We have seen that an increase in income corresponds to shifting the budget line outward in a parallel manner. We can connect together the demanded bundles that we get as we shift the budget line outward to construct the income offer curve. This curve illustrates the bundles of goods that are demanded at the different levels of income, as depicted in Figure 6.3A. The income offer curve is also known as the income expansion path. If both goods are normal goods, then the income expansion path will have a positive slope, as depicted in Figure 6.3A.
For each level of income, m, there will be some optimal choice for each of the goods. Let us focus on good 1 and consider the optimal choice at each set of prices and income, Xi(pi,p2,m). This is simply the demand function for good 1. If we hold the prices of goods 1 and 2 fixed and look at how demand changes as we change income, we generate a curve known as the Engel curve. The Engel curve is a graph of the demand for one of the goods as a function of income, with all prices being held constant. For an example of an Engel curve, see Figure 6.3B.
An inferior good. Good 1 is an inferior good, which means that the demand for it decreases when income increases.
How demand changes as income changes. The income offer curve (or income expansion path) shown in panel A depicts the optimal choice at different levels of income and constant prices. When we plot the optimal choice of good 1 against income, m, we get the Engel curve, depicted in panel B.
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