Other
Elasticities

Explore income elasticity, cross-price elasticity, and elasticity of supply: how quantities respond to changes beyond just a good's own price.

AP Microeconomics

What Is Elasticity?

Elasticity measures responsiveness: how much one economic variable changes when another variable changes. You already know price elasticity of demand. Now we extend the same logic to three new elasticities that appear on the AP exam.

The Three New Elasticities

Income Elasticity

How $Q_d$ responds to a change in consumer income.

Cross-Price Elasticity

How $Q_d$ of one good responds to a change in the price of another good.

Elasticity of Supply

How $Q_s$ responds to a change in a good's own price.

Why Do These Matter?

Firms and governments need to predict how markets react to more than just price changes. Consider:

1

Recession hits: Which products lose sales (luxury) vs. gain sales (inferior goods)? Income elasticity tells you.

2

A competitor raises prices: Does your product gain customers? Cross-price elasticity answers this.

3

Government imposes a tax: How quickly can producers adjust output? Elasticity of supply determines the burden split.

Income Elasticity of Demand

$E_I > 0$

Normal good: demand rises with income.

$E_I < 0$

Inferior good: demand falls as income rises.

Normal: Necessity vs. Luxury

Among normal goods ($E_I > 0$), we can further distinguish between necessities and luxuries based on the magnitude of the coefficient.

Necessity

$0 < E_I < 1$: Demand rises, but less than proportionally to income. Examples: groceries, toothpaste.

Luxury

$E_I > 1$: Demand rises more than proportionally to income. Examples: designer clothes, vacations.

Cross-Price Elasticity of Demand

$E_{XY} > 0$

Substitutes: Coke and Pepsi. If $P_Y$ rises, $Q_X$ rises.

$E_{XY} < 0$

Complements: Hot dogs and buns. If $P_Y$ rises, $Q_X$ falls.

Price Elasticity of Supply

Supply elasticity works like demand elasticity, but for producers. Since supply curves are typically upward-sloping, $E_S$ is almost always positive.

The Sign Tells the Story

Unlike price elasticity of demand (where we often drop the sign), for income and cross-price elasticity, the positive or negative sign is the critical piece of information.

Elasticity	Positive (+)	Negative (−)
Income $E_I$	Normal good	Inferior good
Cross-Price $E_{XY}$	Substitutes	Complements
Supply $E_S$	Always positive	N/A (supply slopes up)

Determinants of Supply Elasticity

1

Time horizon: Supply is more elastic in the long run because firms can build factories, hire workers, and adjust capacity.

2

Availability of inputs: If raw materials are scarce, producers cannot easily increase output, making supply inelastic.

3

Spare capacity: Firms with idle resources can ramp up production quickly, making supply more elastic.

4

Flexibility of production: Can the firm switch from one product to another? Greater flexibility = more elastic supply.

How to Calculate Any Elasticity

1

Identify the type: Are you measuring response to income, another good's price, or own price (supply)?

2

Find $\%\;\Delta\;Q$: Use the midpoint method: $\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2} \times 100$

3

Find the $\%\;\Delta$ of the other variable: Use the same midpoint formula for income, $P_Y$, or $P$.

4

Divide: $\text{Elasticity} = \frac{\%\;\Delta\;Q}{\%\;\Delta\;\text{Variable}}$

5

Interpret the sign and magnitude: Classify the good or relationship based on the result.

Example: Income Elasticity

A consumer's income rises from $\$40{,}000$ to $\$50{,}000$. Their purchases of organic coffee rise from 20 bags to 30 bags per year.

Example: Cross-Price Elasticity

The price of butter rises from $\$3$ to $\$5$. As a result, the quantity demanded of margarine rises from 100 tubs to 140 tubs.

Example: Supply Elasticity

The price of wheat rises from $\$6$ to $\$8$ per bushel. Farmers increase output from 500 bushels to 550 bushels.

Common Mistakes to Avoid

✕ Dropping the Sign

For income and cross-price elasticity, the sign matters. A positive vs. negative result changes the classification entirely.

✕ Wrong Denominator

For cross-price: the denominator must be the price of the other good, not the good whose quantity you are measuring.

✕ Forgetting Midpoint

Using simple $\%$ change instead of the midpoint method gives a different answer. The AP exam expects midpoint unless stated otherwise.

Summary Comparison

Feature	Income $E_I$	Cross-Price $E_{XY}$	Supply $E_S$
Numerator	$\%\;\Delta\;Q_d$	$\%\;\Delta\;Q_d\text{ of X}$	$\%\;\Delta\;Q_s$
Denominator	$\%\;\Delta\;\text{Income}$	$\%\;\Delta\;P_Y$	$\%\;\Delta\;P$
Positive means	Normal good	Substitutes	Upward supply
Negative means	Inferior good	Complements	N/A
Sign matters?	Yes	Yes	Always +

Question 1 of 5

When consumer income rises by 10%, the quantity demanded of ramen noodles falls by 8%. What is the income elasticity of demand, and what type of good is ramen?

Quantity fell when income rose, so the sign is negative: $E_I = \frac{-8\%}{+10\%} = -0.8$. A negative income elasticity means ramen is an inferior good.

Question 2 of 5

The cross-price elasticity of demand between peanut butter and jelly is $-0.4$. This means peanut butter and jelly are:

A negative cross-price elasticity means when the price of one rises, demand for the other falls. This is the hallmark of complements: goods used together.

Question 3 of 5

A good has an income elasticity of $+0.3$. This good is best classified as a:

$E_I = +0.3$ is positive (normal good) and less than $1$ (income-inelastic). This means demand rises with income, but less than proportionally: a necessity like basic groceries.

Question 4 of 5

Using the midpoint method: the price of laptops rises from $\$800$ to $\$1{,}200$, and quantity supplied rises from 200 to 300 units. What is $E_S$?

$\%\;\Delta\;Q_s = \frac{300-200}{(300+200)/2} \times 100 = \frac{100}{250} \times 100 = 40\%$. $\%\;\Delta\;P = \frac{1200-800}{(1200+800)/2} \times 100 = \frac{400}{1000} \times 100 = 40\%$. So $E_S = \frac{40\%}{40\%} = +1.0$: unit elastic supply.

Question 5 of 5

Which of the following would most likely cause the price elasticity of supply for a good to increase?

Supply becomes more elastic over longer time horizons because firms can build new facilities, hire workers, and find new input sources. All other options describe constraints that make supply less elastic.