The assumption that all possible bundles of consumption are on a straight line when the budget is fully consumed can be proven by looking at the mathematical relationship between income and expenditure. If we name the budget $\mathit{Budget}$, the price of Good 1 $P1$, the amount of Good 1 $x$, the price of Good 2 $P2$ and the amount of units of Good 2 $y$, we get: $\mathit{Budget}=x\ast P1+y\ast P2$ or, if we solve this equation (budget equation) for $x$:

$$\text{y}=\frac{\text{Budget}}{P2}-\text{x}\frac{P1}{P2},$$ |

thus, a straight line equation with the unknowns
$x$ and
$y$ with the
slope $\frac{P1}{P2}$.
This straight line is called budget line or budget constraint. It contains
all consumption bundles that the household can afford when its
$\mathit{Budget}$ is
completely consumed. Bundles of consumption below the budget line, represented
here by the green area, can as well be afforded by the consumer, but there would
still be income left. Bundles of consumption above the budget line cost more than
the household has at its disposal. When showing test point T, the appearing text
explains the situation: if we move T into the green area, the costs of the
consumption bundle are lower than the income, on the budget line they
correspond exactly to the income and if T is above the red budget line, the costs
are higher than the income. The point C in turn represents a bundle of goods
where the budget is actually used up. If you move this point, it becomes
clear once again that additional consumption of one good reduces the
consumption of the other good. The extent to which this exchange takes
place is reflected by the slope of the budget line (the negative sign of
the slope is ignored here for reasons of simplification). For example, if
the slope is 2, for each unit more of Good 1 , we have to give up two
units of Good 2 . This can be illustrated by shifting point C. The slope of
the budget line is the relative price of the two goods. For example, if a
unit of Good 1 costs 6 € and one unit of Good 2 3 €, the ratio of the
price of Good 1 to the price of Good 2 is 6 : 3 = 2. One unit of Good
1 is twice as expensive as one unit of Good 2 . In other words, for the
price of one unit of Good 1 , you can get 2 units of Good 2 . Here, we
could read this ratio in the light blue box: a relative price of two units of
Good 2 per unit of Good 1 corresponds to a slope of the budget line of
2.

(c) by Christian Bauer

Prof. Dr. Christian Bauer

Chair of monetary economics

Trier University

D-54296 Trier

Tel.: +49 (0)651/201-2743

E-mail: Bauer@uni-trier.de

URL: https://www.cbauer.de