Income–consumption curve

As an income-consumption curve (also: income expansion path ) is called in economics and there varies especially in microeconomics the locus of all household Optima obtained if you let all goods prices constant but the level of household income.

Definition

Formally

One calls with the Marshallian demand for the goods at prices at a household income of y. Consider now special Marshallian demands that satisfy the additional condition that the prices to be left constant in each case, that is. Taking into account the definition of the Marshallian demand, so this means that so exactly a bundle of goods then (and only then ) situated on the income-consumption curve when there is a positive income y, applies to the:

Illustrative ( two-goods case )

There are two goods considered, whose prices are assumed to be constant. Looking first at a certain income level y, then one can determine an optimal amount combination of these two goods with knowledge of the preferences of the consumer. Graphically, this is done by first inscribing the belonging to the household budget budget line in a x1 -x2 diagram. On it are all quantity combinations of good 1 and good 2, the full use of the disposable income of the consumer. Then you can draw some indifference curves: On them are all quantity combinations of good 1 and good 2, through the consumption of the household, an equal benefit. While there are an infinite number of indifference curves, it ultimately only interested in those who as high as possible ( in the sense of far away from the origin ) are - this corresponds to the assumption of non- saturation ( "more is better "). Thus, if a given budget constraint, just interested only that indifference curve just been so touched the budget line. The tangency between the indifference curve and budget line is then the use of optimum quantity combination that can inquire with a given budget the budget.

If you change the income now, a new budget line; obvious example is a budget line the farther away from the origin, the higher disposable income. The transition from budget line B1 to B2 so marked, for example, an increase in income in Figure 1. There is again a new " highest" indifference curve, which leads to a new point of contact for this new budget line. If this procedure is now not just for two income levels, but for all income levels through and the prices of goods can be always the same, then you can see the resulting utility-maximizing points of contact with each other to form a curve - state: the income-consumption curve - connect.

Course of the income-consumption curve

Consider the income-consumption curve in the two-goods case. The income-consumption curve rises when both goods are normal, that is, if an income increase to an increased demand for the respective goods leads ( see Figure 1). On the other hand it falls, if it is one of the goods to an inferior good is ( Fig. 2). ( This is known as a Good inferior when demand [ absolute] decreases with increasing income. )

With perfect substitutes, the income-consumption curve is a straight line whose location is only them, depending which of the two goods more expensive. For example, if the price of good 1 ( which is plotted on the horizontal axis ) is smaller than that of good 2, then any increase in income only in increased consumption of good 1 flows; the resulting income-consumption curve is a horizontal line on the x1 - axis ( Fig. 3). With perfect complements, the income-consumption curve is a straight line through the origin ( positive slope ); provided that the axes operate with identical units, it is as much as a 45- degree line ( Fig. 4). The reason for this is that it is optimal for complement; always consume the same amount of each of the two materials.

This can be generalized. Are the preferences of the observed household homothetic ( as indicated in the special case when perfect substitutes / complements ), then the income-consumption curve is a line through the origin.

Related to the Engel curve is

From the income-consumption curve, the Engel- curve can be derived. Graphically speaking one need only note that pertains to the respective budget line disposable income and transfer it there together with the optimally consumed amount of Good 1 in a x1 -y diagram. The resulting curve then called Engel curve.