Explain the relationship between a firm’s short-run production function and its short-run cost function. Focus on the marginal product of an input and the marginal cost of production.

The relationship between the Firm's short-run production and cost function is that they help a firm to make suitable adjustments in its production approach to achieve the cost efficiency.

In short-run of production, some costs are fixed while others are variable.  However, in long-run of production, all costs become variable.

In the short-run production function, the firm employs two inputs which is labor and capital

Since the firm is operating in a short-run production period, the relationship can be seen through the production function and cost function assuming that the firm uses a certain level of technology.

in the short-run production function, it is assumed that firm utilize state-of-the-art technology in the production process.

In conclusion, the relationship between the Firm's short-run production and cost function is that they help a firm to make suitable adjustments in its production approach to achieve the cost efficiency.

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Short-run Production Function and Short-run Cost Function

In the short-run, some costs are fixed while others are variable.  This is not the case in the long-run because, in the long-run, all costs become variable.

Therefore, the relationship between a firm’s short-run production function and its short-run cost function is depicted by the variability of the cost and the quantity of production in the short-run, when some costs are variable while other costs are fixed.

This implies that the quantity that the firm can produce in the short-run is determined by the variable (marginal) cost of production input.  Similarly, the total variable cost of a product is a function of the quantity and the marginal cost per unit.

Explanation:

The short-run production function shows the different volumes of output that a firm can produce, where some costs are fixed and some are variable.  This function is expressed as Q = f (L, K), where Q = quantity of production, L = labor input, and K = capital input.    Here, the firm assumes that labor input is variable while capital input is fixed.  This implies that the marginal cost of the product is equal to the labor cost.  Therefore, if the firm employs one more unit of labor, it results in a marginal increase in the units of production.  The marginal cost of production is expressed as a function of the change in the total cost divided by the change in the quantity.

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