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Mathematical Proof of the Relationship Between Marginal and Average Product
The formal proof that connects marginal and average product involves differentiating the average product of labor (APL) function with respect to the input, such as hours of work (). This differentiation is specifically carried out using the quotient rule. The proof's objective is to show that for the APL to be diminishing, its derivative must be negative. By setting the result of the differentiation to be less than zero, it is mathematically demonstrated that the marginal product must be less than the average product.
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