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

a. True, a 10% increase in price will reduce the quantity demanded by 20%. b. True, an increase in consumer income will likely increase the price and quantity of Beetles sold because the car is a normal good with an income elasticity greater than 1 and the supply is elastic.

Step-by-step solution

Understanding Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price, and is defined as the percentage change in quantity demanded divided by the percentage change in price. Since the price elasticity of demand for Volkswagen Beetles is given as 2, it means that for a 1% increase in price, the quantity demanded will decrease by 2%.

Calculating Change in Quantity Demanded

To calculate the change in quantity demanded due to a price change, multiply the price elasticity of demand by the percentage change in price. In this case, a 10% increase in price would lead to a 2 (price elasticity of demand) times 10% (change in price) equals 20% decrease in quantity demanded.

Understanding Income Elasticity of Demand

Income elasticity of demand measures the responsiveness of the quantity demanded to a change in consumer income, defined as the percentage change in quantity demanded divided by the percentage change in income. A positive elasticity greater than 1, as in this case (1.5), indicates that the good is a normal good and is income-elastic, meaning demand will rise more than proportionally as income increases.

Analyzing Impact of Income on Price and Quantity

An increase in consumer income will lead to an increase in the quantity demanded for Beetles since they are normal goods with income elasticity greater than 1. This rise in demand could also lead to an increase in price, especially if the supply is elastic as stated, which means suppliers can increase production without a significant increase in price.

Key concepts

Income Elasticity of Demand

Income elasticity of demand is a core concept in understanding how consumer demand for a product changes with income levels. It reflects the sensitivity of the quantity demanded for a good to the change in consumer income. Mathematically, it's represented by the ratio of the percentage change in quantity demanded to the percentage change in income:
\[ \text{Income Elasticity of Demand} = \frac{\text{% Change in Quantity Demanded}}{\text{% Change in Income}} \]
A positive income elasticity indicates that the product is a normal good, meaning its demand increases as consumer income increases. If the income elasticity of demand is greater than 1, the good is considered luxury, as the increase in demand outpaces the increase in income. Conversely, if it's less than 1 but still positive, the good is a necessity, seeing a smaller proportional increase in demand. It's crucial for businesses to understand the income elasticity of their products, as it helps them anticipate changes in demand due to economic shifts and make informed pricing and production decisions.

• Normal Goods: For normal goods like Volkswagen Beetles, with an income elasticity of 1.5, we can infer that a rise in income by 10% might lead to a 15% increase in demand.
• Analysis of Beetle's Demand: As incomes rise, more consumers are likely to buy Volkswagens, suggesting a higher quantity demanded, which may contribute to a price increase, especially if the market can bear it.
• Implications for Markets: Knowing the income elasticity helps market participants understand and predict how market demand and consumer purchasing behavior might evolve as economic conditions change.

Elasticity of Supply

Elasticity of supply is the measure of how much the quantity supplied of a good responds to a change in its price. In general:
\[ \text{Elasticity of Supply} = \frac{\text{% Change in Quantity Supplied}}{\text{% Change in Price}} \]
When the supply of a product is described as elastic, as is the case with Volkswagen Beetles, it can adapt relatively easily to changes in price. An elastic supply means that producers can increase output without a significant rise in cost. Therefore, if there is a rise in demand and price, manufacturers can quickly respond by supplying a larger number of units to the market without a substantial increase in price, unlike the case with inelastic supply.

• High Responsiveness: A high elasticity of supply, often greater than 1, signifies that the quantity supplied reacts strongly to price changes.
• Impact on Pricing: Elasticity of supply has significant implications for pricing strategies. For goods with an elastic supply, prices may not need to increase significantly if the demand increases since the market can provide more products relatively easily.
• Production Capability: Manufacturers with elastic supply chains can capitalize on market opportunities more effectively by ramping up production when necessary.

Normal Goods

The term 'normal goods' refers to goods whose demand increases as consumer incomes rise, which is in contrast to inferior goods, whose demand decreases as income increases. Normal goods have a positive income elasticity of demand. The degree to which demand responds to income changes can tell us much about consumer preferences and economic status:

• Income Sensitivity: The demand for normal goods is closely tied to income levels. As people's disposable income rises, they generally purchase more normal goods.
• Classification: Within normal goods, we can further categorize as either necessities or luxuries. Luxuries have a higher income elasticity of demand, meaning they are often purchased in larger quantities with increased income.
• Economic Indicator: The proportion of normal goods in consumer purchases can serve as an indicator of the overall economic health and the distribution of wealth within a society.
• Volkswagen Beetles: Given their income elasticity of demand of 1.5, Beetles are considered a normal good, and thus their demand should grow as consumer income increases.

Knowing whether a good is normal or inferior is essential for businesses and policymakers, as it helps predict how consumption patterns may shift with economic changes and guide strategies for production, marketing, and regulation.