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### Course: Microeconomics>Unit 3

Lesson 3: Income elasticity of demand and cross-price elasticity of demand

# Elasticity in areas other than price

Elasticity also applies in labor markets and in financial capital markets

## Key points

• Elasticity is a general term, referring to percentage change of one variable divided by percentage change of a related variable that can be applied to many economic connections.
• Elasticity applies in labor markets and financial capital markets just as it does in markets for goods and services.
• Cross-price elasticity of demand is the percentage change in the quantity of good A that is demanded as a result of a percentage change in the price of good B.

## Elasticity in areas other than price

The basic idea of elasticity—how a percentage change in one variable causes a percentage change in another variable—does not just apply to the responsiveness of supply and demand to changes in the price of a product.
Quantity demanded, $\text{Qd}$, depends on more than just price, it also depends on income, tastes, preferences, the prices of related goods, and so on. Similarly, quantity supplied, $\text{Qs}$, depends on the cost of production and other factors, as well as on price.
Elasticity can be measured for any determinant of supply and demand, not just the price.

## Income elasticity of demand

The income elasticity of demand is the percentage change in quantity demanded divided by the percentage change in income.
For most products most of the time, the income elasticity of demand is positive. In other words, a rise in income will cause an increase in the quantity demanded. This pattern is common enough that these goods are referred to as normal goods.
However, for a few goods, an increase in income might mean that a person will purchase less of the good; for example, those with a higher income might buy fewer hamburgers because they are buying more steak instead. Those with a higher income might buy less cheap wine and more imported beer. When the income elasticity of demand is negative, the good is called an inferior good.
A higher level of income for a normal good causes the demand curve to shift to the right, which means that the income elasticity of demand is positive. How far the demand shifts depends on the income elasticity of demand. A higher income elasticity means a larger shift.
For an inferior good, however, a higher level of income would cause the demand curve for that good to shift to the left. Again, how much it shifts depends on how large the negative income elasticity is.

## Cross-price elasticity of demand

A change in the price of one good can shift the quantity demanded for another good.
If the two goods are complements, like bread and peanut butter, then a drop in the price of one good will lead to an increase in the quantity demanded of the other good. However, if the two goods are substitutes, like plane tickets and train tickets, then a drop in the price of one good will cause people to substitute toward that good, reducing consumption of the other good. Cheaper plane tickets lead to fewer train tickets and vice versa.
The cross-price elasticity of demand puts some meat on the bones of these ideas. The term cross-price refers to the idea that the price of one good affects the quantity demanded of a different good. Specifically, the cross-price elasticity of demand is the percentage change in the quantity of good A that is demanded as a result of a percentage change in the price of good B.
Substitute goods have positive cross-price elasticities of demand. If good A is a substitute for good B—like coffee and tea—then a higher price for B will mean a greater quantity consumed of A.
Complement goods have negative cross-price elasticities. If good A is a complement for good B—like coffee and sugar—then a higher price for B will mean a lower quantity consumed of A.

## Elasticity in labor and financial capital markets

The concept of elasticity applies to any market, not just markets for goods and services. In the labor market, for example, the wage elasticity of labor supply—that is, the percentage change in hours worked divided by the percentage change in wages—determines the shape of the labor supply curve.
The wage elasticity of labor supply for teenage workers is generally thought to be fairly elastic—a certain percentage change in wages will lead to a larger percentage change in the quantity of hours worked. On the other hand, the wage elasticity of labor supply for adult workers in their 30s and 40s is thought to be fairly inelastic. When wages move up or down by a certain percentage amount, the quantity of hours that adults in their prime earning years are willing to supply changes, but by a lesser percentage amount.
In markets for financial capital, the elasticity of savings—the percentage change in the quantity of savings divided by the percentage change in interest rates—determines the shape of the supply curve for financial capital.
Sometimes laws are proposed that seek to increase the quantity of savings by offering tax breaks so that the return on savings is higher. Such a policy will increase the quantity if the supply curve for financial capital is elastic because then a given percentage increase in the return to savings will cause a higher percentage increase in the quantity of savings.
However, if the supply curve for financial capital is highly inelastic, then a percentage increase in the return on savings will cause only a small increase in the quantity of savings.
The evidence supporting the supply curve of financial capital is controversial but, at least in the short run, the elasticity of savings with respect to the interest rate appears fairly inelastic.

## Expanding the concept of elasticity

We've already looked at a variety of factors we can examine using the concept of elasticity. Let's take it even further—the elasticity concept doesn't even need to relate to a typical supply or demand curve at all!
For example, imagine that you are studying whether the Internal Revenue Service should spend more money on auditing tax returns. The question can be framed in terms of the elasticity of tax collections with respect to spending on tax enforcement; in other words, what is the percentage change in tax collections derived from a percentage change in spending on tax enforcement?
With all of the elasticity concepts that have just been described—some of which are listed below—the possibility of confusion arises.
When you hear the phrases “elasticity of demand” or “elasticity of supply”, they refer to the elasticity with respect to price. Sometimes, either to be extremely clear or because a wide variety of elasticities are being discussed, the elasticity of demand or the demand elasticity will be called the price elasticity of demand or the “elasticity of demand with respect to price”.
Similarly, elasticity of supply or the supply elasticity is sometimes called—to avoid any possibility of confusion—the price elasticity of supply or “the elasticity of supply with respect to price”. But in whatever context elasticity is invoked, the idea always refers to percentage change in one variable—almost always a price or money variable—and how it causes a percentage change in another variable—typically a quantity variable of some kind.
$\begin{array}{ccc}\text{Wage elasticity of labor supply}& =& \frac{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{quantity}\mathrm{of}\mathrm{labor}\mathrm{supplied}}{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{wage}}\end{array}$
$\begin{array}{ccc}\text{Wage elasticity of labor demand}& =& \frac{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{quantity}\mathrm{of}\mathrm{labor}\mathrm{demanded}}{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{wage}}\end{array}$
$\begin{array}{ccc}\text{Interest rate elasticity of savings}& =& \frac{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{quantity}\mathrm{of}\mathrm{savings}}{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{interest}\mathrm{rate}}\end{array}$
$\begin{array}{ccc}\text{Interest rate elasticity of borrowing}& =& \frac{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{quantity}\mathrm{of}\mathrm{borrowing}}{\mathrm{%}\mathrm{change}\mathrm{in}\mathrm{interest}\mathrm{rate}}\end{array}$

## Summary

• Elasticity is a general term, referring to percentage change of one variable divided by percentage change of a related variable that can be applied to many economic connections.
• Elasticity applies in labor markets and financial capital markets just as it does in markets for goods and services.
• Cross-price elasticity of demand is the percentage change in the quantity of good A that is demanded as a result of a percentage change in good B.

## Self-check questions

What would the gasoline price elasticity of supply mean to UPS or FedEx?
Assume the average annual income rises from $25,000 to$38,000 and the quantity of bread consumed in a year by the average person falls from 30 loaves to 22 loaves. What is the income elasticity of bread consumption? Is bread a normal or an inferior good?
Suppose the cross-price elasticity of apples with respect to the price of oranges is 0.4, and the price of oranges falls by 3%. What will happen to the demand for apples?

## Review Questions

• What is the formula for the income elasticity of demand?
• What is the formula for the cross-price elasticity of demand?
• What is the formula for the wage elasticity of labor supply?
• What is the formula for elasticity of savings with respect to interest rates?

## Critical-thinking questions

• Normal goods are defined as having a positive income elasticity. We can divide normal goods into two types: those whose income elasticity is less than one and those whose income elasticity is greater than one. Think about products that would fall into each category. Can you come up with a name for each category?
• Suppose you could buy shoes one at a time, rather than in pairs. What do you predict the cross-price elasticity for left shoes and right shoes would be?

## Want to join the conversation?

• Twice in the article cross-price elasticity of demand is defined as "the percentage change in the quantity of good A that is demanded as a result of a percentage change in good B." Is this correct? Price isn't even mentioned in that definition.
• It should be "... percentage change in the price of good B." Does that help?
• why nursing job would be inelastic?
(1 vote)
• I didn't understand why in the third self-check quesion we multiply by -3%. If demand is inelastic, it would be more logical just to suppose that demand for apples wouldn't
change a lot, why should we multiply and get absolutely different answer?
(1 vote)
• So how do you know if an inferior good is elastic or inelastic after calculating the income elasticity of demand of the good? Or are inferior goods always elastic/inelastic?
(1 vote)
• Does cross-elasticity of supply exist? If it does, can someone explain it briefly?
(1 vote)
• If consumer spends all his money income on 2 goods x and y. Elasticity of x is unity. So will the cross elasticity of good y with respect to x be 0?
(1 vote)
• will be cross elasticities of shoes in question two equal with each other and equal with price elasticity of demand for left and right shoes?
(1 vote)
• nothing