Question

The average annual income rises from 25,000 dollar to 38,000 dollar 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 bread consumption (E) is -0.513, which indicates that bread is an inferior good. As the average annual income increases, the quantity of bread consumed decreases.

Step-by-step solution

Calculate the Percentage Change in Income

To calculate the percentage change in income, use the formula: Percentage change in income = \(\frac{\text{(Final Income - Initial Income)}}{\text{Initial Income}} \times 100\) Initial Income: $25,000 Final Income: $38,000 Percentage change in income = \(\frac{38,000-25,000}{25,000}\) x 100 = 0.52 x 100 = 52%

Calculate the Percentage Change in Quantity of Bread Consumed

Next, we need to calculate the percentage change in the quantity of bread consumed using the formula: Percentage change in quantity = \(\frac{\text{(Final Quantity - Initial Quantity)}}{\text{Initial Quantity}} \times 100\) Initial Quantity: 30 loaves Final Quantity: 22 loaves Percentage change in quantity = \(\frac{22-30}{30}\) x 100 = -0.2667 x 100 = -26.67%

Calculate the Income Elasticity of Bread Consumption

Income Elasticity of Demand (E) can be calculated by dividing the percentage change in quantity by the percentage change in income: E = \(\frac{\text{Percentage change in quantity}}{\text{Percentage change in income}}\) E = \(\frac{-26.67\%}{52\%}\) = -0.513

Determine if Bread is a Normal or Inferior Good

Based on the value of income elasticity, we can determine the type of good: - If E > 0, the good is a normal good; as income increases, the quantity demanded also increases. - If E < 0, the good is an inferior good; as income increases, the quantity demanded decreases. In this case, E = -0.513, which is less than zero. This suggests that bread is an inferior good. As the average annual income increases, the quantity of bread consumed decreases.

Key concepts

Percentage Change in Income

Understanding the percentage change in income is vital for analyzing how various factors affect consumer behavior. It measures the relative change in an individual's income over a period of time.

To calculate the percentage change, you subtract the initial income from the final income, divide the result by the initial income, and then multiply by 100 to express it as a percentage. Mathematically, it is expressed as: \[\begin{equation}\text{Percentage change in income} = \left(\frac{\text{Final Income - Initial Income}}{\text{Initial Income}}\right) \times 100 \ \end{equation}\]
This formula gives us valuable insights into consumer purchasing trends and helps us recognize the shifts in economic capabilities. For example, a 52% increase in income, as seen in our exercise, could generally mean that people have more purchasing power. However, when paired with the demand for various goods, it can reveal much more about consumption patterns and preferences.

Percentage Change in Quantity

When studying market dynamics, the percentage change in quantity is another fundamental concept. It indicates how the demand for a product changes in response to various economic factors, such as a change in consumer income. \[\begin{equation}\text{Percentage change in quantity} = \left(\frac{\text{Final Quantity - Initial Quantity}}{\text{Initial Quantity}}\right) \times 100 \ \end{equation}\]
Using this calculation, we can determine whether the demand for a product is sensitive, or elastic, to changes in income. A negative percentage change, as observed in the bread consumption example with a -26.67% result, implies that the demand for the product has decreased. This information is crucial, as it helps us understand consumer behavior and the demand for goods under varying economic conditions.

Normal and Inferior Goods

In economics, goods are categorized based on how their demand changes with consumer income. Normal goods are items for which demand increases when income increases and decreases when income decreases. Conversely, inferior goods have an inverse relationship; demand decreases as income increases.

These distinctions are essential for businesses and economists as they forecast market trends and consumer preferences. The income elasticity of demand, which measures the sensitivity of the quantity demanded to income changes, helps in categorizing goods. An income elasticity greater than zero indicates a normal good, whereas a negative income elasticity suggests that the good is inferior.In our textbook problem, bread is identified as an inferior good because of its negative income elasticity of -0.513. This means as people's income rose, they chose to consume less bread. Inferior goods are often replaced by more preferred alternatives as individuals' purchasing power improves. Understanding these concepts assists firms in aligning their production and marketing strategies with economic conditions and consumer income levels.