TOPIC 5 ► THEORY OF PRODUCTION

LEARNING OUTCOMES

By the end of this topic, you should be able to:

1. Explain the concept of production, plant, firm and industry;
2. Differentiate between the concept of long-run and short-run in production;
3. Apply the concept of diminishing marginal returns;
4. Compare isoquants and isocosts; and
5. Differentiate the three types of returns to scale for long-run production.

INTRODUCTION

We now know that there are two main sectors in the circular flow of income; namely the household sector and the firm sector. In the previous topics, we discussed the household sector, including the background of demand theory, through theory of utility, theory of indifference, or the theory of consumer behaviour in general. The theory of consumer behaviour explains the behaviour of rational consumers who make decisions based on consideration of cost (price), and benefit (utility). In this topic, we will look at the rationale that underlies the behaviour of producers that influences the theory of supply. We will start by discussing the concept related to the production process. Subsequently we will discuss production in the short-run and finally production in the long-run.

5.1 PRODUCTION PROCESS

Production is very important in an economy; in fact many economists consider the success in production activities as an indication of progress of a country. Production is important due to its role in changing inputs into more valuable materials. The value enhancement will result in a higher consumption satisfaction.
In connection with that, we can define the following:

Production as any activity or process of combining inputs to transform into outputs that produce utility at the present time or in the future.

Firms are organisations that perform production processes, by combining inputs in the production process to produce outputs.

The behaviour of firms is important in determining the type of goods and services to be produced for the society, price and its quantity. In short, firms have to face questions as shown in Figure 5.1.

Figure 5.1: Questions faced by firms

Therefore, the behaviour of firms is influenced by consumers, competitors and the environment.
The way production process is carried out and the combination of input used depends on technology. Hence, technology determines the form of production function. Production function shows the technical relationship between inputs and outputs. It explains the method used by firms to change inputs into outputs.
The general production function = Q = f (L, K, M, …..),
where Q = output, L = labour, K = capital, M = raw materials.
We can summarise the firm’s decision making process into three steps:

1. Choosing the quantity to be produced and listing all efficient methods in producing the specified quantity;
2. Choosing the economically efficient method, that is, the method of lowest cost to produce the specified quantity; and
3. Repeat step 1 and 2 for all the other quantities.

Of all the various production technologies available, one of it is assumed to be the most efficient. An efficient production technique is the production method that does not waste resources, that is, one of the inputs cannot be reduced without the addition of other inputs. If an input can be reduced without adding other inputs, the method is still considered inefficient.
Each technology only shows certain combinations of inputs that can be used to produce a certain amount of output, and firms must decide on the production plan for the most efficient technology. Basically, production technology can be divided into two, namely:

1. Labour-intensive technology – If the production process uses more labour force compared to capital.
2. Capital-intensive technology –If more capital is used compared to labour.

Firms will definitely take into account the cost and profit in choosing technology besides determining the level of efficiency. Thus, the technology chosen is a technology that is able to minimise production cost. For example, if a firm operates in a country which has abundant cheap labour but lacking in capital goods, the most optimal production method will be the one that is labour-intensive.

5.1.1 Firm, Plant and Industry

The three prime movers in a production process are firm, plant and industry. We will look at the following explanations to understand the meaning of firm, plant and industry:

1. Firm A firm is an organisation that buys resources from the household or other firms to be used in the production of goods or services that will be sold to consumers. Firm size may vary, from a peddler selling snacks by the sidewalk to multinational firms operating worldwide.
   
   Why do firms exist? Households have various needs and these needs cannot be fulfilled by the household itself due to various constraints such as the lack of resources, lack of expertise or high cost.  Are you able to build your own house or design a television set or refrigerator? Firms have substantial compared benefits in the use of inputs in production processes. The advantage is due to a number of factors including specialisation and economies of scale.
2. Plant 
   Most firms have more than one plant, that is, an area, machine or tools and equipments used in the production process. Plant is the unit of production, while the firm is the unit of ownership and control. Plants owned by a large firm may consist of a number of factories with high-tech production equipments in a few areas or countries. For a small firm such as a tailor, the plants owned may consist of a few sewing machines.
3. Industry An industry consists of all firms that are competing in one market. Examples of industries are such as the fast-food industry, clothing industry and automobile industry. The interaction of firms within an industry determines the form of market structure that gives different implications towards the level of output and price. Examples of market structure are such as the perfect competition market, and monopoly, which will be discussed in the following unit.

ACTIVITY 5.1

Use the Venn diagram to illustrate the relationship between firm, plant and industry.

5.1.2 Input and Output

Resource used in the production process is known as input.

Input includes raw materials, labour, area of production, machines and intermediate goods purchased from other firms.

Output is a good or service that is produced from the production process.

Output produced by a firm might be purchased by consumers, other firms or the government.
Input can be categorised into variable inputs and fixed inputs, as shown in Figure 5.2.

Figure 5.2: Types of input

Variable inputs are inputs that can be added or reduced within a short period of time.

Variable input will change according to the change in output. Its quantity is influenced by the change in output.

Fixed inputs are inputs that cannot be added or reduced within a short period of time.

Examples are such as an area of agricultural land for a farmer or plant owned by a firm. Land for a farmer is an input that is very hard to be altered. A farmer may not buy land gradually when he wants to increase production a little; similarly, he cannot be selling the land in small portions if production is to be reduced a little.
Fixed inputs usually provide service for a long period of time. Factories built can be used for years; land can be used endlessly if not sold. Skilled work force is also considered as fixed input that are paid a monthly salary; it may be quite difficult to change the number of these workers in a short time since advertising and interview process are required. 

5.1.3 Long-Run and Short-Run

What is the relationship between inputs and period of production? Fixed input and variable input are closely relate to the concept of production period.

1. Short-run in production is a period where at least one of the input is fixed and a firm cannot enter or leave the industry.
2. Long-run is the period of production where all inputs are variable, and firms can increase or reduce its production capacity, and also enter or leave the industry. Production period is not an absolute time concept such as days, weeks, months or years. It is a relative concept and refers to the rate of changing fixed input into variable input.

As an example, a short-run for a banana fritters seller may be a day or a week because he can easily find a helper or add in new frying equipments such as stoves and pans. On the contrary, for an electrical power supplier of a town, the short-run will definitely take up a longer time period, maybe 10 years or more. This is because the equipments and plants needed to generate electricity are costly and cannot be easily built without proper planning.
From these two examples, we have obtained another determinant of production period, that is, the cost involved in adding or reducing inputs. If addition or reduction of input involves a high cost, the short-run will become much longer.

SELF-CHECK 5.1

Try to recall the production process. What is the relationship between fixed inputs and variable inputs with production in short-run?

5.2 PRODUCTION IN SHORT-RUN

After going through a few important concepts in production, we will now discuss the implementation of short-run productions. As defined earlier, short-run is a period where at least one input is fixed. Even though a production process usually consists of more than two inputs, we will focus on the short-run production that consists of only one fixed input and one variable input to facilitate the analysis. However, the concepts stated can be applied to any production process which involve at least one fixed input.

5.2.1 Total Product, Average Product and Marginal Product

Here we will discuss the characteristics and production constraints faced by firms that operate in the short-run. To facilitate the analysis, we assume that a firm uses only one fixed input, and one variable input in the production of one type of output. The general production function of this firm can be stated as:

Q = f (K, L)
where Q is the output, capital (K) is the fixed input, and labour (L) is the variable input.

The production function can also be shown using tables and diagrams. Figure 5.3 and Table 5.1 illustrates the production function of a firm producing one type of output.
The table and diagram shows the change in output when a variable input is added to the fixed input in production.
There are three main concepts that you need to understand in a short-run production:

1. Total product is the amount of output that can be produced by combining all inputs in a particular period of time.
2. Average product (AP) is the output per unit of variable input or
   AP = TP/L. In Figure 5.1, we find that the average product for 2 units of labour is 8/2 = 4.
3. Marginal product (MP) is the addition or increment in output when one unit of variable input is added while the total of other input is constant. Marginal product is the gradient of the Total Product curve. Marginal product of capital or MPK is the addition in output as a result of an increase in capital input while total labour remains unchanged. Marginal product of labour or MPL is the increase in output as a result of an additional labour input; while capital remains unchanged. In the short-run model, when labour is the variable input, discussion will be focused on the productivity of labour.

In Table 5.1, marginal product for the fourth labour is:

We divide the change in total product (∆TP) with change in quantity (∆L), and not with one unit of input because some of the variable inputs can only be added in a few units simultaneously. For example, a labour is hired to work eight hours a day. Therefore, in knowing the addition of product by one hour of labour, we must divide the change of output produced with eight units of labour.

Table 5.1: Total Product, Average Product and Marginal Product

Capital	Labour	TP	APL	MPL
1	0	0	-	-
1	1	3	3	3
1	2	8	4	5
1	3	12	4	4
1	4	15	3.75	3
1	5	17	3.4	2
1	6	17	2.83	0
1	7	16	2.29	-1
1	8	13	1.63	-3

Figure 5.3 is drawn based on the information from Table 5.1. Through the diagram, we can obtain information about the features and relationship between these three concepts we have just defined.

Figure 5.3: Total product, marginal product and average product

Based on Table 5.1 and Figure 5.3, we can see that total product increases rapidly with the first and second labour employed. However, the increase in production starts to decline when the third labour is hired. Similarly with MP, initially MP increased rapidly compared to AP, achieving maximum point before AP, then decreases to intersect at the maximum point of AP before reaching zero. MP is zero when TP achieves maximum point, and then becomes negative as TP decreases.
The concepts of marginal and average have a general relation that can be applied in all theories involving these two concepts, which are:

1. If marginal is equivalent to average, average remains unchanged;
2. If marginal is higher or above average, average will increase; and
3. If marginal is lower than average, average will decrease.

An example of an average-marginal relationship is the GPA (Grade Point Average), and CGPA (Cumulative Grade Point Average) you obtain every semester. GPA is marginal while CGPA is average. If the GPA you obtain in a semester is higher than CGPA, then your CGPA will increase. If GPA is lower than CGPA, then CGPA will decrease. Therefore, to ensure your CPGA increases, the GPA should always be increased.

5.2.2 Law of Diminishing Marginal Returns

Based on Figure 5.3, we have seen that the total product initially increases with an increasing rate, but eventually starts to increase at a decreasing rate, before declining further. Meanwhile, the marginal product increases rapidly, and then decreases before achieving negative. The curve of marginal product starts to decline when the total product starts to increase at a decreasing rate; this is the starting point for the law of diminishing returns. This point is denoted by point A in Figure 5.3.

Law of diminishing marginal returns states that if a variable input is added into a production process that uses at least one fixed input, increment in total output may increase at an increasing rate initially, but the rate of increase will decline after one level of input.

This law only happens in the short-run. If seen through marginal product, this law starts to occur when MP starts to decline. Due to this law of diminishing marginal returns, the optimal level of output in the short-run is achieved when MP_L = 0.
This law is very rational and can be used in various fields. In the agricultural field for example, land is a fixed input. When the first labour is hired to tap rubber, he might not be able to tap all trees available in one day. When the second labour is added, yield will increase, but if more tappers are added continuously, it will reach a stage where yield increases but at a lower rate compared to the initial rate of increase. Sooner or later, the land will become congested with rubber tappers until some of them will not have the chance to tap.
It is the same in the manufacturing field that uses machines as its fixed input. The first few labourers hired may increase production at an increasing rate. But when more labourers are hired and machines have reached a high capacity, marginal product will start to decrease.
Some say that if the law of diminishing marginal returns does not occur, the whole world population can be fed from only one flower pot, because seeds can always be added to increase the yield of food. However, through this concept, there are also predictions that at one time, a large number of world population will die of starvation due to shortage of agricultural land. We see that this condition is yet to happen because technology enables the fixed input of agriculture, which is land, to increase its capacity. For instance, in the past, we only can plant rice once a year; but now it can be done twice a year.

SELF-CHECK 5.2

Explain, how does the law of diminishing marginal returns occur?

5.2.3 Production Level

Now we will look at the production level. We can use the relationship between the curves of AP_L with MP_L to define the three levels of production in the short-run, which are Level I, Level II and Level III. Figure 5.4 will help to illustrate these levels.

1. Level I Level I begins with the usage of the first labour until the maximum point of AP_L. At this level, both, the average product and marginal product are positive. Since the marginal product exceeds average product, average product increases. Level I is an irrational production level because AP can always be increased by adding in labour. An increased return to fixed input also occurs at this level. Therefore, rational producers will not operate at this level.
   
   

   

   Figure 5.4: Production levels

2. Level II Level II is the area between the maximum point of AP_L and the point where MP_L is zero. Both MP and AP are still positive but MP is less than AP. Thus, AP decreases. Rational producers will operate at this level because the marginal product of fixed input and variable input is positive.
3. Level III Level III covers the area of negative MP_L and total product decrease. This means that additional variable input will further decrease the total output. Rational producers will not operate at this level.

5.3 PRODUCTION IN LONG-RUN

Do you still remember the important concept in the short-run production? Now, we will look at production in the long-run.
Production process is in the long-run if all inputs are variable. When all inputs are variable, firms have more choices in terms of input combinations, production scale, technology and production location. The firm’s decision on those matters will influence production cost. Hence, firms must make optimal and efficient decisions.
The relationship of input-output in the long-run can be seen using the isoquant curve. For producers who use only two variable inputs, the isoquant curve can be drawn in two dimensions, but it will get more complex if the number of variable inputs increases.
However, the conclusion drawn from the analysis of isoquants-isocost can be used as a general rule for productions that involve more than two variable inputs, which is based on the equi-marginal principle as we will discover in the following section.

5.3.1 Isoquants

What is an isoquant? The concept of isoquant closely resembles the concept of the indifference curve that we discussed in Topic 4. Both these curves are different in terms of the measurement used. For an indifference curve, the choice or priority that determines the shape of curve is an abstract and subjective concept, but on the other hand, the level of output that determines the isoquant curve is true and can be calculated.
If the production process only utilises two variable inputs, namely capital (K), and labour (L), hence the production function is Q = f(K, L). Therefore, the isoquant curve illustrates the compilation of all combinations of L and K that can produce a particular amount of output that fulfils the following equation:

Q₀ = f (K, L)

For example, to produce 10 units of good X, the possible combinations of capital and labour that can be used are as shown in Table 5.2 and Figure 5.5.

Table 5.2: Combinations of Input for Production of 10 Units of Good X

Combination	K	L
A	8	1
B	5	2
C	3	3
D	2	5
E	1	8

Figure 5.5: Isoquant curve

Even though there are five different combinations of inputs, the quantity of output produced is still 10 units. The change of input combination on the isoquant curve does not change the quantity of output produced. For instance, 10 units of output can be produced using 8K and 1L (combination A), or 3K and 3L (combination C).
Now, we can define the isoquant curve as a curve that connects all possible input combinations that can be used to produce a certain amount of output.
When we attain other curves which are obtained based on the combination of inputs for various levels of output, we will obtain a compilation of isoquant map as shown in Figure 5.6. The number of isoquant curves in an isoquant map is unlimited. Figure 5.6 illustrates the isoquant curves for three levels of output production, which are for the production of 10 units, 20 units and 30 units.

Figure 5.6: Isoquant map

One of the main features of a normal isoquant curve is the negative gradient. The isoquant curve has a negative gradient because producers will choose technologies which provides positive marginal product for all inputs. If the isoquant curve has a positive gradient, one of the inputs has a negative MP. As in the indifference curve, the isoquant curve shows a higher level of output at the higher position. The isoquant curve normally has a convex shape towards the origin due to the variable rate of substitution between inputs, which we will discuss in the subsequent section.
Variable rate of substitution between inputs is a general feature of technology. However, there are some technologies featuring the constant technique of substitution as depicted by Figure 5.7 and technologies showing the use of fixed ratio input as shown in Figure 5.8.

Figure 5.7: Isoquant curve for constant substitution production function

Figure 5.8: Isoquant curve for fixed ratio production function

ACTIVITY 5.2

Can isoquant curves intersect? Discuss this matter with your friends.

5.3.2 Diminishing Marginal Rate of Technical Substitution

Quantity of output is constant along an isoquant curve. If labour is added, an increment in the output produced by the additional labour is equivalent to the change in labour (DL) times marginal product of labour (MP_L). Since labour had increased in order to maintain the level of output, capital must be decreased to maintain the output level and the amount of reduction needed is equivalent to ΔK × MP_K. In short, both the increase in labour product and decrease of capital must be equal to maintain the total output. Hence, ΔK × MP_K = ΔL × MP_L, or

Marginal rate of technical substitution (MRTS) is the rate where an input can be substituted with other inputs while total output remains unchanged.

When production only involves the use of labour and capital, MRTS LK is the marginal rate of technical substitution of capital to labour, that is, the rate in which capital is substituted with labour without any change in output.

MRTS_LK = K/L

Figure 5.9: Marginal rate of technical substitution

The gradient of isoquants with a negative sign is ignored. This gradient is also referred to as MRTS or marginal rate of technical substitution. The word “technical” is used to differentiate this term from marginal rate of substitution in the theory of consumers.
A diminishing MRTS means that the rate of substitution between inputs will decrease according to the ratio between inputs. For a concaved isoquant with a negative gradient, when the ratio of capital-labour (K/L) is high, a large amount of K can be foregone or given up to be substituted with one additional unit of labour; when K/L decreases, the rate of capital that can be sacrificed  to be substituted by one additional unit of labour, will decrease. Diminishing MRTS_LK is depicted by a decreasing gradient of the isoquant curve. Figure 5.10 illustrates the diminishing marginal rate of technical substitution of capital to labour, which can be seen from the gradient at point B which is lower than the gradient at point A.

Figure 5.10: Diminishing marginal rate of technical substitution

5.3.3 Isocosts

After learning about the concept of isoquants, you probably want to know what is the concept of isocosts curve. The concept of isocosts curve is similar to the budget line. The budget line is the budget constraint for consumers, while isocosts is the production costs limitation for firms. Isocosts illustrates the maximum spending that can be done by a firm to purchase two production inputs. Figure 5.11 illustrates an isocosts curve where capital (K) input is at the vertical or Y-axis, while labour (L) input at the horizontal or X-axis. The equation of this isocosts curve is C = wL + rK, and C is total cost, w and r are wage per unit of labour, and rental per unit of capital respectively.

Figure 5.11: Isocosts curve

Change in total cost causes a parallel shift of the isocosts curve from the initial curve, as shown in Figure 5.12. Figure 5.12 illustrates an increase of total cost from C₁ to C₂. However, similar changes can happen if the input prices changed at a proportionate rate; for example, if both w and r increased as much as 50 percent respectively, hence the isocosts will experience a parallel shift to the left.
Change in input price will cause the gradient of isocosts to change because ratio of price and isocosts will revolve at the axis of the input with the change in price. Figure 5.13 illustrates the effect of change in labour wage where w declines from w1 to w2.

Figure 5.12: Effect of change in total cost towards isocosts curve

Figure 5.13: Change in labour wage towards isocosts curve

ACTIVITY 5.3

Try to use your own examples to differentiate the concept of isoquants and isocosts. Present your answer in your tutorial.

5.3.4 Combination of Minimum Input Cost

A firm that maximises its profit will choose an optimal combination of inputs by equating MRTS with the ratio of input price. Diagrammatically, the optimal choice input will occur when the isocosts is tangent with the isoquants, that is, the gradient of isocosts is equivalent to the gradient of isoquants, or:

This equilibrium condition is denoted by point E in Figure 5.14.
Why didn’t the firm choose combination A or B? If combination A was chosen, it means that the firm can still reduce cost by substituting some of the capital input with labour input, that is, by moving downwards along curve Q₁. Therefore, optimal efficiency is still not achieved. It is the same if combination B was chosen; cost can still be reduced by substituting some labour with capital. The transition from an inefficient condition to a more efficient condition will finally bring the firm to the point of equilibrium E where cost is minimal and cannot be further reduced, unless if output is also reduced.

Figure 5.14: Combination of minimum input cost

5.3.5 Equal Marginal Principle

The equal marginal principle is applied in choosing the combinations of long-run input using the concept of marginal product (MP).
According to this principle, optimal input combination is achieved when marginal product of one ringgit for all inputs are equal, or

where A, B, ….N are the inputs, and P_A, P_B, …P_N are the input price.
If the long-run production only uses capital (K) and labour (L), hence a combination of optimal input is achieved when:

If:

(due to increase in wage), the firm should substitute a part of the labour input with capital because firms obtain higher returns than the cost spent on capital compared to labour. When more capital is being utilised, diminishing returns to capital will occur until the rule of equilibrium is achieved again.
The main problem in the application of this concept is the difficulty in predicting changes in input price. Therefore, even though the principle of equal marginal is achieved, and the firm has built suitable equipments, (for example, the use of labour-intensive technology due to low wage), an unpredicted increase in wage causes the firm to be in that particular short-run condition for a few years. In this situation, the initial decision made was a mistake due to failure in predicting change in wages.

5.3.6 Returns to Scale

Change in input usage enables a firm to change the production scale.

Here, scale change means that the amount of all inputs is changed in the same ratio.

For example, a firm can double the amount of all inputs used. When the production scale is altered, three possibilities will occur upon the level of production, which are:

1. Constant Returns to Scale This will happen when the change ratio of all inputs is equivalent to the change ratio of output. For example, when all inputs are increased by 10 percent, output will also increase by 10 percent.
2. Increasing Returns to Scale Increasing returns to scale occurs when the ratio of increase in output is much higher than the ratio of increase in all inputs.
3. Decreasing Returns to Scale Decreasing returns to scale occurs when the ratio of increase in output is much lower than the ratio of increase in all inputs. Decreasing returns to scale is different from the diminishing marginal returns that occur in short-run because in short-run, only the variable inputs are increased.

SUMMARY

• The production process involves industry, firm, plant, technology, input and output.
• The production function illustrates the form of technology used in production, that is, the process that combines inputs to produce output.
• Firms are organisations that perform the production process. Firms may own several plants as the production unit.
• Meanwhile, industry consists of all firms competing in one market.
• Inputs used by firms may consist of fixed or variable inputs.
• The use of fixed input will not change with change in output, while variable output changes according to the change in output quantity.
• Time period is crucial in determining the choices made by firms. In short-run, firms are constrained by at least one fixed input. Meanwhile, in long-run, firms have more extensive choices since all the inputs are variable.
• The three important concepts in short-run production are total product, average product and marginal product.
• Fixed input constraints causes short-run production to face the law of diminishing returns.
• This law states that if a variable input is added in a production process that uses at least one fixed input, the increase in total output will eventually diminish after a certain level of input.
• In long-run production that uses more than one variable input, production technology can be illustrated by isoquants.
• Isoquants depict all the combinations of inputs that can be combined to produce a certain amount of output.
• Meanwhile, the isocosts is a curve that connects all the combinations of inputs that gives the same amount of costs.
• Based on isoquants and isocosts, the optimal input combination is achieved when marginal product of one ringgit for all inputs are the same. This principle is referred to as the principle of equal marginal.
• Returns to scale is a long-run production concept that measures the response of output towards expansion of production scale.
• Constant returns is obtained when the percentage of increase in output is equivalent to the increase in all inputs, while decreasing returns to scale occurs when the percentage of increase in output is much lower than the percentage of increase in all inputs.