<P> The marginal product of a given input can be expressed as: </P> <Dl> <Dd> M P = Δ Y Δ X (\ displaystyle MP = (\ frac (\ Delta Y) (\ Delta X))) </Dd> </Dl> <Dd> M P = Δ Y Δ X (\ displaystyle MP = (\ frac (\ Delta Y) (\ Delta X))) </Dd> <P> where Δ X (\ displaystyle \ Delta X) is the change in the firm's use of the input (conventionally a one - unit change) and Δ Y (\ displaystyle \ Delta Y) is the change in quantity of output produced (resulting from the change in the input). Note that the quantity Y (\ displaystyle Y) of the "product" is typically defined ignoring external costs and benefits . </P>

Where does the marginal product cross average product