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Chapter 5: Problem 9

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?

Short Answer

Expert verified
The demand for apples will decrease by 1.2% when the price of oranges falls by 3%.

Step by step solution

01

Identify the formula for cross-price elasticity of demand

We can use the formula for cross-price elasticity of demand (Exy), which is: \[ Exy = \frac{% \Delta Q_x}{% \Delta P_y} \] Where: - \(Exy\) is the cross-price elasticity of demand, - %\(\Delta Q_x\) represents the percentage change in the quantity demanded of good x (apples), - %\(\Delta P_y\) represents the percentage change in the price of good y (oranges).
02

Plug in the given values

We are given that \(Exy = 0.4 \) and the price of oranges falls (decreases) by 3% (\(% \Delta P_y = -3\%\)). We will use these values to solve for %\(\Delta Q_x \): \[ 0.4 = \frac{% \Delta Q_x}{-3 \%} \]
03

Solve for %\(\Delta Q_x \)

We can now solve for %\(\Delta Q_x \) by multiplying both sides of the equation by -3%: \[ % \Delta Q_x = 0.4 \times -3 \% \] %\( \Delta Q_x = -1.2 \% \)
04

Interpret the result

Since %\(\Delta Q_x = -1.2 \% \), this means that the demand for apples decreases by 1.2% when the price of oranges falls by 3%. Thus, the demand for apples will decrease by 1.2%.

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Most popular questions from this chapter

The average annual income rises from 25,000 dollar to 38,000 dollar, 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 normal or an inferior good?

In a market where the supply curve is perfectly inelastic, how does an excise tax affect the price paid by consumers and the quantity bought and sold?

Assume that the supply of low-skilled workers is fairly elastic, but the employers' demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? What if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams.

The equation for a demand curve is \(\mathrm{P}=2 / \mathrm{Q}\). What is the elasticity of demand as price falls from 5 to \(4 ?\) What is the elasticity of demand as the price falls from 9 to \(8 ?\) Would you expect these answers to be the same?

Transatlantic air travel in business class has an estimated elasticity of demand of \(0.62, \quad\) while transatlantic air travel in economy class has an estimated price elasticity of \(0.12 .\) Why do you think this is the case?
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