Principles of Economics/Budget Compensation

Increase in price of good 1

In this case an increase in the price of good 1 (along x axis) shifts the budget curve (black) inward. One can no longer obtain as high an indifference curve (blue) as before; the new indifference curve is closer to the origin and entails a lower utility than the original.

Compensated budget

We can draw a compensated budget, compensating one for the increase in the price of a good by increasing their money overall. However, such a double change will lead to a shift in the way the consumer allocates resources between the two goods. The compensated budget curve (which looks like a line), pink in the graph, has the same slope as the new budget curve but has an optimal point on the original indifference curve (just like the original budget). This new compensated budget allows a consumer to attain exactly the same level of utility despite the fact that the price of a good has increased.

Income and substitution effects

The key position of the compensated budget is the position of resource (money) apportionment that a consumer would make, here labeled with the purple point. The compensated budget offers effectively the same income as the original budget (because it is compensated and the same utility as before is reachable). Therefore, any change in the allotment of what goods a consumer wants to buy, going from the original point to the compensated point, must come entirely from the substitution effect.

Because any shift from original to new budget must result from the combined effect of substitution and income effect, the remainder of the shift is attributable to the income effect. Alternatively, the shift from the purple point to the left blue point (final budget optimal point) involves no change in resource apportionment ratios because the new and compensated budget curves have the same slope (a unit of good 1 is worth the same multiple as much as a unit of good 2). Hence we come to the same conclusion.

If the final blue point is to the left of the purple point, the two effects are acting in harmony and the good along the x axis is considered a normal good.