Question

Show that if there are only two goods (Xand \(F\) ) to choose from, both cannot be inferior goods. If Xis inferior, how do changes in income affect the demand for \(\mathrm{F}\) ?

Short answer

Explain the effect on the demand for good F when good X is an inferior good. Answer: No, both goods X and F cannot be inferior goods in a two-good economy. When good X is an inferior good, good F must be a normal good. In this scenario, as the consumer's income increases, demand for good X decreases, and they will substitute it with good F. As a result, the demand for good F increases when the income increases.

Step-by-step solution

Define an inferior good

An inferior good is a good for which the demand decreases as the consumer's income increases. This is due to the fact that when income increases, consumers tend to replace inferior goods with more desired (normal) goods. Formally, an inferior good can be defined as one where the income elasticity of demand is negative.

Introduce the income-consumption curve

The income-consumption curve represents the relationship between a consumer's income and their optimal consumption bundle given their budget constraint and preferences. In a two-good economy consisting of goods X and F, as the consumer's income increases, they will adjust their consumption of X and F to maximize their utility.

Show that not both goods can be inferior

Suppose, for the sake of argument, that both goods X and F are inferior goods. In this case, as the consumer's income increases, they will buy less of both goods. However, this creates a contradiction, since the consumer's income must be spent on the two goods. As their income increases, they cannot decrease their consumption of both goods indefinitely because they have to spend their entire budget, and there are only two goods available. Therefore, we conclude that both goods X and F cannot be inferior goods.

Understand the scenario where good X is inferior

Now we consider the case where good X is an inferior good. In this scenario, as the consumer's income increases, they will decrease their consumption of good X and substitute it with another good, in this case, good F.

Determine the effect of changes in income on the demand for good F

As established in step 3, if good X is inferior, good F must be a normal good. Since F is a normal good, the income elasticity of demand for good F will be positive. Therefore, when income increases, consumers will substitute away from the inferior good X and increase their consumption of the normal good F. As a result, changes in income will have a positive effect on the demand for good F. In conclusion, it has been shown that in a two-good economy with goods X and F, both goods cannot be inferior. If good X is inferior, good F must be a normal good, and demand for good F will increase with an increase in income.

Key concepts

Income Elasticity of Demand

The income elasticity of demand is a measure that helps us understand how the demand for a good changes in response to a change in a consumer's income. It's like a gauge that tells us whether people buy more or less of something when they earn more money.

• If the income elasticity of demand is positive, the good is typically considered a normal good. This means that as people's income goes up, they purchase more of the good because it's deemed more desirable.
• If the elasticity is negative, the good is termed an inferior good. In this case, as consumers have more income, they tend to buy less of this good, opting for something they perceive as better.

Calculating it is straightforward. It's the percentage change in quantity demanded of a good divided by the percentage change in income: \[ \text{Income Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Income}} \]This metric is crucial in figuring out consumer behavior patterns and adjusting market strategies accordingly.

Normal Goods

Normal goods play an essential role in consumer economics. They have a positive income elasticity of demand, which signifies that as consumer income rises, the quantity demanded for these goods also increases. Normal goods are often viewed as desirable items, as opposed to inferior goods. When incomes rise, consumers naturally gravitate toward these products, sometimes replacing inferior goods. Examples of normal goods can include things like branded clothing, electronics, or dining out at restaurants. These goods often become part of a consumer's purchase list when there is more financial flexibility. In practical scenarios, companies focus heavily on normal goods for maximizing profits during economic upturns. Understanding the normal goods demand pattern helps businesses align their supply and pricing strategies effectively.

Income-Consumption Curve

The income-consumption curve offers a visual representation of how a consumer's choices adjust with changes in their income. It plots various combinations of two goods that a person might buy at different income levels, holding preferences constant. As a consumer's income rises, they may choose to purchase different quantities of two goods, let's say X and F. Here's how it works:

• If both goods are normal, the curve will slope upwards to the right, showing an increase in consumption for both goods as income increases.
• When one good is inferior, and the other is normal, the consumer will buy less of the inferior good and more of the normal good as income rises. This results in a different slope direction on the graph.

The income-consumption curve can reveal significant insights, such as whether a good is essential or luxurious, and help in predicting demand trends based on income changes. By examining this curve, businesses and economists can gauge effective strategies for targeting different income brackets.