Consider that all inputs in a production process are constant except only one input. If the total product in this case is at its maximum, the corresponding marginal product is :
Zero
When all inputs except one are held fixed, production is governed by the law of variable proportions. Marginal product (MP) is the change in total product (TP) from one extra unit of the variable input: \(MP = \dfrac{\Delta TP}{\Delta L}\).
As the variable input increases, TP first rises at an increasing rate, then at a diminishing rate, reaches a maximum, and finally declines. TP keeps rising only as long as MP is positive. At the exact point where TP attains its maximum, the slope of the TP curve is zero, so \(\dfrac{dTP}{dL} = MP = 0\). Beyond that point MP becomes negative and TP falls, which marks the start of the third stage of production.
MP is at its maximum at the inflexion point of TP, well before TP peaks, so a maximum MP does not match. MP is rising only in the early phase of increasing returns, and although MP is falling in the second stage, at the precise TP peak its value is not just falling but equal to zero.
Zero option is correct.
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