Best if printed in landscape.

What if a manager could use different inputs to produce the same product? Restated, if a manger had to decide which of two variable inputs? Can economic theory help explain how much of each input should be used to maximize profit?

Example 1 -- a business is producing a crop (output) on a fixed quantity of land (fixed input) and a limited amount of cash to be used for fertilizer and irrigation (variable inputs). How much of the cash should be used to buy and apply fertilizer and how much of the cash should be used to operate the irrigation system?

Example 2 -- a business is manufacturing a consumer product (output) in a manufacturing facility (fixed input) with a limited amount of cash (again) that can be used to buy steel or to hire workers (variable inputs). How much of the cash should be spent on steel and how much of the cash should be spent on labor?

Using the second example, if the business spends most of the cash on steel and only a little on labor, there may not be enough workers so the steel remains unused at the end of the production period. Alternatively, if the cash is spent on workers and not enough steel, the workers may find themselves standing around because there is no steel with which to manufacture the products. Another alternative is to buy plenty of steel and hire plenty of workers, but two matters limit this strategy -- the size of the facility and the amount of cash. These two matters are the fixed inputs and cannot be altered during the production period.

Economic theory states that the answer to the question of how much steel and how much labor can be stated as

MPPx1/Px1 = MPPx2/Px2, or

MPPx1/MPPx2 = Px2/Px1

The ratios in the second formula are referred to in economic theory as the marginal rate of substitution and the inverse price ratio.

These formulas focuses the manager's attention on the relationship between the quantity of output produced (MPP) and the cost of the variable input (Px). Due to the reality of diminishing marginal productivity, the MPP for both inputs changes as more variable input is used. The manager does not want to use so much of one input and so little of the other input that neither of the levels of use is close to being the profit maximizing combination of inputs. However, the manager also needs to consider the relative cost of each variable input. Accordingly, the manager considers how adjusting the relative quantity of the variable input impacts total production of the output and the relative cost of the variable inputs.

This mathematical statement is based on the premise that there is a production function for the steel and for labor; that is, how much output is there for the steel and how much output is there for the labor.

In these two disjointed relationship (that is, the relationship between steel and output is presumably not impacted by the amount of labor, and the production function for labor is presumably not impacted by the availability of steel), there is an individual production function for each variable input.

The primary fixed input for the individual production functions for steel and labor is presumed to be the manufacturing facility, not the cash.

The solution, however, is limited by the amount of cash available to the business, therefore, (Px1 * X1) + (Px2 * X2) must not exceed the amount of available cash.

Because of the cash limitation, the firm may not produce where MVP = MIC, but instead has to settle for producing at some point where MVP > MIC. This is based on the assumption that even though the business is profitable and there is room to expand, there is no opportunity during this production period to acquire more cash with which to purchase more variable inputs.

Managers also may want to consider the economic theory that explains deciding how much to produce and what to produce.

Last Updated October 28, 2008

Email: David.Saxowsky@ndsu.edu

This material is intended for educational purposes only. It is not a substitute for competent professional advice. Seek appropriate advice for answers to your specific questions.

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Published by Agricusiness and Applied Economics
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