Question 8 of 26beginner🔧 ApplyNumerical3 marks

Suppose a consumer can afford to buy 6 units of good 1 and 8 units of good 2 if she spends her entire income. The prices of the two goods are Rs 6 and Rs 8 respectively. How much is the consumer’s income?

Correct Answer

Given:

  • Units of good 1 (x₁) = 6
  • Units of good 2 (x₂) = 8
  • Price of good 1 (p₁) = Rs 6
  • Price of good 2 (p₂) = Rs 8

Budget equation: When the consumer spends her entire income on a bundle, the budget constraint becomes: p₁x₁ + p₂x₂ = M

Calculation: M = (6×66 \times 6) + (8×88 \times 8) M = 36 + 64 M = Rs 100

Answer: The consumer's income is Rs 100.

Exercise: EXERCISES | Q: 8
For More Understanding

Explanation

This question tests the understanding of the budget constraint from the textbook. The budget set consists of all bundles (x₁, x₂) such that p₁x₁ + p₂x₂ ≤\leq M. When the consumer spends her entire income on a particular bundle, the inequality becomes an equality. The context shows in Example 2.1 that bundles costing exactly the income amount are affordable. By substituting the given prices and quantities into the equation, we can directly calculate the consumer's total income.

Solution Steps

  1. Step 1: Write the budget equation when entire income is spent: p₁x₁ + p₂x₂ = M

  2. Step 2: Substitute the given values: M = (6×66 \times 6) + (8×88 \times 8)

  3. Step 3: Calculate: M = 36 + 64 = 100

  4. Step 4: Consumer's income = Rs 100

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