The effect of an uncompensated change in the price of a good equals the effect of a compensated change in the price of the good (the substitution effect), plus the effect of removing the compensation (the income effect).
The substitution effect is negative for a price increase and positive for a price reduction. If a good is normal, the income effect is negative for a price increase and positive for a price reduction. If a good is inferior, the income effect is positive for a price increase and negative for a price reduction.
For a normal good, the income effect reinforces the substitution effect, so the demand curve slopes downward.
For an inferior good, the income effect and the substitution effect work in opposite directions.
If a good is sufficiently inferior, and if it accounts for a sufficiently large fraction of the consumer's spending, its demand curve may slope upward.
Measuring changes in consumer welfare using demand curves
Economists often evaluate the gains or losses that consumers experience when economic circumstances change by computing compensating variations.
Consumer surplus is the compensating variation associated with the loss of access to a market.
The height of a good's demand curve indicates the consumer's willingness to pay for another unit of the good.
One common method of calculating the consumer surplus derived from a good is to determine the area below the good's demand curve and above a horizontal line drawn at the good's price.
The compensating variation for a price change equals the resulting change in consumer surplus. Therefore, economists use the change in consumer surplus as a measure of the change in the consumer's well-being.
Measuring changes in consumer welfare using cost-of-living indexes
A cost-of-living index allows us to approximate changes in a consumer's well-being caused by changes in prices without knowing preferences or demand elasticities.
With a perfect cost-of-living index, the consumer would be better off when real income rises according to the index, and worse off when real income falls according to the index.
In theory, it's possible to construct a perfect price index by computing compensating variations. In practice, doing so requires knowledge of consumer preferences, which vary across the population.
Most price indexes indicate the change in the cost of a fixed bundle of goods.
Laspeyres price indexes suffer from substitution bias because they fail to capture the consumer's tendency to moderate the impact of a price increase by substituting away from goods that have become more expensive. As a result, they tend to overstate increases in the cost of living.
Inflation is the change in the cost of living over time. A common official measure of inflation is based on the Consumer Price Index (CPI), which is a Laspeyres index. Recent estimates suggest that the CPI significantly exaggerates the rate at which the cost of living increases.
Labor supply and the demand for leisure
To understand the supply of labor, we study the demand for leisure, treating the wage rate as the price of leisure.
The substitution effect of an increase in the wage rate decreases leisure demand and increases labor supply.
Since consumers are sellers of their time rather than buyers, income effects are reversed. When leisure is a normal good, the income effect and the substitution effect work in opposite directions. As a result, labor supply curves may bend backwards. There is evidence that, for many prime-age men, labor supply usually does not change much and may even decline as the wage rate rises.
An increase in the wage rate should increase labor force participation. This principle helps to explain the dramatic increase in female labor force participation during the second half of the last century.
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Another type of demand curve
Compensated demand curves always slope downward.
Different compensated demand curves correspond to different levels of the consumer's well-being.
For a normal good, wherever a compensated demand curve intersects an uncompensated demand curve, the uncompensated demand curve is necessarily flatter. For an inferior good, wherever a compensated demand curve intersects an uncompensated demand curve, the uncompensated demand curve is either steeper or upward sloping. If a good is neither normal nor inferior, the compensated and uncompensated demand curves coincide with each other.
To compute consumer surplus exactly, we must use compensated demand curves. If we calculate consumer surplus using uncompensated demand curves, we obtain an approximation of consumer surplus. This approximation will be good if income effects are small.
