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M03.L01 — The Production Function: Total, Average, and Marginal Product

Module: Module 03 — Production and Costs
Lesson: L01 of 05
Duration: ~30 minutes
Level: Introductory
Provenance: OpenStax Principles of Microeconomics 3e | Khan Academy Microeconomics

Learning Objective

Understand how total, average, and marginal product relate to production inputs in the short run.

The Production Function

In Australian manufacturing, a production function shows the relationship between inputs (like labour and capital) and outputs. In the short run, at least one input (usually capital) is fixed. Total Product (TP) is the total output produced. Average Product (AP) is TP divided by the quantity of the variable input (usually labour, L). Marginal Product (MP) is the change in TP from adding one more unit of L.

Graphically, TP initially increases at an increasing rate (MP rising), then at a decreasing rate (MP falling but positive), and eventually decreases (MP negative). AP rises when MP > AP, falls when MP < AP, and is at its maximum when MP = AP.

Worked Example

Australian Wheat Farm Production

A wheat farm in Western Australia employs workers to harvest crops: 1. With 0 workers: TP = 0 2. 1 worker: TP = 10 tonnes (MP=10, AP=10) 3. 2 workers: TP = 25 tonnes (MP=15, AP=12.5) 4. 3 workers: TP = 45 tonnes (MP=20, AP=15) 5. 4 workers: TP = 60 tonnes (MP=15, AP=15) 6. 5 workers: TP = 70 tonnes (MP=10, AP=14) 7. 6 workers: TP = 75 tonnes (MP=5, AP=12.5) 8. 7 workers: TP = 70 tonnes (MP=-5, AP=10)

Common Misconception

"Marginal product can never be negative."

Actually, MP can become negative when adding more workers leads to overcrowding or inefficiency, reducing total output - as seen when the 7th worker decreases TP from 75 to 70 tonnes.

Key Takeaways

  • TP shows total output from given inputs
  • AP = TP/L shows output per worker
  • MP = ΔTP/ΔL shows output from the last worker added
  • MP crosses AP at AP's maximum point
  • TP increases until MP becomes negative

Practice

  1. If TP is 100 units with 5 workers and 120 units with 6 workers, what is MP of the 6th worker?
  2. Why does AP rise when MP > AP?
  3. Draw TP, AP, and MP curves showing their relationships.

Further Resources

Provenance: OpenStax Principles of Microeconomics 3e | Khan Academy Microeconomics