely the price line as its slope symbolizes the ratio of prices of the two goods (that is, OM of Good X = OL of good Y).

 Figure: Consumer’s Equilibrium

The consumer acquires the maximum possible satisfaction from his specified income at point C on the indifference curve I₃. At this point, he purchases a combination of OX₁ amount of Good X and OY1 amount of Good Y. Any other probable combination of the two goods will either outcome lesser satisfaction or will not be unobtainable at current prices, with the specified amount of income of the consumer.

At the point of equilibrium (i.e., point C) the price-line LM is tangential to the indifference curve I₃. At point C, the indifference curve and the price-line have similar slope. Now the slope of the indifference curve symbolizes the marginal rate of replacement; and the budget line exhibits the ratio of prices among the two goods. At point C the marginal rate substitution among the two goods as pointed by the slope of the indifference curve I3 and the ratio of prices among the two goods as indicated by the price-line LM are equivalent. This point, hence, points out the ideal combination among the two commodities, providing the consumer the highest satisfaction possible with his inadequate income. At this point, thus the consumer is in equilibrium.

The basic condition of equilibrium is that the marginal rate of substitution of commodity X for commodity Y must be equivalent to the ratio of prices among the two goods. Hence, the condition for equilibrium is

MRS_xy = P_x / P_y

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