Economics · Ch 9 — Production and Costs

Marginal Product

9.3.3

Marginal Product

Marginal Product – Definition and Meaning

Marginal product answers a simple question: if you hire one more worker (or use one more unit of any input), while keeping everything else fixed, how much extra output do you get? The textbook defines it precisely as the change in output per unit change in the input, with all other inputs held constant.

When capital is fixed (say, you have 4 machines and cannot add more), the marginal product of labour is the ratio of the change in total product to the change in labour input. In symbols:

MP_L = \frac{\Delta TP}{\Delta L}

Here $\Delta$ (the Greek capital letter Delta) stands for "change in". So $\Delta TP$ is the increase in total product when labour changes by $\Delta L$ units. The subscript $L$ reminds us that this is the marginal product of labour specifically.

Note

The definition works for any input, not just labour. If you varied capital while holding labour fixed, you would compute $MP_K = \Delta TP / \Delta K$ . The textbook focuses on labour because it is the most common variable input in short-run analysis.

Numerical Example from the Textbook

The third column of Table 3.2 in the NCERT text gives a numerical illustration of marginal product of labour, using the same production function that appeared in Table 3.1. Capital is fixed at 4 units throughout.

To obtain each entry in that column, you take the change in total product between two successive levels of labour employment and divide by the change in labour. For instance, if total product rises from 0 to 10 when labour increases from 0 to 1, the marginal product of the first worker is $(10 - 0)/(1 - 0) = 10$ . If total product then goes from 10 to 24 when labour goes from 1 to 2, the marginal product of the second worker is $(24 - 10)/(2 - 1) = 14$ , and so on.

The full labour schedule (the same one as Table 3.2, with capital held fixed at 4 units) is reproduced below:

Labour (L)	Total Product (TP)	Average Product (AP = TP/L)	Marginal Product (MP = ΔTP/ΔL)
0	0	—	—
1	10	10	10
2	24	12	14
3	40	13.33	16
4	50	12.5	10
5	56	11.2	6
6	57	9.5	1

Reading the schedule:

From $L = 1$ to $L = 3$ , marginal product rises ( $10 \to 14 \to 16$ ), so total product increases at an increasing rate.
From $L = 4$ onwards, marginal product falls ( $10 \to 6 \to 1$ ), so total product still rises but at a diminishing rate. Total product keeps increasing throughout — it reaches $57$ at $L = 6$ and does not decline over this range.
Average product rises while $L$ goes from $1$ to $3$ (reaching $13.33$ ) and falls thereafter. It stays above the falling marginal product on the right, and the marginal product curve cuts the average product curve from above at the maximum of average product.

Note

The identity $MP_L = TP_L - TP_{L-1}$ is easy to verify: for the second unit, $\Delta TP = 24 - 10 = 14$ , so $MP = 14$ ; for the third unit, $\Delta TP = 40 - 24 = 16$ , so $MP = 16$ , and so on.

Watch out

A common mistake is to confuse marginal product with the total product itself. Marginal product is always a rate of change — it tells you how fast total product is increasing at a given point, not the total output level.

Relationship Between Marginal Product and Average Product

The textbook makes an important conceptual link: the average product of an input at any level of employment is the average of all marginal products up to that level. In other words, if you have employed $n$ units of labour, the average product of labour is:

AP_L = \frac{MP_1 + MP_2 + \dots + MP_n}{n}

where $MP_1$ is the marginal product of the first unit, $MP_2$ of the second, and so on. This is not a separate formula — it follows directly from the definition of average product as total product divided by labour, and the fact that total product is the sum of all marginal products. …

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