Budget constraint

A budget line (also consumption possibilities frontier, budget constraint, balance sheet line) referred to in the microeconomics that straight line on which there are all the points that represent combinations of goods where the output total of a consumer equal to its income (budget) is. According to the theory of consumers, each consumer is faced because of his limited income with a budget constraint. Each consumer strives to achieve his personal optimum benefit, that is to achieve its optimum budget.

Construction

A consumer consumes or buys with his budget, which he claims to complete, ( for simplicity ) only two goods. The amount consumed per unit of time (eg one month) of one good ( good 1 ) is plotted on the horizontal, the amount of the other good ( good 2 ) on the vertical axis of a two-dimensional coordinate system in the positive range (1st quadrant). The budget line is now represented as a straight line from the point of the vertical axis in which the person spends its entire budget for Good 2, to the point on the horizontal axis, in which the person their entire budget for Good 1 outputs ranges. The budget line now represents all combinations of two goods that can acquire with its fixed -income consumers. At either extremity ( intersection of the line with an axis ) only a good is consumed, that is, the total income is spent on this commodity only. Between these extremes any goods combination can be selected on the budget line the consumer with an existing income.

Example

Mr. P. only buys water bottles ( Good 1 ) and loaves of bread ( good 2 ). A water bottle costs 1 euro, 2 euros a loaf of bread. Mr. P. has a monthly income of 40 euros. He can, as on the budget line can be seen, choose either 40 bottles of water and no loaf of bread, 20 loaves of bread and no water bottle or any combination of the two goods, which lies on the budget line (eg, 10 loaves of bread and 20 water bottles or 8 loaves of bread and 24 water bottles ). Of course, he can also consume less than it would be possible by his income; then its use would not emerge graphically on the budget line, but within the triangle between the straight line and the coordinate origin.

Calculation

The income is the sum of the products ( price of good 1 × amount of good 1 ) and ( price of good 2 × amount of good 2 ). Shown as a formula:

For the " extreme values ​​" ( intersections with the axes, and saturation amount ) are calculated by transforming the equation, the following representations:

• Only consumption of good 1:
• Only consumption of good 2:

The slope of the budget line corresponds to the negative quotient of the two prices, namely

Note: X1, X2 are the amounts of the goods; p1, p2 are the respective prices; Y (English: yield ) is the income.

Intertemporal budget constraint

The budget line can be constructed also for multiple time points. How could a consumer faced with a decision to spend his income in period 1 for good x, or to save and consume only in period 2. Allows you beyond that money saved can be invested to earn interest r with a savings interest rate, so can set up the following equation:

Or

If the household borrows money in one period, he must repay borrowing rate r it in period 2:

Or or

The last two equations are identical. The difference is explained by the term. If this is positive, then the household has saved ( m1 > xp1 ) or it is negative, then the household has to borrowed money (m1 < xp1 ). In the first case you earn interest r, the second one pays interest r.

On this basis, many other considerations are possible.