Question 14 of 26intermediate🔧 ApplyNumerical4 marks

Suppose there are two consumers in the market for a good and their demand functions are as follows: d1(p)=20−pd_1(p) = 20 - p for any price less than or equal to 20, and d1(p)=0d_1(p) = 0 at any price greater than 20. d2(p)=30−2pd_2(p) = 30 - 2p for any price less than or equal to 15 and d1(p)=0d_1(p) = 0 at any price greater than 15. Find out the market demand function.

Correct Answer

The market demand function is:

For price less than or equal to 15: D(p) = 50 - 3p

For price greater than 15 and less than or equal to 20: D(p) = 20 - p

For price greater than 20: D(p) = 0

Exercise: EXERCISES | Q: 14
For More Understanding

Explanation

This question tests the concept of horizontal summation of individual demand curves to derive market demand. The key insight is that consumers exit the market at different price thresholds. Consumer 2 exits when price exceeds 15, while Consumer 1 exits when price exceeds 20. Therefore, we need to consider three price ranges: when both consumers are active (p ≤\leq 15), when only Consumer 1 is active (15 < p ≤\leq 20), and when neither is active (p > 20).

Solution Steps

  1. Step 1: Identify the price ranges where each consumer is active. Consumer 1 is active for p ≤\leq 20. Consumer 2 is active for p ≤\leq 15.

  2. Step 2: For p ≤\leq 15, both consumers are active. Market demand D(p) = d₁(p) + d₂(p) = (20 - p) + (30 - 2p) = 50 - 3p.

  3. Step 3: For 15 < p ≤\leq 20, only Consumer 1 is active. Market demand D(p) = d₁(p) + 0 = 20 - p.

  4. Step 4: For p > 20, neither consumer is active. Market demand D(p) = 0.

PreviousNext