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 normal or an inferior good?

Short answer

The income elasticity of bread consumption is approximately -0.514, indicating that bread is an inferior good. As income increases, the demand for bread decreases.

Step-by-step solution

Calculate the Initial and Final Incomes and Quantities

Initially, the average annual income (I1) is \(25,000, and the final average annual income (I2) is \)38,000. The initial bread consumption (Q1) is 30 loaves, and the final bread consumption (Q2) is 22 loaves.

Calculate the Percentage Changes in Income and Quantity Demanded

We will now find the percentage change in Income and percentage change in Quantity Demanded. % change in Income = (I2 - I1) / I1 % change in Quantity Demanded = (Q2 - Q1) / Q1 % change in Income = (38,000 - 25,000) / 25,000 = 13,000 / 25,000 = 0.52 or 52% % change in Quantity Demanded = (22 - 30) / 30 = -8 / 30 = -0.267 or -26.7%

Calculate the Income Elasticity of Demand

Now we will use the income elasticity formula: Income Elasticity of Demand (E) = (% change in Quantity Demanded) / (% change in Income) E = (-26.7%) / (52%) = -0.267 / 0.52 ≈ -0.514

Determine if Bread is a Normal or Inferior Good

The income elasticity of demand for bread is approximately -0.514. Since this value is negative, bread is an inferior good. When the income increases, the demand for bread decreases, which is a characteristic of inferior goods. In conclusion, the income elasticity of bread consumption is approximately -0.514, and bread is an inferior good.

Key concepts

Inferior Good

In economic terms, an inferior good is one for which demand decreases as the income of the consumer increases. Unlike luxury or normal goods, where demand typically rises with an increase in income, inferior goods have a negative relationship with consumer income. This can be due to consumers choosing to buy higher-quality alternatives as their purchasing power grows.

For example, with the rise in income, a person might opt for dining out more frequently instead of buying instant noodles, which are often considered an inferior good. Therefore, when analyzing the income elasticity of demand—which measures how sensitive the quantity demanded of a good is to a change in income—inferior goods will have a negative elasticity. As shown in the exercise, the quantity of bread demanded fell when income rose, indicating that bread, in this scenario, behaves as an inferior good.

Understanding whether a good is inferior is crucial for businesses and policymakers. It helps in forecasting consumer behavior changes due to economic shifts and in adjusting marketing or production strategies accordingly.

Quantity Demanded

The quantity demanded is the amount of a product that consumers are willing and able to purchase at a particular price, over a specified period of time. It's not just a simple desire to have a good, but it is specifically the consumers' plans to buy certain amounts at specific prices.

In the provided exercise, the quantity demanded refers to how many loaves of bread consumers buy in a year at their current income levels. The change in quantity demanded is highlighted by the difference in bread consumption as the average income shifts. It's vital to remember that 'quantity demanded' is not static; it changes with price, income, and other factors. When the text teaches about the 'law of demand,' which states that, all else being equal, as the price of a product falls, the quantity demanded will usually increase (and vice versa), students should grasp that this is separate from changes in demand due to income effects.

Percentage Change Calculation

Percentage change calculation is a mathematical tool used to measure the degree of change over time. It is widely used in various fields, especially economics, to express the relative change in quantities. The formula for calculating a percentage change is a simple yet powerful tool: the difference between the final and initial values, divided by the initial value, all multiplied by 100.

In our exercise, percentage change calculations are crucial for determining the income elasticity of demand. The percentage changes in both income and quantity demanded were calculated as intermediate steps before finding the elasticity. This process helps in quantifying how the quantity demanded of a good responds to changes in income and is a prerequisite for deciding whether a product is a normal or an inferior good. By mastering percentage change calculations, students can better analyze economic data and develop a deeper understanding of market dynamics.