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Diminishing Marginal Productivity

Diminishing marginal productivity recognizes that a business manager cannot change the quantity of all inputs at one time. Instead, altering the level of one or more inputs while holding the level of other inputs constant is the realistic means of adjusting productivity. However, adding an input while holding other inputs constant will not increase productivity indefinitely. The reality that output will decline as more of one input is added is referred to a diminishing marginal productivity. The challenge is to determine the level of input that will maximize profit, rather than maximize production.

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A common business goal is to earn a profit.  Often this goal is stated as wanting to maximize profit or to earn as much profit as possible with the available resources.

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Management has been described as decision making. Among the many decisions that managers make are questions about producing a good or service to achieve the goal of earning a profit. The questions include "what product should I produce," "how should I produce this product," and "how much should I produce" to maximize profit.

Or more practically, the questions might be "Should I change the way I produce my product to increase profit? Should I use a different quantity of the input to increase profit? Should I use a different input? Should I use a different combination of inputs? Should I try to produce more or less of the product? Should I produce a slightly different product? Should I make a major change by producing an entirely different product, and the list of questions goes on. What is consistent among these questions is the objective of earning a profit or increasing profit, and the need to analyze the business operation.

The answer to these questions is unique for each business and the manager needs to make these decisions. No one can make these decisions for the manager. It is his or her responsibility to consider these important issues.

Even though the goal of increasing profit may be the primary criterion for these decisions, it may not be the only criteria. However for the purpose of this discussion, it is assumed that the manager will always strive to make the decision that maximizes profit.

The purpose of this series of web pages is to review economic concepts that can help managers analyze their business situations. The explanation will not answer the managers' questions nor will it provide the detailed data needed to analyze the business' alternatives. Instead, the explanation provides a conceptual framework with which managers can assess their own opportunities.

The economic concepts reviewed in these pages can be referred to as production theory, and addresses the three questions introduced above -- what product should I produce to maximize profit, how should I produce the product to maximize profit, and how much of the product should I produce to maximize profit. The majority of the discussion addresses the third question -- how much should I produce. The other two questions are briefly addressed thereafter.

Note that each of these questions is based on the premise that one of the manager's goal is to maximize profit.

Throughout this discussion, an underlying proposition is that diminishing marginal productivity is real. This bit of reality will be the foundation for all of this discussion. Diminishing marginal productivity is discussed more fully in a subsequent section on this page.

 

How much output or product should the business produce to maximize profit (factor-product)

The purpose of this series of web pages is to present a general overview of several economic concepts relating to the broad topic of production theory. The topics include

  • diminishing marginal productivity
  • the production function
  • stages of production
  • determining the profit maximizing quantity of variable input and profit maximizing level of production
  • determining demand for the variable input
  • defining and determining the cost of producing the product
  • determining supply of the product, and
  • minimizing loss if the business is unable to generate a profit

Embedded in these topics are secondary discussions about 1) short-run versus long-run, 2) fixed inputs and variable inputs, and 3) fixed costs and variable costs. The discussion often uses "advancing technology" as an example to illustrate the application of these economic concepts. A relationship between enterprise analysis and production response also is suggested.

Several assumptions form the foundation for this discussion. The first assumption (as already introduced) is that the manager wants to produce the quantity of output that will maximize profit. A second assumption is that the business can increase production or output by using more input, and that increased output means increased profit.

As the second assumption is discussed in subsequent sections, it will become clear that this assumption is NOT always true. There are times when using more input will increase production and increase profit, but there also are times when using more input will increase output but decrease profit. Furthermore, there are times when using more input decreases production and profit.

Increasing input will NOT always lead to increased profit. Accordingly, the manager will not want to maximize production, but instead will want to use the level of input that produces the level of output that achieves the goal of maximizing profit.

The manager's task is to determine the profit maximizing level of quantity or level of input. The manager's decision could be restated as "how much input should I use to maximize profit."

This web page introduces why the answer to the simple question of "how much should I produce" is complex. The page also introduces how a manager can decide how much input to use to maximize profit.

Although the stated goal for managers may be to maximize profit, some of the concepts addressed on these pages also can be illustrated with other examples. For example, there are many recipes for making a chocolate cake but the recipes differ and thus the resulting cakes may differ. Despite these differences, those of us who enjoy chocolate cake would likely find many of these cakes to be acceptable, that is, they are substitutable even though they are not identical.

A third assumption is that there is more than one way or one "recipe" for producing a product. Take the example of a chocolate cake but think about it from a slightly different perspective. Instead of asking "how much input should I use to maximize profit," a baker may ask " how much chocolate should I use in making the cake?" That is, the baker could bake several cakes using the same amount of flour, sugar and milk and the same number of eggs, but vary the amount of chocolate in each cake. The cake made with a small quantity of chocolate may not have much flavor and thus not achieve the goal of baking a good chocolate cake. At the other extreme if the baker uses a large quantity of chocolate in one cake, the flavor may be bitter. Neither of these decisions achieve the goal of baking a good chocolate cake. Some quantity of chocolate between these two extremes will likely result in an acceptable cake.

A similar situation can arise for a wheat farmer who uses a small quantity of fertilizer per acre; the farmer may not reach the yield potential for the acre of land. However, using a large quantity of fertilizer may diminish production; that is, too much fertilizer can stunt the growth of the crop. Somewhere between these two extremes is the quantity of fertilizer that achieves the farmer's goal of maximizing profit from raising wheat on the acre of land.

There is more than one way to produce a product and the "recipe" that one business uses will be different than the recipe used by another business. Each manager must determine the "recipe" the works best for his or her business. What one manager does may not make sense for another manager. Each manager needs the skills to decide which "recipe" is most appropriate for his or her business.

In summary, the purpose of these materials is to introduce principles, including economic principles that help describe a decision making process for the baker, the farmer and many other managers. Restated, this series of web pages demonstrates that these economic concepts are relevant in making numerous production decisions.

  • The discussion initially assumes the managers (the decision makers) know what product (good or service) they want to produce.
  • The discussion recognizes that there are different ways to produce similar products.
  • The discussion also initially assumes that the managers know how to produce the product; that is, the managers have a general understanding of how they want to produce the product. Restated, the manager has determined what technology will be used to produce the product and what inputs will be used in the production process.
  • The discussion assumes a goal for the manager is to earn a profit from producing and selling the product. This goal is often stated as maximizing profit, but maximizing profit may not always be the managers' only goal.
  • Adding inputs is expected to increase production and profit, but in reality, adding inputs can decrease profit and in some situations, decrease production.
  • The purpose for these materials is to help decision makers understand how to analyze their business in order to make decisions that will advance the goal of earning a profit.

The next section introduces the concept of diminishing marginal productivity -- a natural phenomenon that impacts decision making.

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Diminishing Marginal Productivity

This page introduces the economic concepts of 1) diminishing marginal productivity, 2) short-run and long-run, 3) fixed and variable inputs and 4) fixed and variable costs.

Diminishing marginal productivity is the understanding that using additional inputs will generally increase output, but there also is a point where adding more input will result in a smaller increase in the output, and there is another point where using even more input will lead to a decrease in output.

A hypothetical example: 

  • Using no fertilizer to produce wheat may yield 15 bushels per acre. 
  • Using 50 pounds of fertilizer may increase the yield to 25 bushels; that is, an increase of 10 bushels as a result of using 50 pounds of fertilizer. 
  • Using another 50 pounds (for a total of 100 pounds) may increase the yield to 32 bushels; that is, the second 50 pounds of fertilizer increased the yield by only 7 bushels. 
  • Furthermore, adding another 50 pounds (for a total of 150 pounds) may result in a yield of only 30 bushels; that is, the final 50 pounds of fertilizer actually damaged the crop and reduced the yield by 2 bushels.

We could develop a similar example using student study time; some study time will result in an improved understanding of the subject matter, but there will be a point where additional study time (e.g., repeatedly reviewing the same material) will not enhance the student's understanding. (However, this does NOT mean that students can get by investing NO time in studying!!)

A third example to illustrate diminishing marginal productivity could involve determining how many people should be assigned to the crew of a piano moving truck. One truck and one worker may not be an effective piano moving business because it is difficult for one person to move a piano. One truck with two or three workers might be quite productive. One truck with four, five or six workers may be less productive than if there were fewer workers. With too many workers, they begin to trip over one another, there is not enough room for all of them to lift on the piano at one time (so some workers merely watch the others move the piano), and there may not be enough room in the truck for all of them to travel from site to site.

We also can return to our previous example of a chocolate cake; adding more chocolate to the batter initially improves the taste of the cake, but adding even more chocolate will eventually detract from the taste of the cake.

As stated by others, if diminishing marginal productivity was not a reality, we could raise all the food we need in a flower pot by simply adding more seed, fertilizer, water, etc.

An almost endless list of examples could be developed to illustrate diminishing marginal productivity.

Diminishing marginal productivity is a natural phenomenon that economists recognize they must acknowledge and incorporate into their thinking and analysis.

The following sections explain the impact of diminishing marginal productivity. The impacts of the concept are illustrated with the production function and cost curves. The discussion also considers how the concept of diminishing marginal productivity influences decision making. Finally, the relationship between these concepts and enterprise budget/analysis is introduced.

Assumptions

  • Business people want to make decisions that increase profit so the additional profit can be used by the business owners for personal needs and desires, such as food, housing, clothing, health care, education, and recreation.  This assumption is usually stated as “a manager strives to maximize the business’ profit.”

 

  • One strategy to increase profit is to produce and sell more product in a given period of time (e.g., monthly, quarterly annually); this strategy is often based on the assumption that increased production by this one firm will not decrease the market price for the product.

 

  • Increased production requires additional input (we cannot produce something from nothing).
    • This assumption is revisited in a subsequent section that discusses the impact of advancing technology.

 

  • Often when a manager decides to use more input to produce more output, there is not an opportunity (there is not enough time) to increase all inputs; that is, some inputs (perhaps a building) are unchanged even though a larger quantity of other inputs are being used to increase output (such as, more flour is being made into dough and baked into bread inside the building).  One of the preceding hypothetical examples held the land (one acre) constant as the amount of fertilizer was increased from 0 to 150 pounds. Another example held the number of trucks constant while changing the number of workers.
    • Each of these examples assumes that at least one input cannot be changed (the building, the land, the truck) while another input can be altered (the quantity of flour, fertilizer, or workers).

 

Short-run and Long-run

An assumption is that the manager wants to increase profit as quickly as possible, but this also implies there will not be enough time to increase ALL inputs, so the business will increase only SOME inputs. Restated, assuming that the manager wants to increase profit as soon as possible, there is not enough time to change the level of all inputs.

Not being able to change some inputs is defined as the short-run -- not enough time to change all inputs. The manager will try to change the level of production by changing only the level of variable inputs. Restated, there will be both fixed inputs and variable inputs. A fixed input is any input that cannot be changed in the time period the manager is contemplating.

Diminishing marginal productivity is the concept that using increasing amount of some inputs (variable inputs) during the production period while holding other inputs constant (fixed inputs) will eventually lead to decreasing productivity. Diminishing marginal productivity is a natural phenomenon that humans cannot avoid or eliminate.

 

The inability to change the level or quantity of at least one input due to the shortness of time is designated in economic theory as the short run. The long run, by comparison, means the business manager is contemplating a period of time that is long enough to alter or change all of the business assets.

Example. Buying additional flour or hiring another worker for a bakery usually can be accomplished in a relatively short time whereas constructing an addition to a building or buying another truck generally takes longer. If the business manager is contemplating a time frame in which additional flour can be purchased but the building cannot be expanded, economic theory would call that the short run because there is not enough time to change all the assets the business is using. If the business manager, however, is considering a time period long enough to change all the business assets, including an expansion of a building, for example, economic theory would describe that as the long run.

Many management decisions are made with the manager contemplating the short run; that is, enough time to change some inputs but not all inputs. The implication of thinking about the short-run is addressed again in a subsequent section.

  • Long-run is a period time long enough for the manager to alter the level or quantity of all inputs being used in the production process.
  • Short-run is a period of time that allows the manager to alter the level of some inputs but there is not enough time to alter the level of other inputs.

Assume the Short-run

Managerial decisions are often made under circumstances where the manager cannot alter all inputs being used in the production process.  Instead, the manager can make some changes but has to rely on and use other resources as they currently exist; there just is not enough time to change everything.  This is referred to as the “short-run.” 

The concept of diminishing marginal productivity assumes the manager is making decisions to maximize profit in the short run.

The discussion on these pages assumes the short-run; that is, the manager wants to increase profit as quickly as possible. There is not enough time to increase all inputs; the business will try to increase output by increasing only some inputs.

 

Fixed inputs and Variable Inputs

The short-run introduces another economic concept -- fixed inputs and variable inputs. As already stated, in the short-run the quantity of some inputs can be changed but the quantity of other inputs cannot be altered. Economic theory refers to the inputs that can be changed as variable inputs and the inputs that cannot be altered in this time period as fixed inputs.

    • Variable inputs are the production inputs that can be altered in the short-run, for example, the business manager can easily use a greater quantity or a lesser quantity of the input during this production period.
    • Fixed inputs are the production inputs that cannot be altered in the short-run; even if the manager wants to use more or less of the input, there is not enough time to change the quantity of the input during this production period.

Fixed input v. long-term asset -- they are not the same.

Fixed inputs are those that cannot be easily altered. For example, land leased on a 3-month basis may be a variable input rather than a fixed input, but land that is leased on a 7-year contract may be relatively fixed. In the first case, the manager could discontinue leasing the land within 3 months whereas as the second manager is "stuck" with the land for as long as seven years even if the manager no longer wants to use the land.

Owned land may be more of a variable input than leased land. It may be easier to sell a tract of land if it is no longer needed than it may be to get out of a long-term lease agreement. Even though owned land is often used as an example of fixed input, it may not be a fixed asset if there are opportunities to sell it in a short time.

A piece of equipment that can be readily sold may be a variable input whereas a piece of specialized equipment that no one else is interested in buying would be a fixed input.

Some labor or workers might be a variable input -- hourly workers who can be told to "stay home today" because there is no work for them. Other workers, however, may be a fixed input such as those who are hired under a several-year contract that need to be paid even if there is no work for them.

Consider a family business. Is the labor provided by family members a variable input or a fixed input? How easy is it to "discharge" a family member if their labor is no longer needed in the family business?

Bottom line -- a fixed input is one that is not easily acquired or disposed of whereas inputs that can be easily bought and sold (even though they have a long useful life) may be viewed as a variable input. Do not confuse the economic definition of a fixed input with an asset that has a long useful life.

Fixed input becomes a variable input.

Fixed inputs become variable inputs as 1) the manager extends the time period being considered in the decision making process and 2) as the input reaches the point that it needs to be replaced. For example, a item of specialized equipment (as suggested above) is a fixed input if there is limited opportunity to sell the item. However, as the item grows old and reaches the end of its useful life, the manager now has an opportunity to decide whether to replace it or simply quit using it. At this point, this specialized equipment may shift (in the manager's mind) from being a fixed input to being a variable input.

The description of fixed inputs are addressed again in subsequent sections.

 

Variable and Fixed Costs

The issue of "fixed" versus "variable" cost is addressed in more detail in subsequent sections, but recognize for now that the costs of fixed inputs are considered “fixed costs” and the costs of variable inputs are considered “variable costs.”

Examples of cost associated with a fixed input include depreciation, maintenance, interest on debt associated with the asset, and opportunity cost of equity invested in the asset.

An important characteristic of a fixed input is that even if a fixed input is not being used, its cost is still being incurred. For example when a business decides to cease operation, the manager can eliminate the variable cost by not using any of the variable input (perhaps electricity), but the cost associated with the fixed inputs (which cannot be immediately disposed of) will continue to be incurred by the business (e.g., rent on a long-term lease that cannot be terminated) even if the business is not producing any product (revenue).

 

Applying the Concept of Diminishing Marginal Productivity in the Short-run

The concept of diminishing marginal productivity is apparent as managers make decisions in the short-run; that is, "how much variable input should I combine with my fixed inputs to achieve my goal of maximizing profit during this production period."

  • Diminishing marginal productivity describes the concept that productivity will decline if a manager tries to expand production by using a larger quantity of some (variable) inputs while using the same quantity of other (fixed) inputs during a time period.

In summary --

  • It is generally assumed that the level of output is directly related to the level of input, but our understanding (as summarized in economic theory) goes beyond that.
  • The inability to alter the productive capacity of an input (e.g., adopt new technology) or the length of time needed to vary the quantity of an input forces firms to use different proportions of inputs; that is, to increase output in the short run, the manager uses more of some inputs even though there is no opportunity to increase the quantity of all inputs.

    In the short run, there is not enough time to change the quantity of all inputs. The inputs that can be changed are referred to as variable input and their costs are variable costs. By comparison, inputs that cannot be changed are referred to as fixed inputs and result in fixed costs.

    In the long-run, all inputs can be altered; restated, all inputs and all costs are variable in the long-run.

  • The manager's timeframe is important. If there is not enough time to alter the level of use of all inputs, some inputs (fixed inputs) will remain unchanged even though other inputs (variable inputs) are being used in greater quantity in an effort to increase output.

    A THOUGHT:  By identifying fixed and variable inputs, the manager knows which inputs can be changed during the production period.

  • Diminishing marginal productivity:  if more units of a variable input are used in combination with fixed inputs, the rate of increase in total output will eventually decrease.

    A manager cannot add increasing amounts of variable input to fixed inputs during a production period without eventually decreasing output.

    As suggested in a “principles of economics” text (and as stated previously), we could raise all the food needed to feed the world in a flowerpot if diminishing marginal productivity was not real.

  • The inability to immediately alter the quantity of some inputs (e.g., fixed inputs) and the resulting reality of diminishing marginal productivity complicate managerial questions such as "should I change how much I produce," "should I change how I produce," and "should I change what I produce."

 

The next section illustrates an application of the concept of diminishing marginal productivity with a description of the production function.

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