Chapter 4, Problem 18PA

To determine

(a)

To find the cross-price elasticity and to check whether the goods are complements or substitutes.

Answer to Problem 18PA

The cross-price elasticity is -0.5 and goods are complements.

Explanation of Solution

Cross-price elasticity measures the degree of responsiveness of a change in the quantity demanded of a good for a given change in the price of some other good.

It is calculated by dividing the percentage change in the quantity demanded of one good by the percentage change in the price of the other good.

When an increase in price of one good leads to an increase in the quantity demanded of the other good, then the goods are close substitute of each other. The cross-price elasticity is positive in this case.

However, when an increase in price of one good leads to adecrease in the quantity demanded of the other good, then the goods are complementarygoods. The cross-price elasticity is negative in this case.

Initial price of peanut butter (P₁) = $2

Final price of peanut butter (P₂) = $3

Initial quantity of jelly (Q₁) = 20

Final quantity of jelly (Q₂) = 15

The percentage change in price of peanut butter is:

  $\begin{array}{c}Percentagechangeinprice=\frac{P_2-P_1}{P_1}\times 100\\ =\frac{3-2}{2}\times 100\\ =\frac{1}{2}\times 100\\ =50\%\end{array}$

The percentage change in the quantity demanded of jelly is:

  $\begin{array}{c}Percentagechangeinquantity=\frac{Q_2-Q_1}{Q_1}\times 100\\ =\frac{15-20}{20}\times 100\\ =-\frac{500}{20}\\ =-25\%\end{array}$

Cross-price elasticity of demand between peanut butter and jelly is calculated as follows:

  $\begin{array}{c}=\frac{\%Changeinquantitydemanded}{\%Changeinprice}\\ =\frac{-25\%}{50\%}\\ =-0.5\end{array}$

Since, the cross-price elasticity is negative. Thus, goods are complements.

To determine

(b)

To find the cross-price elasticity and check whether the goods are complements or substitutes.

Answer to Problem 18PA

The cross-price elasticity is +0.6 and goods are substitutes.

Explanation of Solution

Cross-price elasticity measures the degree of responsiveness of a change in the quantity demanded of a good for a given change in the price of some other good.

It is calculated by dividing the percentage change in the quantity demanded of one good by the percentage change in the price of the other good.

When an increase in price of one good leads to an increase in the quantity demanded of the other good, then the goods are close substitute of each other. The cross-price elasticity is positive in this case.

However, when an increase in price of one good leads to a decrease in the quantity demanded of the other good, then the goods are complementary goods. The cross-price elasticity is negative in this case.

Initial price of peanut butter (P₁) = $2

Final price of peanut butter (P₂) = $3

Initial quantity of jelly (Q₁) = 15

Final quantity of jelly (Q₂) = 20

The percentage change in price of peanut butter is:

  $\begin{array}{c}Percentagechangeinprice=\frac{P_2-P_1}{P_1}\times 100\\ =\frac{3-2}{2}\times 100\\ =\frac{1}{2}\times 100\\ =50\%\end{array}$

The percentage change in the quantity demanded of jelly is:

  $\begin{array}{c}Percentagechangeinquantity=\frac{Q_2-Q_1}{Q_1}\times 100\\ =\frac{20-15}{15}\times 100\\ =\frac{500}{15}\\ =33.33\%\end{array}$

Cross-price elasticity of demand between peanut butter and jelly is calculated as follows:

  $\begin{array}{c}=\frac{\%Changeinquantitydemanded}{\%Changeinprice}\\ =\frac{33.33\%}{50\%}\\ =+0.6\end{array}$

Since, the cross-price elasticity is positive. Thus, goods are substitutes.