Question

If your income goes down by 15 percent and you cut back on your manicures by 25 percent, then your demand for manicures is (LO4) a) income elastic b) income inelastic c) income elastic and income inelastic d) neither income elastic nor income inelastic

Short answer

The demand for manicures is income elastic, as the Income Elasticity of Demand is 1.67 (greater than 1). This means that a change in income significantly impacts the demand for manicures. The correct answer is (a) income elastic.

Step-by-step solution

Calculate Percentage Changes

The first step is to identify the changes provided in the exercise. We know that the income has decreased by 15 percent. This is our %Change in Income. Additionally, we know that the demand for manicures has decreased by 25 percent. This is our %Change in Quantity Demanded.

Plugging Numbers into the Formula

Now, we can apply these values to the formula. Income Elasticity of Demand = \( \frac{-25 \%}{-15 \%} \)

Simplifying the Equation

Simplifying this equation gives Income Elasticity of Demand = 1.67

Interpreting the Result

Since the resulting value is greater than one, the demand for manicures is "income elastic". This means that a change in income significantly impacts the demand for manicures. So, the correct answer is (a) income elastic.

Key concepts

Percentage Change

Understanding percentage change is important in evaluating how much a value has shifted over time. Imagine you are on a diet and you've lost weight. If you weighed 200 pounds and lost 20 pounds, you've experienced a 10% reduction in weight. This calculation is exactly what economists use to understand changes in quantities, like income or demand.

To compute the percentage change, you use the formula:

• Percentage Change = \( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \% \)

In the case of the exercise, your income went down by 15%. That's our percentage change in income. Similarly, your demand for manicures dropped by 25%, which is the percentage change in quantity demanded.

Income Effect

The income effect refers to how changes in a person’s income affect their consumption of goods and services. When your income falls, you have less money to spend on non-essential services like manicures. In this scenario, it led to a 25% reduction in manicures.

Why do these changes happen? It’s because your purchasing power has been altered. When income decreases, people may have to cut back on luxury goods—items they don't need for survival. Conversely, if income rises, people often increase their spending on these extras.

The magnitude of the income effect can vary. It depends on several factors including preferences, necessity of the good, and individual financial situations. In the exercise, the demand for manicures is income elastic, showing a significant reaction to an income change.

Quantity Demanded

Quantity demanded refers to the amount of a good or service consumers are willing to buy at a given price. It can fluctuate based on external factors like income changes, preferences, and prices of related goods.

In situations where the quantity demanded decreases noticeably with a reduction in income, it signals that the good is not a necessity but more of a "luxury." With manicures in the exercise, the 25% decrease reflects this notion.

• Goods with high sensitivity to income changes, such as manicures in this scenario, are labeled as luxury goods.
• When income decreases, people often cut back on such goods, highlighting the elasticity in demand relative to income shifts.

Therefore, understanding quantity demanded helps in categorizing goods and predicting consumer behavior changes when monetary situations change.