theory of production, in economics, an effort to explain the principles by which a business firm decides how much of each commodity that it sells (its “outputs” or “products”) it will produce, and how much of each kind of labour, raw material, fixed capital good, etc., that it employs (its “inputs” or “factors of production”) it will use. The theory involves some of the most fundamental principles of economics. These include the relationship between the prices of commodities and the prices (or wages or rents) of the productive factors used to produce them and also the relationships between the prices of commodities and productive factors, on the one hand, and the quantities of these commodities and productive factors that are produced or used, on the other. The various decisions a business enterprise makes about its productive activities can be classified into three layers of increasing complexity. The first layer includes decisions about methods of producing a given quantity of the output in a plant of given size and equipment. It involves the problem of what is called short-run cost minimization. The second layer, including the determination of the most profitable quantities of products to produce in any given plant, deals with what is called short-run profit maximization. The third layer, concerning the determination of the most profitable size and equipment of plant, relates to what is called long-run profit maximization. However much of a commodity a business firm produces, it endeavours to produce it as cheaply as possible. Taking the quality of the product and the prices of the productive factors as given, which is the usual situation, the firm’s task is to determine the cheapest combination of factors of production that can produce the desired output. This task is best understood in terms of what is called the production function, i.e., an equation that expresses the relationship between the quantities of factors employed and the amount of product obtained. It states the amount of product that can be obtained from each and every combination of factors. This relationship can be written mathematically as y = f (x1, x2, . . ., xn; k1, k2, . . ., km). Here, y denotes the quantity of output. The firm is presumed to use n variable factors of production; that is, factors like hourly paid production workers and raw materials, the quantities of which can be increased or decreased. In the formula the quantity of the first variable factor is denoted by x1 and so on. The firm is also presumed to use m fixed factors, or factors like fixed machinery, salaried staff, etc., the quantities of which cannot be varied readily or habitually. The available quantity of the first fixed factor is indicated in the formal by k1 and so on. The entire formula expresses the amount of output that results when specified quantities of factors are employed. It must be noted that though the quantities of the factors determine the quantity of output, the reverse is not true, and as a general rule there will be many combinations of productive factors that could be used to produce the same output. Finding the cheapest of these is the problem of cost minimization. The cost of production is simply the sum of the costs of all of the various factors. It can be written: in which p1 denotes the price of a unit of the first variable factor, r1 denotes the annual cost of owning and maintaining the first fixed factor, and so on. Here again one group of terms, the first, covers variable cost (roughly“direct costs” in accounting terminology), which can be changed readily; another group, the second, covers fixed cost (accountants’ “overhead costs”), which includes items not easily varied. The discussion will deal first with variable cost. The principles involved in selecting the cheapest combination of variable factors can be seen in terms of a simple example. If a firm manufactures gold necklace chains in such a way that there are only two variable factors, labour (specifically, goldsmith-hours) and gold wire, the production function for such a firm will be y = f (x1, x2; k), in which the symbol k is included simply as a reminder that the number of chains producible by x1 feet of gold wire and x2 goldsmith-hours depends on the amount of machinery and other fixed capital available. Since there are only two variable factors, this production function can be portrayed graphically in a figure known as an isoquant diagram (). In the graph, goldsmith-hours per month are plotted horizontally and the number of feet of gold wire used per month vertically. Each of the curved lines, called an isoquant, will then represent a certain number of necklace chains produced. The data displayed show that 100 goldsmith-hours plus 900 feet of gold wire can produce 200 necklace chains. But there are other combinations of variable inputs that could also produce 200 necklace chains per month. If the goldsmiths work more carefully and slowly, they can produce 200 chains from 850 feet of wire; but to produce so many chains more goldsmith-hours will be required, perhaps 130. The isoquant labelled “200” shows all the combinations of the variable inputs that will just suffice to produce 200 chains. The other two isoquants shown are interpreted similarly. It is obvious that many more isoquants, in principle an infinite number, could also be drawn. This diagram is a graphic display of the relationships expressed in the production function.
Get a Britannica Premium subscription and gain access to exclusive content. Subscribe Now
In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.
Learning Objectives
We can summarize the ideas so far in terms of a production function, a mathematical expression or equation that explains the relationship between a firm’s inputs and its outputs: [latex]Q=f\left[NR\text{,}L\text{,}K\text{,}t\text{,}E\right][/latex] A production is purely an engineering concept. If you plug in the amount of labor, capital and other inputs the firm is using, the production function tells how much output will be produced by those inputs. Production functions are specific to the product. Different products have different production functions. The amount of labor a farmer uses to produce a bushel of corn is likely different than that required to produce an automobile. Firms in the same industry may have somewhat different production functions, since each firm may produce a little differently. One pizza restaurant may make its own dough and sauce, while another may buy those pre-made. A sit-down pizza restaurant probably uses more labor (to handle table service) than a purely take-out restaurant. We can describe inputs as either fixed or variable. Fixed inputs are those that can’t easily be increased or decreased in a short period of time. In the pizza example, the building is a fixed input. Once the entrepreneur signs the lease, he or she is stuck in the building until the lease expires. Fixed inputs define the firm’s maximum output capacity. This is analogous to the potential real GDP shown by society’s production possibilities curve, i.e. the maximum quantities of outputs a society can 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 order more ingredients with a phone call, so ingredients would be variable inputs. The owner could hire a new person to work the counter pretty quickly as well. Variable inputs increase or decrease as output changes. Economists often use a short-hand form for the production function: [latex]Q=f\left[L\text{,}K\right][/latex] where L represents all the variable inputs, and K represents all the fixed inputs. Economists also differentiate between short and long run production. The short run is the period of time during which at least some factors of production are fixed. During the period of the pizza restaurant lease, the pizza restaurant is operating in the short run, because it is limited to using the current building—the owner can’t choose a larger or smaller building. The long run is the period of time during which all factors are variable. Once the lease expires for the pizza restaurant, 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 short run, since the firm’s fixed inputs are fixed, the only way to vary a firm’s output is by changing its variable inputs. Let’s explore production in the short run using a specific example: tree cutting (for lumber) with a two-person crosscut saw.  Figure 1. Production in the short run may be explored through the example of lumberjacks using a two-person saw. (Credit: Wknight94/Wikimedia Commons) Since by definition capital is fixed in the short run, our production function becomes [latex]Q=f\left[L\text{,}\stackrel{-}{K}\right]\text{or }Q=f\left[L\right][/latex] This equation simply indicates that since capital is fixed, then changing the amount of output (e.g. trees cut down per day) depends only on changing the amount of labor employed (e.g. number of lumberjacks working). We can express this production function numerically as Table 1 below shows. You can also see it graphically in Figure 2a.
Figure 2. Total Product and Marginal Product Curves. The short run total product for trees (top) shows the amount of output produced with fixed capital. In this example, one lumberjack using a two-person saw can cut down four trees in an hour. Three lumberjacks using a two-person saw can cut down twelve trees in an hour. The marginal product for trees (bottom) shows the additional output created by one more lumberjack. Note that we have introduced some new language. We also call Output (Q) Total Product (TP), which means the amount of output produced with a given amount of labor and a fixed amount of capital. In this example, one lumberjack using a two-person saw can cut down four trees in an hour. Two lumberjacks using a two-person saw can cut down ten trees in an hour. We should also introduce a critical concept: marginal product. Marginal product is the additional output of one more worker. Mathematically, Marginal Product is the change in total product divided by the change in labor: [latex]MP=\Delta TP/\Delta L[/latex] In the table above, since 0 workers produce 0 trees, the marginal product of the first worker is four trees per day, but the marginal product of the second worker is six trees per day. Why might that be the case? It’s because of the nature of the capital the workers are using. A two-person saw works much better with two persons than with one. Suppose we add a third lumberjack to the story. What will that person’s marginal product be? What will 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 water to the two people sawing. What you see in the table is a critically important conclusion about production in the short run: it may be that as we add workers, the marginal product increases at first, but sooner or later additional workers will have decreasing marginal product. In fact, there may eventually be no effect or a negative effect on output. This is called the Law of Diminishing Marginal Product and it’s a characteristic of production in the short run. Diminishing marginal productivity is very similar to the concept of diminishing marginal utility that we learned about in the chapter on consumer choice. 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 will see this more clearly when we discuss production in the long run. We can show these concepts graphically, as you can see in Figure 2 above. Figure 3 shows the more general cases of total product and marginal product curves. Figure 3. Total Product and Marginal Product Curves. The top graph shows the general shape of a total product 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.
Watch this video to review all of the production function and to see an example of the law of diminishing marginal product. Dr. McGlasson wants to hire students for her company to make “I love economics” signs, but she must consider how much output she can gain with each additional employee.
These questions allow you to get as much practice as you need, as you can click the link at the top of the first question (“Try another version of these questions”) to get a new set of questions. Hover your cursor over the “hint” link for tips. Practice until you feel comfortable doing the questions.
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, capital, land, and raw or finished component materials to produce outputs. fixed inputs: factors of production that can’t be easily increased or decreased in a short period of time long run: period of time during which all of the firm’s inputs are variable production: 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 firm can produce with given amounts of inputs short run: period of time during which at least one or more of the firm’s inputs is fixed variable inputs: factors of production that a firm can easily increase or decrease in a short period of time Did you have an idea for improving this content? We’d love your input. Improve this pageLearn More |
What equation shows the maximum output of a commodity that a firm can produce per period with each set of inputs?
zusammenhängende Posts
Urheberrechte © © 2024 frojeostern Inc.
