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M02.L04 - Market Demand: Horizontal Summation of Individual Demands

Module: Module 02 - Demand and Willingness to Pay Lesson: L04 of 05 Duration: ~30 minutes Level: Introductory Provenance: OpenStax Principles of Microeconomics 3e | MIT OCW 14.01

Learning Objective

Construct a market demand curve by summing individual demand curves horizontally.

Market Demand Construction

Market demand aggregates individual demands at each price. Example: Australian wheat farmers sell to domestic and international buyers.

Horizontal Summation Steps: 1. List quantities demanded by each buyer at set prices. 2. Sum quantities at each price. 3. Plot the summed quantities.

Kink at Choke Price: The price where some buyers drop out (e.g., luxury car imports).

Worked Example

Brisbane Organic Farmers' Market

  1. Buyer A: 2kg at $10, 1kg at $15.
  2. Buyer B: 3kg at $10, 0kg at $15.
  3. Market demand: 5kg at $10, 1kg at $15.
  4. Curve kinks at $15 (Buyer B exits).

Common Misconception

"Market demand is just the average of individual demands."

Summing is additive, not averaged, reflecting total quantity demanded.

Key Takeaways

  • Market demand is the horizontal sum of individual demands.
  • Kinks occur at choke prices where buyers exit.
  • Aggregation applies to commodities (e.g., iron ore exports).

Exam-Style Calculation Practice

Key technique: convert to Q = f(P), sum, then invert back to P = f(Q)

When summing individual demand curves algebraically: (1) rewrite each as quantity demanded, (2) add quantities, (3) invert the result to get the market inverse demand.

Example: Two consumers of concert tickets: - Anna: p = 40 − q → q_A = 40 − p (valid for p ≤ 40) - Boris: p = 80 − 4q → q_B = 20 − p/4 (valid for p ≤ 80)

For prices between 40 and 80 only Boris buys: Q = q_B = 20 − p/4 → p = 80 − 4Q

For prices below 40 both buy: Q = q_A + q_B = (40 − p) + (20 − p/4) = 60 − 5p/4

Invert: 5p/4 = 60 − Q → p = 48 − (4/5)Q → market demand: p = 48 − 0.8Q

Note the kink at p = 40 where Anna enters the market — the curve becomes flatter below that price.

Practice

  1. Two buyers: A has p = 30 − 2q; B has p = 50 − q. Derive the market demand curve for prices below 30. (Hint: convert each to Q, sum, invert.)
  2. Sum demands for two Sydney cyclists: A (1 bike at $500, 0 at $600) and B (2 at $500, 1 at $600).
  3. For the Anna/Boris example above, verify that at p = 20 total market demand Q = 40 − 20 + 20 − 5 = 35.

Further Resources

Provenance: OpenStax Principles of Microeconomics 3e | MIT OCW 14.01