Theory of Production: Short-run, Long-run

The theory of production offers the question of ”How to produce?” In a broader sense, the theory of production is the theory of the firm, in which the main objective is to explain the behavior of producers.

Accordingly, it analyzes how a rational producer takes production decisions under the given conditions; in other words, how the producer comes to the equilibrium and how production decisions adjust when the given condition changes?

Any economic activity that satisfies human needs is called the product of economics. It is also called the ”creation of utility or addition of value”. This is done by transforming a set of inputs into some output of a good or service.

The inputs used in the process of production may be goods either supplied by nature or produced by other industries. These inputs are called the ”factors of production.” There are four categories of factors of production namely, land, labor, capital, and entrepreneurship.

Theory of Production: Production Function?

In the production process, a set of inputs transforms into outputs. The level of output depends on the level of inputs. In other words, the output is a function of inputs. production function can define as the relationship between inputs and output. It shows the technical relationship between inputs and output.

Production function can present as an algebraic equation, table/schedule, or as graph. In easy to handle, mostly production function can express as an equation.

Q= f( L, K, R, T)

• L = Labor
• K = Capital
• R = Row Material
• T = Technology

Production function involves and provides measurements for many concepts. The main concepts are:

1. The marginal productivity of factors of production.
2. The marginal rate of technical substitution (MRTS).
3. The elasticity of substitution.
4. Factor intensity
5. The efficiency of the technology
6. Returns to scale
7. Average product

1. The marginal productivity of factors of production

The marginal product (MP) of an input is the change in the total product as a result of a change in the quantity of a particular input by one unit. In other words, MP is the contribution of an additional unit of a particular input to the total output.

For example, the marginal product of labor (MP_L) can define as the change of total output as a result of a change of labor input by one unit. This concept is important in decision-making in many ways; mainly, it shows the limit or boundary of the input usage.

Mathematically, the marginal product can obtain by dividing the change of total output by the change of input:

MP = Change of Output / Change of Input

2. The marginal rate of technical substitution (MRTS)

The marginal rate of technical substitution (MRTS) is when one factor must decrease, so as a result of that, the other factor increase. And also remains on the same level of output. Simply, it is a measure of substitutability between factors of production.

3. The elasticity of substitution

This indicates the easiness with which one input say capital, can be substituted for other input say labor.

4. Factor intensity

Factor intensity property of technology shows the quantity of capital about the other factor, say labor. The capital-labor ratio use as a measure of the factor intensity of the technology.

5. The efficiency of the technology

This reflects the quality of technology. An increase in efficiency of technology would increase the output for a given level of inputs, and other characteristics of the technology.

6. Returns to scale

This measures the proportionate change in output due to equi-proportionate change in all inputs. There may be increasing returns to scale, decreasing returns to scale, or constant returns to scale within a production process.

7. Average product

Average product (AP) measures the output per unit of a particular input. AP of a particular input can calculate by dividing total output (q) by the total quantity of the input. For example, the average product of labor can calculate as follows:

Decision Period Relate theory of Production Analysis

In analyzing the behavior of producers or a production process, we have to take into account the time factor involves in the production process. Two different time periods involved in the theory of production.

1. short-run production
2. long-run production

Theory of Production: short-run production

In the short-run production, there are two types of inputs as fixed and variable inputs. The idea of that is we can not change or increased some factors of production, such as capital in the short run. We can increase only the number of units of the variable input to increase the level of output.

As a result of that marginal return productivity of input, the change will be diminished. This means as additional units of a variable input are combined with a fixed input at some point, additional output (marginal product) starts to diminished, which is known as the law of diminishing returns.

The law of diminishing marginal product is the economic concept shows increasing one production variable while keeping everything else the same will firstly increase overall production but will generate less returns the more that variable is increased.

This law is valid when the following assumptions are satisfied.

1. There is at least one fixed factor with the variable factor operates in production.
2. All units of the variable factor are homogeneous.
3. The state of technology is constant.
4. The fixed factor and the variable factor combine in varying proportions in the process of production.

Because of the last condition, the law is also known as the ”the law of variable proportion.”

The Behavior of Short-run Production

In the production process, which applies labor (L) as a variable input with a fixed amount of capital (K), when increases input L by an equal amount, total output/product (TP) will increase first at an increasing rate, and then decreasing rate following this law. After a certain input level, the TP of variable input will decline.

Within the range of TP is increasing at an increasing rate, MP of variable input will increase. It will increases up to the point that TP starts to increase at a decreasing rate.

At this point, MP reaches the maximum, and throughout the range that TP increases at decreasing rate, MP declines. At the maximum output level, MP becomes zero and beyond that output level, MP will negative.

AP of the variable factor will also rise first and then declines. However, up to a certain point, it increases at a lower rate than the increase of MP. The input level that AP maximizes is higher than the input level that MP maximizes.

Therefore, up to the maximum point of AP, MP is higher than AP, and MP and AP are equal at the maximum point of AP. When AP declines MP also declines but a higher rate than AP. Since TP is always positive, AP will also positive and it will not become zero. At the highest level of AP, it equals the MP.

Theory of Production: Three stages of Production

There are three types of marginal productivities.

1. Increasing MP_L
2. Decreasing MP_L
3. Negative MP_L

• Increasing MP_L – Every additional unit of L increases the TP, AP, and MP. This is shown in the graph by increasing the slope of the TP curve.
• Decreasing MP_L – Every additional unit of L decreases MP though TP still increases. This is shown in the graph by the negative slope of MP and decreasing the positive slope of the TP curve.
• Negative MP_L – Every additional unit decreases MP as well as TP. This is shown in the graph by the negative slope of MP as well as TP curves.

Based on the relationship between TP, AP, and MP of the variable factor, three stages of production can be defined as shown in the graph below:

Theory of Production: The Best Stage of Production 

Stage 1 goes from origin to the point where the AP maximizes. In this stage, MP raises, reaches a maximum, and then falls.

Stage 2 goes from the point where AP is highest to the point where MP is zero. In this stage, the marginal product falls till it becomes zero while the average product keeps on falling but is positive.

Stage 3 occurs when the marginal product is negative.

A rational producer will not operate in stages 1 and 3. In stage 3, the contribution of an additional unit of labor to the total product is negative. Thus, it will be unwise to take production decisions at the input level that reduces the total product.

Stage 1 where the average product is raising also an irrational production range because the increase in input increases output in greater proportion.

The only stage where the production can take place is stage 2, where both marginal and average products are declining, but they are positive. To determine the exact point where the producer operates within this stage depends on the price of output and the cost of variable inputs.

However, if the output maximization is the goal, and there are no constraints, then the end of stage II, i.e., the point where the MP curve cuts the horizontal axis (MP = 0) will be the most efficient input combination.

Explanation of Stages of Production

Stages	TP	MP	AP
Stage I MP>AP	Increases at an increasing rate and later at a decreasing rate.	First increases and reaches the maximum point and then start to decline.	Increases through and reaches its maximum point. At the endpoint of the stage AP=MP.
Stage II MP<AP	It increases at a diminishing rate and reaches its maximum point.	Decreases gradually and become zero at point N2.	After reaching its maximum the point begins to decrease.
Stage II MP<0	It begins to fall.	Becomes negative.	Continues to decline but remains positive.

Theory of Production: Loan-run Production

In the long-run, a firm has enough time to change the amount of all of its input. Thus there is no difference between fixed and variable input. Nevertheless, the law of diminishing marginal returns would apply to some stage, even in the long-run production.

In the long-run production, the firm can change or increase both inputs. Therefore if the firm or if the producer doubles its what inputs.

The long run described by laws of returns to scale. It describes,

• The effect of changes of all input together
• The changes in the scale of production.

There are three types of returns to scale as,

• Constant returns to scale: with increase all inputs together in some proportion, output also increases by the same proportion. For instance, when all inputs are increased by 10 percent, the output will be increased by the same percentage, i.e., 10 percent.
• Increasing returns to scale: with increasing all inputs together in some proportion, output increases in a greater proportion. For instance, when all inputs are increased by 10 percent, the output will be increased by more than 10 percent say, 20 percent.
• Decreasing returns to scale: with increase all inputs together in some proportion, output increases in less proportion. For instance, when all inputs are increased by 10 percent, the output will be increased by less than 10 percent say, 5 percent.

Homogeneous and Non-homogeneous Production Functions

A long-run production function can show constant or increasing or decreasing returns to scale or all three types of returns to scale.

The production functions which reflect either increasing or decreasing or constant returns to scale throughout the production process are called the homogeneous production function

For example, if a production function shows constant returns to scale continuously throughout the production process, it is defined as a production function with constant returns to scale or more precisely homogeneous production function of the degree 1

The production functions which reflect all three types of returns to scale are called non-homogeneous production functions. Such function can be shown increasing returns first and then constant returns, lastly decreasing returns to scale.

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Conclusion

All right then. In this article, we discussed about the theory of production on short-run, Long-run. Next, you need to know about the types of the production function. There are three main types of the production function. Read this on here.

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Production Function: 3 Types of Production Function