# Engel curve

The Engel curve shows us how the demand for a good varies in the face of a change in income, considering that the prices of the goods remain constant.

For each income level, there is an optimal basket of goods that depends on consumer preferences. In graphic terms, the optimal basket for a given level of income is the point of tangency between the indifference curve and the balance line or budget constraint. When the consumer's disposable income changes, his demand for the goods adjusts, this adjustment is what is reflected in the Engel curve.

## The slope of the Engel curve

The slope of the Engel curve depends on the nature of the good:

• When the good is normal, the slope will be positive because an increase in income is accompanied by an increase in the demand for the good. Thus, for example, beef is a normal good, when income increases we expect its demand to increase and therefore the Engel curve will have a positive slope.
• When the good is lower, the slope will be negative since as income increases, the consumer will prefer to reduce his demand for the good. For example, stale bread is an inferior good. If the consumer has little income, he will buy the cheapest bread he can find, but as his income increases he will seek to replace it with another good of higher quality. In this way, the Engel curve will have a negative slope.

## How to derive the Engel curve, case with two goods.

For simplicity, suppose there are two goods (X and Y). As we know, with an increase in income, the balance line shifts to the right (out in parallel) and the consumer can reach a higher indifference curve.

If we graph all possible budget lines and consumer indifference curves, we can obtain a curve that joins all the optimal combinations of goods (X and Y). From this graph we can obtain the Engel curve that presents the demand for a good (for example X) at different levels of income.

Demand curve

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