#AP Microeconomics: Elasticity Deep Dive 🚀

Hey! Let's get you totally prepped for the exam. We're going to break down elasticity, focusing on income and cross-price, and make sure you're ready to ace those questions!

#Elasticity: Beyond Price

Okay, so we've tackled price elasticity, but that's just the beginning. Remember, elasticity is all about how sensitive one thing is to another. Now, we're adding income and other goods into the mix. This is where it gets interesting!

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Key Concept

Types of Elasticity

Price Elasticity: How much demand/supply changes with price changes.
Income Elasticity: How much demand changes with income changes.
Cross-Price Elasticity: How much demand for one good changes with the price of another good.

#Income Elasticity of Demand

#What is It?

Income elasticity measures how sensitive the quantity demanded is to changes in income. The big question: when your income goes up or down, how does that affect what you buy? 🤔

#Normal vs. Inferior Goods

Normal Good: As income increases, demand increases. Think of things you buy more of when you have more money, like new clothes or fancy meals. 📈
Inferior Good: As income increases, demand decreases. These are things you might buy less of when you have more money, like ramen noodles or bus tickets. 📉

Memory Aid

Think: Normal goods go up with income, like a normal person's spending habits. Inferior goods go down with income, because you're too good for them now! 😉

#The Formula

$E_i = \frac{%\Delta Q_d}{%\Delta I}$

Where:

$E_i$ = Income Elasticity
%ΔQd = Percentage change in quantity demanded
%ΔI = Percentage change in income

#Interpreting the Results

Positive Ei: Normal good (income and demand move in the same direction).
Negative Ei: Inferior good (income and demand move in opposite directions).
Zero Ei: Sticky good (change in income has no effect on demand).

#Example

If a 10% increase in income leads to a 5% increase in demand for organic food, the income elasticity is 0.5 (5%/10%). This is a normal good.

Practice Question

Multiple Choice Question

If the income elasticity of demand for a good is -2, the good is: (A) A normal good (B) An inferior good (C) A luxury good (D) A necessity
A 5% increase in income leads to a 10% increase in the demand for movie tickets. What is the income elasticity of demand and what type of good are movie tickets? (A) -2, inferior good (B) 2, normal good (C) 0.5, normal good (D) -0.5, inferior good

FRQ

Assume that the market for used cars is initially in equilibrium. Suppose that consumer incomes decrease due to a recession. As a result, the demand for used cars increases.

(a) Is a used car a normal good or an inferior good? Explain using the definition of income elasticity. (b) Draw a correctly labeled graph of the market for used cars, showing the effect of the decrease in consumer income on the equilibrium price and quantity. (c) Suppose that the cross-price elasticity of demand between used cars and new cars is positive. What does this imply about the relationship between used cars and new cars? Explain.

Answer Key

(a) Used cars are an inferior good. According to the definition of income elasticity of demand, when income decreases, the demand for an inferior good increases.

(b) The graph should show a rightward shift of the demand curve for used cars, leading to a higher equilibrium price and quantity. The graph should include: - Correctly labeled axes (Price and Quantity) - Initial demand curve (D1) and supply curve (S1) intersecting at the initial equilibrium (P1, Q1) - A new demand curve (D2) shifted to the right of D1 - New equilibrium (P2, Q2) at the intersection of D2 and S1, with P2 > P1 and Q2 > Q1

(c) A positive cross-price elasticity of demand indicates that used cars and new cars are substitutes. This means that as the price of one good increases, the demand for the other good increases. For instance, if the price of new cars increases, consumers might switch to used cars, increasing the demand for used cars.

#Cross-Price Elasticity of Demand

#What is It?

Cross-price elasticity measures how sensitive the quantity demanded of one good is to a change in the price of another good. It helps us figure out if goods are related.

#Substitutes vs. Complements

Substitutes: Goods that can be used in place of each other (e.g., Coke and Pepsi). If the price of one goes up, demand for the other goes up. 🔄
Complements: Goods that are used together (e.g., coffee and sugar). If the price of one goes up, demand for the other goes down. 🤝

Memory Aid

Think: Substitutes are like substitutes in a sports game—one replaces the other. Complements complement each other, like peanut butter and jelly. 🥪

#The Formula

$E_{a,b} = \frac{%\Delta Q_{da}}{%\Delta P_b}$

Where:

$E_{a,b}$ = Cross-Price Elasticity of Demand
%ΔQda = Percentage change in quantity demanded of good A
%ΔPb = Percentage change in price of good B

#Interpreting the Results

Positive Eda,b: Substitutes (price of B and demand for A move in the same direction).
Negative Eda,b: Complements (price of B and demand for A move in opposite directions).
Zero Eda,b: Unrelated goods (price of B has no effect on demand for A).

#Example

If a 10% increase in the price of coffee leads to a 5% increase in the demand for tea, the cross-price elasticity is 0.5 (5%/10%). Coffee and tea are substitutes.

#Sample Problems

Complements

Substitutes

Practice Question

Multiple Choice Question

If the cross-price elasticity of demand between two goods is -1.5, then the two goods are: (A) Substitutes (B) Complements (C) Unrelated (D) Normal goods
A 20% increase in the price of hot dogs leads to a 10% decrease in the demand for hot dog buns. What is the cross-price elasticity of demand and what type of goods are hot dogs and hot dog buns? (A) -0.5, complements (B) 0.5, substitutes (C) -2, complements (D) 2, substitutes

FRQ

Suppose the market for smartphones is in equilibrium. A new technology is introduced that lowers the cost of producing smartphone cases. At the same time, the price of a popular brand of a competing smartphone increases.

(a) Draw a correctly labeled graph of the market for smartphone cases, showing the effect of the new technology on the equilibrium price and quantity. (b) What will happen to the demand for smartphones as a result of the price increase of the competing brand? Explain using the concept of cross-price elasticity of demand. (c) Assume that the income elasticity of demand for smartphones is positive. How will a decrease in consumer income affect the market for smartphones? Explain.

Answer Key

(a) The graph should show a rightward shift of the supply curve for smartphone cases, leading to a lower equilibrium price and a higher equilibrium quantity. The graph should include: - Correctly labeled axes (Price and Quantity) - Initial supply curve (S1) and demand curve (D1) intersecting at the initial equilibrium (P1, Q1) - A new supply curve (S2) shifted to the right of S1 - New equilibrium (P2, Q2) at the intersection of S2 and D1, with P2 < P1 and Q2 > Q1

(b) The demand for smartphones will increase. Since the price of a competing brand increased, consumers are likely to switch to the relatively cheaper smartphones. This is an example of positive cross-price elasticity of demand, indicating that the two brands are substitutes.

(c) A decrease in consumer income will decrease the demand for smartphones. Since the income elasticity of demand for smartphones is positive, they are considered a normal good. A decrease in income leads to a leftward shift of the demand curve, resulting in a lower equilibrium price and quantity for smartphones.

#Final Exam Focus

#Key Topics

Income Elasticity: Know how to calculate it and identify normal vs. inferior goods. 💡
Cross-Price Elasticity: Understand how to calculate it and identify substitutes vs. complements. 🤝
Relationship between Elasticities: Be able to apply these concepts in different market scenarios.

#Common Question Types

Multiple Choice: Expect questions that ask you to identify the type of good based on elasticity coefficients.
FRQs: Be ready to draw graphs and explain how changes in income or prices of related goods affect demand.

#Exam Tips

Exam Tip

Pay attention to signs: Positive vs. negative coefficients are crucial for determining the type of good.
Use examples: When explaining concepts, use real-world examples to make your points clear. 📝
Practice, practice, practice: The more you practice, the more comfortable you'll be with these concepts. 💪

#Common Mistakes

Common Mistake

Forgetting the signs: Not paying attention to whether elasticity is positive or negative.
Mixing up substitutes and complements: Make sure you know which is which!
Not explaining the relationship: Don't just calculate—explain what the numbers mean in context.

You've got this! Keep reviewing, and you'll be ready to rock the AP Micro exam! 🎉