Question

The average annual income rises from \(25,000 to \)38,000, 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 a normal or an inferior good?

Short answer

The income elasticity of demand for bread is -0.513, which indicates that bread is an inferior good. As income increases, the demand for bread decreases.

Step-by-step solution

Calculate the percentage change in income.

The change in income is from \(25,000 to \)38,000. The percentage change in income is given by the formula: \[ \frac{{\text{{new value}} - \text{{old value}}}}{{\text{{old value}}}} \times 100\% \] Plugging in the given values: \[ \text{{Percentage change in income}} = \frac{{38000 - 25000}}{{25000}} \times 100\% = 52\%\]

Calculate the percentage change in quantity demanded.

The change in quantity is from 30 loaves to 22 loaves. Percentage change in quantity demanded is given by the same formula as above: \[ \text{{Percentage change in quantity demanded}} = \frac{{22 - 30}}{{30}} \times 100\% = -26.67\%\]

Calculate the income elasticity of demand

Using this formula: \[ \text{{Income Elasticity of Demand}} = \frac{{\text{{Percentage change in quantity demanded}}}}{{\text{{Percentage change in income}}}}\] We find: \[ \text{{Income Elasticity of Demand}} = \frac{{-26.67}}{{52}} = -0.513.\]

Interpret the income elasticity of demand

Since the income elasticity of demand for bread is -0.513 (negative), it suggests bread is an "inferior good". This means that as income increases, consumers demand less of the good, which is characteristic of an inferior good. In this case, as people's income rose, they consumed less bread. This implies that bread is an inferior good.

Key concepts

Inferior Good

An 'inferior good' is a term used in economics to describe a type of product for which demand decreases as the income of the consumer increases. This is inversely related to 'normal goods', where demand increases with an increase in consumer's income. In real life, examples of inferior goods can include off-brand grocery items or budget-friendly clothing brands.

When consumers experience an increase in income, they have more purchasing power and often choose to 'trade up' to more expensive alternatives, reducing the consumption of the inferior goods. In the case of the bread consumption exercise, the decline in the quantity of loaves demanded as income rises indicates that bread is considered an inferior good by the average person in this scenario.

Percentage Change in Income

Understanding the 'percentage change in income' is crucial for analyzing consumer behavior. This term represents the degree to which an individual's income changes over a period. It can be calculated by using the formula:
\[ \frac{{\text{{new income}} - \text{{old income}}}}{{\text{{old income}}}} \times 100\% \]

Percentage change in income is an important indicator in economics as it can influence spending patterns, savings, and investments. In our exercise, a 52% increase in income was observed, which is a significant change that underlines the potential for shifts in consumption patterns for various goods.

Percentage Change in Quantity Demanded

The 'percentage change in quantity demanded' tells us how the quantity of a good that consumers want to buy changes in response to a change in income. This metric is essential when calculating elasticity, especially income elasticity of demand:
\[ \frac{{\text{{new quantity demanded}} - \text{{original quantity demanded}}}}{{\text{{original quantity demanded}}}} \times 100\% \]

In this context, our exercise revealed a decrease in quantity demanded by -26.67%, indicating that as incomes rose, the demand for bread fell. This percentage change in quantity demanded is an essential part of calculating the income elasticity and interpreting if a good is an inferior or normal good.