Short-run Production and Marginal Product
A production function describes the maximum output obtainable from given inputs and technology. In the short run, at least one input is fixed. A bakery may change workers and flour today but cannot instantly add another oven or enlarge the kitchen.
With capital fixed and labor variable, write . Three measures organize the data:
Total product is all output, marginal product is output added by the next worker, and average product is output per worker.
Short-run production line
Schedule five workers; ship at least 9 units
Select a worker, then a station. Placements lock for the shift, and crowding the same fixed machine cuts the next worker's marginal product.
Read marginal and average correctly
Suppose output with two workers is 30 and with three is 52. The third worker's marginal product is ; average product with three workers is . MP attributes the change to the added worker under the model, but in team production it reflects how the whole team and fixed equipment work after staffing changes.
The relationship between MP and AP follows a general average rule. If MP exceeds AP, adding that observation raises AP. If MP is below AP, it lowers AP. On smooth curves, MP crosses AP at AP's maximum.
Production measures are physical, not monetary. A high MP does not alone justify hiring. The firm must value the added output and compare that value with the worker's opportunity cost. Product quality, safety, and waste should also be included when output counts alone are incomplete.
Turn a production table into a story
Suppose total product with one through five workers is 18, 42, 69, 93, and 110. Marginal products are 18, 24, 27, 24, and 17. Early workers improve specialization, so MP rises. Later workers share the same oven and counters, so MP falls while total product still rises.
Average product is 18, 21, 23, 23.25, and 22. MP above AP pulls the average upward; MP below AP pulls it downward. This is the same logic as adding a score above or below a student's current average.
Connect physical output to hiring
If each tray sells for 5, the fifth worker's value of marginal product is . A wage of 100 is not covered, even though output rises. Hiring decisions compare the value of the added output with the added input cost, not total output with total wages.
KNOWLEDGE QUIZ
Build a bakery production report
With one fixed oven, daily output for 0–6 workers is 0, 18, 42, 69, 93, 110, and 120 trays.
- Calculate marginal product for every worker.
- Calculate average product for one through six workers.
- Graph TP, MP, and AP and mark where MP crosses AP.
- If each tray sells for 5 and a worker costs 100, use value of marginal product to choose employment.