Budget constraint

Budget constraint, where $A={\frac {m}{P_{y}}}$ and $B={\frac {m}{P_{x}}}$

In economics, a budget constraint represents all the combinations of goods and services that a consumer (or other decision-maker) can purchase given current prices and a given level of income or wealth. In consumer theory, the budget constraint and a preference map (or system of indifference curves) are the basic tools used to analyse consumer choice. In the standard two-good case, the budget constraint can be represented graphically as a straight line showing the trade-off between the two goods. If $x$ and $y$ denote the quantities of two goods, with prices $P_{x}$ and $P_{y}$, and $m$ denotes income, the budget line is given by

$P_{x}x+P_{y}y=m.$

Solving for $y$ yields

$y={\frac {m}{P_{y}}}-{\frac {P_{x}}{P_{y}}}\,x,$

where $m/P_{y}$ is the vertical intercept (the maximum amount of $y$ the consumer can buy if $x=0$) and $-P_{x}/P_{y}$ is the slope of the budget line, representing the opportunity cost of one more unit of $x$ in terms of $y$ forgone. Similar constraints appear in models of labour–leisure choice, intertemporal consumption, firm behaviour and international trade.