Math Problem Statement

Shown in the table is the income of an individual with the corresponding unit of goods it can purchase. Fill in the blanks and solve for the income elasticity. Also, indicate the classification of goods.

Solution

The table you're working with relates income (M) to the quantity of a good (Q) consumed, asking you to calculate income elasticity of demand and classify the goods accordingly.

To solve this, we'll follow these steps:

Step 1: Calculate the percentage change in income (%ΔM) and quantity (%ΔQdx).

The formula for percentage change between two values is:

%ΔM=M2M1M1×100\% \Delta M = \frac{M_2 - M_1}{M_1} \times 100

%ΔQdx=Q2Q1Q1×100\% \Delta Qdx = \frac{Q_2 - Q_1}{Q_1} \times 100

Where M1M_1 and M2M_2 are successive income levels, and Q1Q_1 and Q2Q_2 are the quantities of good X corresponding to those income levels.

Step 2: Calculate income elasticity of demand (Ei) using the formula:

Ei=%ΔQdx%ΔMEi = \frac{\% \Delta Qdx}{\% \Delta M}

Step 3: Classify the goods based on income elasticity:

  • Ei > 1: The good is a luxury good.
  • 0 < Ei < 1: The good is a normal good.
  • Ei < 0: The good is an inferior good.

I will start by calculating the percentage changes and income elasticity for each interval in the table and fill in the blanks accordingly. Let me do the calculations for you.Here's the completed table based on the given data and the calculations for income elasticity and the classification of goods:

Income ($)Quantity of Good X (units/yr)%ΔM%ΔQdxIncome ElasticityClassification of Goods
12,000280140.00180.001.29Luxury good
20,00050466.6780.001.20Luxury good
29,00070545.0039.880.89Normal good
40,00084637.9320.000.53Normal good
53,00075032.50-11.35-0.35Inferior good
65,00067722.64-9.73-0.43Inferior good

Summary:

  • Luxury goods have an income elasticity greater than 1.
  • Normal goods have an income elasticity between 0 and 1.
  • Inferior goods have a negative income elasticity.

Would you like further explanations or details on any of the steps? Here are 5 follow-up questions to deepen your understanding:

  1. How does income elasticity influence the demand for a good?
  2. What factors might cause a good to be classified as inferior?
  3. Can a good change its classification over time? Why or why not?
  4. What is the significance of a negative income elasticity?
  5. How might luxury goods affect consumer spending during economic downturns?

Tip: To distinguish between normal and inferior goods, consider how consumer purchasing behavior changes as their income rises.

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Math Problem Analysis

Mathematical Concepts

Elasticity of Demand
Percentage Change
Classification of Goods

Formulas

%ΔM = (M2 - M1) / M1 * 100
%ΔQdx = (Q2 - Q1) / Q1 * 100
Ei = %ΔQdx / %ΔM

Theorems

Income Elasticity of Demand

Suitable Grade Level

Grades 11-12