Definition: the compensated demand curve is a demand curve that ignores the income effect of a price change, only taking into account the substitution effect. To do this, utility is held constant from the change in the price of the good. In this section, we will graphically derive the compensated demand curve from indifference curves and budget constraints by incorporating the substitution and income effects, and use the compensated demand curve to find the compensating variation.

• Let us consider a price increase for a normal good, a good whose demand increases as income increases. In Figure 7.e.1, assume that the price of Y (PY) is $1, and that the individual has an income of $100. The initial price of X (PX) is $1, so the individual’s initial budget constraint is therefore BC1, with a vertical intercept of 100, and a horizontal intercept of 100. The individual reaches his optimum (maximizes utility) at point A, where his initial budget constraint BC1 is tangent to the indifference curve IC1. Let’s say that at this point, he maximizes his utility by consuming 43 units of good X.

If PX increases from $1 to $2, his budget constraint will rotate inward until it reaches BC2 where there is now a horizontal intercept of 50. The individual now reaches his new optimum where the indifference curve IC2 is tangent to BC2 at the point B, where he maximizes his utility by consuming 18 units of good X. We can use these points to plot a demand curve for good X: According to Figure 7.e.1, when PX is $1, the individual maximizes utility at point A where he consumes 43 units of X. This information can be replotted on a curve showing the relationship between the price of X and the quantity of X consumed (figure 7.e.2). At a price of $1, the individual will consume 43 units of X, so the point A will replot on figure 7.e.2 as the point A’. Similarly at point B, at a price of $2, the individual will consume 18 units of X, so...

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