A Production Function Shows Output That Can Be Produced From

Learning Objectives

• Explain the concept of a product office
• Differentiate between fixed and variable inputs
• Differentiate between full and marginal production
• Depict diminishing marginal productivity

We tin can summarize the ideas so far in terms of a product function, a mathematical expression or equation that explains the human relationship between a firm's inputs and its outputs:

[latex]Q=f\left[NR\text{,}L\text{,}K\text{,}t\text{,}East\correct][/latex]

A production is purely an applied science concept. If you plug in the amount of labor, capital and other inputs the firm is using, the production function tells how much output volition be produced by those inputs. Product functions are specific to the production. Dissimilar products accept dissimilar production functions. The corporeality of labor a farmer uses to produce a bushel of corn is likely different than that required to produce an motorcar. Firms in the same industry may take somewhat unlike production functions, since each firm may produce a little differently. One pizza restaurant may make its ain dough and sauce, while some other may buy those pre-made. A sit-downwardly pizza restaurant probably uses more labor (to handle table service) than a purely have-out eating house. We tin describe inputs as either fixed or variable.

Fixed inputs are those that tin can't hands be increased or decreased in a short period of fourth dimension. In the pizza example, the edifice is a stock-still input. One time the entrepreneur signs the lease, he or she is stuck in the building until the charter expires. Fixed inputs define the business firm'southward maximum output capacity. This is analogous to the potential real GDP shown by club'southward production possibilities curve, i.east. the maximum quantities of outputs a society tin produce at a given time with its available resources. Fixed inputs do not change as output changes.

Variable inputs are those that can easily be increased or decreased in a short period of time. The pizzaiolo can gild more ingredients with a telephone call, and then ingredients would be variable inputs. The owner could hire a new person to work the counter pretty chop-chop as well. Variable inputs increase or decrease as output changes.

Economists oft use a short-mitt form for the product function:

[latex]Q=f\left[L\text{,}K\right][/latex]

where L represents all the variable inputs, and K represents all the stock-still inputs.

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Economists also differentiate betwixt brusque and long run product. Theshort run is the period of time during which at least some factors of production are fixed. During the menstruum of the pizza eating house lease, the pizza restaurant is operating in the short run, because it is limited to using the electric current building—the owner tin't choose a larger or smaller building. Thelong run is the period of fourth dimension during which all factors are variable. One time the lease expires for the pizza eatery, the shop owner can move to a larger or smaller place.

Note that there is another important distinction between fixed and variable inputs. In the brusk run, since the firm'southward stock-still inputs are fixed, the just way to vary a firm's output is past changing its variable inputs. Let's explore production in the curt run using a specific case: tree cutting (for lumber) with a two-person crosscut saw.

Figure 1. Production in the curt run may be explored through the example of lumberjacks using a 2-person saw. (Credit: Wknight94/Wikimedia Commons)

Since past definition capital is stock-still in the short run, our production office becomes

[latex]Q=f\left[L\text{,}\stackrel{-}{K}\right]\text{or }Q=f\left[50\right][/latex]

This equation simply indicates that since capital is fixed, then changing the corporeality of output (e.g. trees cut down per day) depends merely on irresolute the amount of labor employed (e.g. number of lumberjacks working). We can express this product function numerically equally Tabular array one beneath shows. You can besides run across it graphically in Figure 2a.

Tabular array 1. Short Run Production Role for Trees

# Lumberjacks	1	two	three	4	five
# Copse (TP)	iv	10	12	xiii	13
MP	four	6	2	ane	0

Effigy two.Full Product and Marginal Production Curves. The short run full product for trees (superlative) shows the amount of output produced with stock-still uppercase. In this instance, one lumberjack using a two-person saw can cut downwardly four copse in an hour. Three lumberjacks using a two-person saw tin cut downwardly twelve trees in an hour. The marginal production for trees (lesser) shows the additional output created by one more lumberjack.

Note that we take introduced some new language. We also call Output (Q) Full Product (TP), which means the amount of output produced with a given amount of labor and a fixed amount of capital. In this case, one lumberjack using a two-person saw can cut downwards iv copse in an 60 minutes. Ii lumberjacks using a two-person saw tin can cut downward x trees in an 60 minutes.

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We should also introduce a disquisitional concept: marginal product. Marginal production is the additional output of one more worker. Mathematically, Marginal Product is the change in full product divided past the change in labor: [latex]MP=\Delta TP/\Delta L[/latex] In the table to a higher place, since 0 workers produce 0 trees, the marginal product of the first worker is iv copse per day, but the marginal production of the second worker is six trees per twenty-four hour period. Why might that be the case? Information technology'due south because of the nature of the capital the workers are using. A two-person saw works much meliorate with two persons than with one. Suppose nosotros add a third lumberjack to the story. What will that person'southward marginal product be? What volition that person contribute to the team? Perhaps he or she can oil the saw's teeth to keep it sawing smoothly or he or she could bring h2o to the two people sawing.

What you meet in the table is a critically important conclusion about production in the brusque run: it may be that every bit nosotros add workers, the marginal product increases at outset, but sooner or later additional workers volition have decreasing marginal product. In fact, there may eventually be no result or a negative effect on output. This is called theLaw of Diminishing Marginal Production and information technology's a characteristic of product in the brusque run. Diminishing marginal productivity is very similar to the concept of diminishing marginal utility that nosotros learned about in the chapter on consumer option. Both concepts are examples of the more general concept of diminishing marginal returns. Why does diminishing marginal productivity occur? It's because of fixed capital. We volition see this more clearly when we talk over product in the long run.

We can prove these concepts graphically, as y'all can meet in Figure 2 above. Effigy iii shows the more than general cases of total product and marginal production curves.

Figure three. Total Product and Marginal Product Curves. The superlative graph shows the general shape of a full production curve, with total product initially increasing, then tapering off due to the law of diminishing marginal product. The bottom graph shows how marginal product falls with additional labor.

Try It

Watch Information technology

Watch this video to review all of the production function and to see an example of the constabulary of diminishing marginal product. Dr. McGlasson wants to rent students for her visitor to brand "I love economics" signs, but she must consider how much output she can proceeds with each boosted employee.

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These questions allow you to get as much practice every bit you need, every bit you tin can click the link at the top of the first question ("Try another version of these questions") to go a new set of questions. Practice until yous experience comfy doing the questions.

Glossary

factors of production (or inputs):

resources that firms use to produce their products, for example, labor and capital

firm:

an organization that combines inputs of labor, uppercase, land, and raw or finished component materials to produce outputs.

fixed inputs:

factors of product that can't exist hands increased or decreased in a brusque period of time

long run:

period of time during which all of the business firm'south inputs are variable

product:

the process of combining inputs to produce outputs, ideally of a value greater than the value of the inputs

production function:

mathematical equation that tells how much output a business firm can produce with given amounts of inputs

short run:

period of fourth dimension during which at least one or more than of the business firm'southward inputs is fixed

variable inputs:

factors of product that a firm can easily increase or decrease in a short period of time

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Source: https://courses.lumenlearning.com/wmopen-microeconomics/chapter/the-production-function/

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