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Summary

These several pages provide a general overview of production theory. The following points summary some of the key points of this economic concept.

• Production theory is based on the assumption that business managers strive to make decisions to maximize profit (TR -TC).

• A business can increase profit by increasing revenue (TPP x Py) and/or reducing cost (TFC + (X x Px)). Assuming that the business cannot alter the market price for the output (Py) or inputs (e.g., Px), the primary way to increase revenue is to increase production (TPP) and the primary way to reduce cost is to reduce the quantity of input (X).

• Other than a change in technology, reducing input will reduce output, and an increase in input is assumed to increase output.

• However, diminishing marginal productivity describes the reality that increased input will not always increase production, especially if there is not enough time to increase the level of all inputs (i.e., the short run).

• Thus, a manager will increase input as long as the revenue from the increased production due to the additional input (VMP) is greater than the cost of the additional input (MIC). Restated, a manager will increase production as long as the revenue from the last unit of output (MR) is greater than the added cost of producing that last unit of output (MC).

• The manager has maximized profit when production has reached the point that the cost of the additional input equals the revenue generated by using the additional input (VMP = MIC and MR = MC).

• Maximum production SELDOM means maximum profit.

• The price a manager is willing to pay for an input is the value of the product that the input produces (VMP is the business' derived demand for X).

• A manager is willing to produce and sell a product as long as the price of the product is equal to or greater than the added cost of producing that product (MC is the business' supply of Y).

• Likewise, a manger will keep on operating the business even though it is incurring a loss as long as the loss incurred by continuing to operate is less than the loss that would be incurred if the business quit operating (TR > TVC).

• In a business where the manager can use two different inputs to produce the output, the manager will use the combination of inputs where the ratio of the productivity of the first input relative to the cost of the first input equals the ratio of the productivity of the second input relative to the cost of the second input (MPx1/Px1 = MPx2/Px2).

• In a business where the manager can produce two different products from the same input, the manager will produce the combination of products where "the value of each product produced by the last unit of input applied [is equal] for all products using the ... input" (VMPy1 = VMPy2).

Implications

Managers are almost constantly making decisions about their business -- what product to produce, how much input to use, what combination of inputs to use, how to finance the operation, how and when to sell the product, what selling price should the manager set or accept, and the list goes on. This discussion does not address all of these managerial questions, but instead focuses on production questions, such as how much input should the business use to maximize profit.

Managerial questions relating to production are being made on a continuous basis, should the business hire more workers or lay off some workers in order to increase or decrease output and thereby increase profit, should the business expand its building, should the business invest the capital to purchase new equipment, and again, the list goes on.

Some of these decisions are made on almost a daily basis, e.g., should the business hire more day-workers (often unskilled workers who are willing to work for one day at a time). Other decisions are made occasionally and have a long term impact, e.g., should the business expand the size of the building or buy new equipment. Not only is this second category of decisions made occasionally, they also take more time to implement (it may take months from the time a manager decides to expand a building until the new space is ready to be used), and the decision is not easily reversed (it would be difficult and expensive to remove a portion of a building if the manager determines that it is no longer needed).

The purpose of these web pages is to describe economic concepts managers may consider in thinking about (analyzing) production decisions.

Short-run and Long-run

When managers face such a variety of decisions, such as hiring more day- workers versus deciding whether to expand the building, the time period being considered becomes a factor. In deciding whether to hire more day-workers, the manager knows the decision can be easily changed (i.e., the business can hire a different number of day-workers the next day) and some aspects of the business will remain unchanged (e.g., regardless of how many day-workers are employed, the size of the building and the type of equipment being used will not be changed every day).

In deciding whether to expand the building, the manager recognizes that implementing the decision will take time (months or years), the decision is not easily reversed, and there is enough time to change just about every aspect of the production process (e.g., what equipment will be installed in the new building, what energy source will be used, how many workers will be needed to operate the new equipment in the new facility, and the lsit goes on). The decision about expanding the building could impact the daily operation of the business for years into the future.

Economic theory describes the first decision as being in the short-run -- easily altered and there is not enough time to alter all aspects of the business. The second decision would be described in economic theory as the long-run -- a period of time in which all aspects of the business can be altered. The discussion on this web page assumes the short-run -- enough time to alter some inputs (e.g., the number of day-workers) and easily altered. The criteria for both decisions, however, likely includes "how does the manager expect the decision to impact achieving the business goal of earning profit."

Several Other Important Concepts Relating to the Short-run

The input that can be changed in the short-run (e.g., number of day-workers) is considered a variable input. The inputs that cannot be changed in the short-run (e.g., the building and equipment) are considered fixed inputs. The cost associated with the variable input is the variable cost; the cost associated with the fixed input is a fixed cost.

Fixed input and their fixed cost are constant in the short-run regardless of how much variable input is used. Total variable cost will rise and fall in the short-run, depending on how much variable input is used.

Diminishing Marginal Productivity

One way to adjust output in the short-run is to alter the level of variable input; that is, use more or less variable input with the constant amount of fixed input to find the level of production that maximizes profit in the short-run. For example, the manager might have to decide whether the business should hire 4 workers today, or 7 workers? Will the business earn more profit today by paying the cost of 4 workers and having the output of 4 workers, or will the business earn more profit today by hiring 7 workers and having the output of 7 workers. Every business is different; there is no one answer to this question. Instead, the manager needs to know the business well enough to be able to make that decision every time the question arises.

In analyzing the business and observing that 7 workers per day is more profitable than 4 workers per day, a manager might conclude that "more is better than less" -- if 7 workers is good, then 10 workers per day must be better, and 13 workers per day must be better than 10 workers per day. "Let's hire as many day-workers as possible." However, nature does not work this way. Even if 7 workers is more profitable than 4 workers, and 10 workers is more profitable than 7 workers, there will be point where more workers is LESS profitable than fewer workers. Why?

There is a point where more workers all trying to use the same building and equipment will actually lead to less productivity. If there are too many workers, they may bump into each other; there is not enough room for all of them to work at the same time. Or some may have to wait until another worker is done using a piece of equipment if there is not enough equipment for all workers.

Economic theory refers to this natural phenomenon as diminishing marginal productivity. As more variable input (e.g., day-workers) is added to the fixed input (e.g., building and equipment) during a period of time, productivity per unit of variable input (e.g., worker) will begin to decline, and if too much variable input is used, total production will decline. Bottom line -- more variable input does not always mean more profit; it may not even mean more output.

Economists refer to the relationship between the level of variable input and the level of output as the production function.

The notion that "the output for each unit of variable input declines as more units of the variable input are used during a particular time period" can be restated as "it takes more variable input to produce additional output if the business uses more variable input during a particular time period." Taking this understanding one step further, the cost to produce the output increases as the business tries to increase production during a time period by using more variable input.

Restated, the cost of producing an additional unit of output during a period of time by using more variable input is higher than the cost of producing the previous unit of output during that production period. A manager will only want to increase output by using more variable input to the point where the cost of producing the last unit of output is equal to the revenue that the last unit of output will generate when it is sold.

Again, it is nature's phenomenon of diminishing marginal productivity that leads to these increasing cost of trying to produce more during a short-run time period.

In economic terms, the additional output resulting from using an additional unit of variable input is referred to as marginal physical product (MPP). The cost of producing an additional unit of output by increasing the level of variable input is marginal cost (MC). The revenue generated by selling an additional unit of output is marginal revenue (MR). The firm will maximize profit by using the quantity of variable input where the added cost of producing the last unit of output (MC) equals the revenue generated by selling that last unit of output (MR). Producing more output than this level decreases profit; producing less output than this level does not maximize profit.

Bottom line -- business will maximize profit during a production period by using the level of variable input where the level of output has MC = MR.

This same economic "rule of thumb" for maximizing profit can be restated as "use the level of variable input where the value of output produced by the last unit of variable input (MVP) equals the cost of the last unit of variable input (MIC)."

The difference between the two statements is that the focus is on level of output when expressing the rule in terms of MC and MR, whereas the focus is on the level of variable input when stating the rule in terms of MVP and MIC.

Note -- fixed cost are not a consideration in the short-run; they do not change regardless of how much variable input is used and how much output is produced.

What Else Can We Learn?

Several other observations can be made about the managerial implication of diminishing marginal productivity.

1. Maximun profit does not mean maximum production unless the input is free or the market price for the output is infinite. Both of these seldom occur, so the basic rule is "maximum profit occurs at some level of production less than maximum production." Profit-maximizing managers will not try to maximize production, but instead produce for maximium profit.

2. Understanding a firm's marginal cost also reveals the firm's supply of the output. If the market price of the output increases, the MR increases meaning the firm is willing to produce more output during that time period even though that new output has a higher MC. This is the basic law of supply -- as price rises, producers are willing to supply a greater quantity. Conversely, if the market price for the product declines (MR), the firm will supply less.

2A. Also consider the impact of an increase in the cost of the variable input, which means the MC for the firm has risen. If the market price for the output (MR) remains unchanged, the firm will maximize profit by producing less output; that is, using less variable input so MR again equals MC.

Thus the firm's marginal cost structure is the foundation for the firm's ability to supply the output.

3. Understanding a firm's marginal value product (MVP), likewise, reveals the firm's demand for the variable input. For example, if the cost of the variable input (MIC) rises but the productivity of the variable input (MPP) and the price of the output both remain constant (i.e., the MVP reamins unchanged), the firm will use less variable input. This is the basic law of demand -- quantity demanded will decline if the price rises. The firm will use (demand) less variable input and produce less output if the cost of the variable input (MIC) rises. This is the same situation previously described in point 2A.

3A. If the price of the output declines, the MVP also declines. If the cost of the variable input (MIC) remains constant, the firm will maximize profit again by using less variable input and producing less output. This is consistent with the previous explanation in point 2.

4. Let's apply these points to recent events. As the market price of agricultural commodities rose in 2007 (MR and MVP increased), producers tried to increase profit by using more variable input to increase output. Willingness to supply more output reflects the relationship between MR and MC; willingness to use more variable input reflects the relationship between MVP and MIC.

4A. How did the supplier of the variable input respond when the buyer of the input enjoys an increased market price for the product produced from the input? Did they raise the price of the variable input, especially those input suppliers whose market is "less than perfectly competitive?" Do these suppliers understand the farmers' MVP so the supplier sets the price of the variable input (MIC) at a point where some or all of the farmers' additional revenue from the higher commodity prices is paid to the supplier even though the suppliers' cost may not have changed much? Does this suggest that the greater farm profits of 2007 and 2008 may decline soon if suppliers are able to raise their market prices?

What can be learned from point 4A? How do the economic concepts of perfect competition and imperfect competition help explain this scenario? What do these concepts and situation suggest for a business manager?

5. As stated above, fixed inputs and fixed costs are not emphasized when analyzing the short-run. They remain constant throughout the time period being considered by the manager.

However, fixed cost are a component of total cost; that is, total cost (TC) is the sum of fixed cost (TFC) and variable cost (TVC) during a period of time. Likewise, profit is the difference between revenue (TR) and total cost (TC) realized during a period of time. Earning a profit in the short-run is presumed to be a goal for the manager, thus, fixed cost, even in the short-run, is considered in determining whether the business is achieving the goal of earning a profit in the short-run.

As long as firm's profit-maximizing revenue exceeds total cost (TR > TC) in the short-run, the firm will certainly continue to operate. However, what does a manager do if the profit-maxmizing revenue is less than total cost? Does the manager discontinue operating the firm? To answer this question, the manager needs to distinguish between variable cost and fixed cost.

To begin the analysis, the manager must recognize that even if no variable inputs are purchased, no variable cost are incurred, no output is produced and no revenue is generated, the firm must still pay its fixed cost (TFC). That is the definition of fixed inputs and fixed cost -- regardless of the level of variable input used and the level of production (even if they both are 0), the fixed cost must be paid. Accordingly, discontinuing operation means the business will incur a loss equal to its fixed cost (TFC).

What is the manager's alternative? A manager can reduce the amount of loss (minimize the loss) by continuing to produce in the short-run as long as revenue exceeds variable cost (TR > TVC). In this situation, the revenue is adequate to pay all the variable cost and a portion of the fixed cost. Thus the unpaid portion of the fixed cost is less than the total fixed cost.

5A. Even though the business is incurring a loss (rather than earning a profit), the loss can be reduced by continuing to operate and generate revenue to pay all variable cost and a portion of the fixed cost.

5B. If revenue drops to the level where it is inadequate to pay all variable cost, the firm would incur a smaller loss by discontinuing its operation and only incurring its fixed cost.

Summary -- loss minimization in the short run means producing as long as total revenue (TR) exceeds total variable cost (TVC).

6. Let's revisit the concept of short-run versus long-run. Costs of some inputs are recategorized as fixed or variable when the manager changes the time frame being considered. Also, the need to replace or an opportunity to sell a production asset (e.g., a piece of equipment) converts a fixed asset/input into a variable input.

What is the managerial implications of recategorizing inputs from fixed to variable? For example, when does a firm shift from "loss minimization" to "no production" because the firm cannot operate at a loss forever? One way to describe what is happening is that even though total cost have not changed, the portion of total cost that is variable has now increased whereas the portion of total cost that is fixed has declined. For the firm operating in loss minimization, the time has come to discontinue production even though the market price for the output and the total cost of production have not changed.

Another example, when does a firm adopt/invest in new technology -- see the next point.

7. How does advancing production technology impact a firm that might use that technology? How does advancing technology impact the industry if several firms begin to use that technology? How does advancing technology impact the consumers of the products produced by the industry that is adopting advanced technology, especially if the market for the product is competitive? How does the adoption of advancing technology by other producers impact a producer who does not adopt the advanced technology? Also, what is the impact on the firm that created and is marketing the new technology (review earlier point on MVP)? How does this understanding of the implications of advancing technology impact the way business people analyze an opportunity to adopt new technology? Let's answer each of these questions.

7A. How does advancing production technology impact a firm that might use that technology?

Initial result is probably a reduction in the cost of variable inputs used in the past; i.e., the new technology usually allows the firm to maintain or increase output even though it is now using less of the variable inputs that it used previously. The technology that reduces variable cost means MC has been reduced (MC is the change in TVC due to producing one more unit of output). Accordingly, a firm which adopts new technology will often increase its output even though the market price for the output has not changed.

But the technology is not free. If it comes in the form of a fixed cost (e.g., new item of equipment), the reduction in TVC has to be enough to pay for an appropriate portion of the fixed cost (e.g., increase in depreciation expense arising from the acquisition of the new fixed input). If the new technology is in the form of a (new) variable input (e.g., more effective information system), the additional output must be adequate to pay the cost of the new variable input.

7B. How does advancing technology impact the industry if several firms begin to use that technology?

If several firms adopt the technology and they each expand production, the industry's supply will increase placing downward pressure on the market price of the output.

7C. How does advancing technology impact the consumers of the products produced by the industry that is adopting advanced technology, especially if the market for the product is competitive?

The consumers will enjoy a lower cost.

7D. How does the adoption of advancing technology by other producers impact a producer who does not adopt the advanced technology?

If a firm does not adopt the technology, its cost will remain where it has been, but the firm will be facing a lower market price for the output. A non-adopting firm may find declining profit due to constant cost but declining revenue.

7E. Also, what is the impact on the firm that created and is marketing the new technology?

The firm that created the technology, especially if it faces less-than-perfect competition, will try to extract as much revenue from its customers as possible. The supplier fo the technology will try to determine the buyers' MVP for the technology and price the technology accordingly. Review point 4A, above.

7F. How does this understanding of the implications of advancing technology impact the way business people analyze an opportunity to adopt new technology?

New technology raises the level of competition among the firms that produce the product that is being impacted by the technology. Firms that are willing and able to acquire the technology will gain an advantage over their competitors. Firms that are unwilling or unable to acquire the technology will soon face a disadvantage relative to their competitiors.

8. Many businesses do not have enough data to develop detailed production functions. This may change with advancing information technology. Mangers need to understand and be able to apply the economic concepts regardless of the level of detailed data.

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.

E-Mail:sswandal@ndsuext.nodak.edu
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