Question

A recent study determined the following elasticities for Volkswagen Beetles: Price elasticity of demand \(=2\) Income elasticity of demand \(=1.5\) The supply of Beetles is elastic. Based on this information, are the following statements true or false? Explain your reasoning. a. A \(10 \%\) increase in the price of a Beetle will reduce the quantity demanded by \(20 \%\). b. An increase in consumer income will increase the price and quantity of Beetles sold.

Short answer

Based on the given information related to Volkswagen Beetles' price and income elasticities, determine if the two statements are true or false. a) A 10% increase in the price of a Beetle will reduce the quantity demanded by 20%. b) An increase in consumer income will increase the price and quantity of Beetles sold.

Step-by-step solution

Statement a: A \(10 \%\) increase in the price of a Beetle will reduce the quantity demanded by \(20 \%\).

From the given elasticities information, Price Elasticity of Demand (\(E_d\)) is \(2\). Using the Price Elasticity of Demand formula, we can find the change in quantity demanded due to a change in price: \(E_d = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}\) Plugging in the values: \(2 = \frac{\% \text{ change in quantity demanded}}{10\%}\) Calculating the percentage change in quantity demanded we get: \(\% \text{ change in quantity demanded} = 2 \times 10\% = 20 \%\) This statement is true, since the 10% increase in price results in a 20% decrease in the quantity demanded.

Statement b: An increase in consumer income will increase the price and quantity of Beetles sold.

The given Income Elasticity of Demand (\(E_i\)) is \(1.5\). Using the Income Elasticity of Demand formula, we can find the change in quantity demanded due to a change in income: \(E_i = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}}\) We are given that consumer income increases but we are not given a specific percentage. However, since the Income Elasticity of Demand is positive, an increase in income will lead to an increase in quantity demanded of Beetles. Now let's consider the effect of this increase in quantity demanded on the price. We are given that the supply of Beetles is elastic. When the supply is elastic, suppliers are highly responsive to changes in price. An increase in the quantity demanded will cause suppliers to respond by increasing the quantity supplied to meet the demand. As a result, the price will also go up. Therefore, the statement is true, since an increase in consumer income will lead to an increase in both price and the quantity of Beetles sold.

Key concepts

Price Elasticity of Demand

Price elasticity of demand measures how sensitive the quantity demanded of a good is to a change in its price. It is calculated using the formula: \[E_d = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}\]In our example with the Volkswagen Beetle, a price elasticity of demand of 2 means that for every 1% increase in price, the quantity demanded decreases by 2%. This is considered elastic demand because the change in quantity demanded is more than proportional to the change in price. Thus, a 10% increase in price indeed results in a 20% decrease in the quantity demanded, confirming the statement as true.

Understanding price elasticity is crucial for businesses when setting prices. Knowing if the demand for a product is elastic or inelastic helps in predicting consumer reaction and planning strategies accordingly.

Income Elasticity of Demand

Income elasticity of demand assesses how much the quantity demanded of a good changes as consumer income changes. The formula used is:\[E_i = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}}\]For the Volkswagen Beetle, the income elasticity of demand is given as 1.5. This indicates that for every 1% increase in income, the quantity demanded of Beetles increases by 1.5%. This means Beetles are a normal good, as the demand increases with higher income. The positive elasticity reflects this relationship.

This elasticity is vital for businesses to predict how changes in the economy could impact demand for their products. Positive income elasticity ensures that as people get wealthier, they purchase more of the good.

Quantity Demanded

Quantity demanded refers to the specific amount of a product that consumers are willing to buy at a given price. This concept is affected by factors such as price, income levels, and tastes and preferences. - **Price Influence**: As seen in the Beetle example, if the price of a product rises, the quantity demanded typically falls, assuming other factors remain constant. - **Income Influence**: An increase in consumer income usually leads to a higher quantity demanded for normal goods, like Beetles, especially when income elasticity is positive.

Understanding quantity demanded helps in assessing how changes in economic factors might lead to different levels of consumer purchasing behavior. Businesses use this information for inventory management and pricing strategies.

Elastic Supply

Elastic supply implies that the quantity supplied of a product is highly responsive to changes in price. This aids suppliers in swiftly adjusting the quantity they are willing to bring to the market when there is a shift in demand. For instance, with Volkswagen Beetles, the elasticity of supply suggests that when the demand increases (perhaps due to higher incomes), suppliers can increase production and supply more vehicles to meet demand. This responsiveness often helps keep severe price increases in check, although prices might still rise due to higher demand.

For companies, knowing supply elasticity is important for making quick adjustments in production levels. An elastic supply allows businesses to capitalize on changing market conditions and consumer demand efficiently.