## The Engel Curve

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The Engel Curve

we will instead show how to derive the relation between income and the quantity demanded. The resulting curve is called the Engel curve.

Look at Figure 4.2. Just as in the previous case, we start with the individual’s maximization problem where she must choose quantities of good 1 and good 2. (Again, think of good 2 as “all other goods.”) However, instead of varying the price, we now vary the income m. This means that the budget line will shift outwards for higher incomes and inwards for lower incomes. We assume that preferences and prices are unchanged. For the increasingly higher incomes m_{1}, m_{2}, and m_{3}, the budget lines become BL_{1}, BL_{2}, and BL_{3}.

In the same way as before, we find the utility maximization points for each budget line: points A, B, and C. If we would do that for all possible incomes, we would get the so-called income-consumption curve. That curve shows the optimal consumption of good 1 and good 2 at different incomes, given preferences and prices.

Similarly to before, we indicate the quantities that correspond to points A, B, and C, i.e. q_{11}, q_{12}, and q_{13} in the diagram below. Then we indicate the incomes m_{1}, m_{2}, and m_{3} on the Y-axis, and the points where the incomes intersect the corresponding quantities: points D, E, and F. Thereafter, we draw a line through the points of intersection, as it would probably have looked if we had performed the same procedure for the points in between. The resulting curve is the so-called Engel curve, and it shows how the optimal consumption of good 1 varies with the income, given preferences and prices.

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