Budget Line (Price Line)

While an indifference map shows what combinations of two goods a consumer would EQUALLY LIKE to have, it says nothing about which of them he can actually afford — that depends on his income and the prices of the two goods. The Budget Line (also called the Price Line) is the locus of all combinations of two goods that a consumer can purchase by spending his ENTIRE money income, given fixed prices for both goods.

If a consumer has income $M$ to spend on goods X (price $P_x$) and Y (price $P_y$), the budget line's equation is:

Setting $y=0$ gives the X-intercept, $x = \dfrac{M}{P_x}$ — the maximum units of X the consumer could buy if he spent his ENTIRE income on X alone. Setting $x=0$ gives the Y-intercept, $y = \dfrac{M}{P_y}$ — the maximum units of Y he could buy spending it all on Y. The slope of the budget line, obtained by rearranging the equation as $y = \dfrac{M}{P_y} - \dfrac{P_x}{P_y}x$, is $-\dfrac{P_x}{P_y}$ — the NEGATIVE of the price ratio of the two goods. This slope tells us the real, market-given rate at which X can be exchanged for Y: to buy one more unit of X, the consumer must give up exactly $\dfrac{P_x}{P_y}$ units of Y.

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