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Chapter 6: Problem 8

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

Expert verified
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

01

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.
02

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.

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