Q.What is meant by production function?

Total Product: From a Farmer's Field to a Factory Floor

Imagine you own a small bakery. You have one oven, one mixing bowl, and a single counter. That's your fixed capital — things that don't change in the short run. Now, you start hiring workers. With one worker, you bake 20 loaves a day. With two workers, you get 50 loaves. With three, 90 loaves. With four, 120 loaves. With five, 140 loaves. With six, 150 loaves. With seven, 150 loaves again (the kitchen is too crowded). With eight, 140 loaves (workers start bumping into each other).

That list of numbers — 20, 50, 90, 120, 140, 150, 150, 140 — is your Total Product at each level of labour.

The Precise Meaning

Total Product (TP) is the total quantity of output produced by a firm using a given amount of variable input (like labour), with all other inputs held fixed (like machinery, land, factory size). In the NCERT Class-12 Economics textbook, it is defined as:

Where:

• $TP$ = Total Product (total output in physical units — loaves, metres, tonnes)
• $MP$ = Marginal Product (the extra output from adding one more unit of the variable input)
• $n$ = the number of units of the variable input employed

There is no separate "formula" for TP beyond this additive relationship. It is simply the sum of all marginal products up to that point. If you know the output at each level, you have TP directly.

Why It Matters

Total Product is the foundation of production analysis. Without it, you cannot calculate:

• Average Product (AP) = $TP / L$ (output per worker) — tells you how productive each worker is on average.
• Marginal Product (MP) = change in TP / change in labour — tells you the contribution of the last worker hired.
• The Law of Diminishing Marginal Returns — which is the single most important pattern in short-run production.

The Three Stages (The Shape of the TP Curve)

If you plot TP on the vertical axis and labour on the horizontal axis, the curve typically looks like a hill that eventually flattens and then falls. NCERT describes three phases:

1. Increasing returns to a factor (TP rises at an increasing rate) — the slope of TP gets steeper. This happens when workers specialise and the fixed capital is underutilised. In our bakery, from 1 to 3 workers, each new worker adds more than the previous one (20, then 30, then 40 loaves).

2. Diminishing returns to a factor (TP rises at a decreasing rate) — the slope of TP gets flatter. This is the most common phase. From 4 to 6 workers, each new worker adds less (30, then 20, then 10 loaves). The oven and counter space are becoming crowded.

3. Negative returns (TP actually falls) — the slope becomes negative. Beyond 7 workers, output drops because workers get in each other's way.