Some texts define a "luxury good" as a good for which the income elasticity of demand is greater than 1. Suppose that a consumer purchases only two goods. Can both goods be luxury goods? Explain

Assume all of one's income is spent on the two goods.

Hint: If a good is elastic and price goes up by, say, 10%. Do one spend more dollars on that good or less dollars.

To determine whether both goods can be luxury goods, we need to understand the concept of income elasticity of demand. The income elasticity of demand measures the relationship between changes in income and changes in the quantity demanded of a particular good.

If the income elasticity of demand for a good is greater than 1, it means that a 1% increase in income results in more than a 1% increase in the quantity demanded of that good. This indicates that the good is income elastic and can be classified as a luxury good.

Now, suppose a consumer purchases only two goods. The income elasticity of demand for each of these goods can be calculated based on the consumer's behavior. If both goods have an income elasticity of demand greater than 1, then both goods can be considered luxury goods.

Here's how you can determine the income elasticity of demand for each good:

1. Identify the initial quantity demanded (Q0) and the initial income level (I0) for each good.
2. Determine the final quantity demanded (Q1) and the final income level (I1) for each good.
3. Calculate the percentage change in quantity demanded: [(Q1 - Q0) / Q0] * 100.
4. Calculate the percentage change in income: [(I1 - I0) / I0] * 100.
5. Calculate the income elasticity of demand: (Percentage change in quantity demanded) / (Percentage change in income).

Repeat these steps for both goods to calculate their respective income elasticities of demand. If both values are greater than 1, then both goods can be considered luxury goods.

However, it's worth noting that whether a good is considered a luxury good is subjective and can vary depending on the context and individual preferences. So, it's possible that one person may consider a good a luxury while another person may not.