Question 15 of 26intermediate🔧 ApplyNumerical3 marks

Suppose there are 20 consumers for a good and they have identical demand functions: d(p)=10−3pd(p) = 10 - 3p for any price less than or equal to 103\frac{10}{3} and d1(p)=0d_1(p) = 0 at any price greater than 103\frac{10}{3}. What is the market demand function?

Correct Answer

The market demand function is:

For price less than or equal to 10/3: D(p) = 200 - 60p

For price greater than 10/3: D(p) = 0

Exercise: EXERCISES | Q: 15
For More Understanding

Explanation

This question tests the concept of deriving market demand from individual demand functions. According to the textbook, 'The market demand for a good at a particular price is the total demand of all consumers taken together.' When all consumers have identical demand functions, the market demand is simply the number of consumers multiplied by the individual demand function. The critical point is to maintain the same price threshold (10/3) beyond which demand becomes zero, as this applies to all consumers identically.

Solution Steps

  1. Step 1: Identify the individual demand function: d(p) = 10 - 3p for p ≤\leq 10/3, and d(p) = 0 for p > 10/3.

  2. Step 2: Note that there are 20 consumers with identical demand functions.

  3. Step 3: Calculate market demand by multiplying individual demand by number of consumers: D(p) = 20 × d(p).

  4. Step 4: For p ≤\leq 10/3: D(p) = 20 × (10 - 3p) = 200 - 60p.

  5. Step 5: For p > 10/3: D(p) = 20×020 \times 0 = 0.

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