When marginal product is at its maximum, what can be said about total product?

Question

BlackTom AI · Accepted Answer

The question asks about the relationship between marginal product (MP) and total product (TP) when MP is at its maximum.
First, recall that total product changes as marginal product accumulates: TP rises whenever MP is positive, and TP falls when MP is negative. When MP is at its maximum, this means MP is at the highest positive value it attains in the relevant range, which implies TP is still increasing at that point because a positive MP always adds to TP.
Another way to see this is to consider that TP is the integral (cumulative sum) of MP with respect to input or time. If MP is positive, its accumulation increases TP; if MP is at its peak, that peak must be above zero in the typical short-run production function where diminishing returns eventually set in. Therefore, TP is increasing at the moment MP is at its maximum.
Be mindful of common misreadings: some might think the maximum MP corresponds to the TP maximum, but TP reaches its own maximum where MP crosses zero (from positive to negative). At the exact MP maximum, MP is positive, so TP is still increasing, not yet at its peak.
In contrast, an option claiming that TP is decreasing or that MP must be negative would conflict with the fundamental relationship between MP and TP in standard production theory. If MP were zero or negative at that point, TP would be no longer increasing; however, a maximum MP by definition is positive and represents the point of greatest incremental output, reinforcing that TP is increasing there.
If you’re unsure about the concept, think of MP as the slope of the TP curve. A steeper positive slope (maximum MP) means TP is climbing most rapidly, which aligns with the idea that TP is increasing when MP is positive.

When marginal product is at its maximum, what can be said about total product?

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