Marginal physical product (MPP) and marginal cost (MC)go in opposite direction as they are inverse of each other. This statement can be represented mathematically as:
MPP is proportional to 1/MC, or MC is proportional 1/MPP.
MPP is defined as the extra quantity of a product that can be produced from increasing the the quantity of a specified factor of production or input by 1 unit, when all other factors of production or inputs are held constant.
Thus MPP = (Increase in production)/(Increase in input)
MC is defined as the extra cost of production required to produce one extra unit of product.
Thus MC = (Increase in input cost)/(Increase in production)
We can see that in above equalities for MPP and MC, Increase in production appears as numerator for MPP and as denominator for MC. However there is some difference the other term. "Increase in quantity" appearing as denominator refers to only a single input, while "Increase in input cost" appearing in numerator of MC refers to cost of all the inputs used. But this total cost itself may be considered as the single input required for production.
Thus it is clear that a higher MPP signifies a lower MC, and a lower MPP signifies a higher MC. In other words MPP and MC move in opposite directions.
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