# Production theory

Production theory is the study of production, or the economic process of converting inputs into outputs. Production uses resources to create a good or service that is suitable for use, gift-giving in a gift economy, or exchange in a market economy. This can include manufacturing, storing, shipping, and packaging. Some economists define production broadly as all economic activity other than consumption. They see every commercial activity other than the final purchase as some form of production.

Production is a process, and as such it occurs through time and space. Because it is a flow concept, production is measured as a “rate of output per period of time”. There are three aspects to production processes:

1. the quantity of the good or service produced,
2. the form of the good or service created,
3. the temporal and spatial distribution of the good or service produced.

A production process can be defined as any activity that increases the similarity between the pattern of demand for goods and services, and the quantity, form, shape, size, length and distribution of these goods and services available to the market place.

## Factors of production

The inputs or resources used in the production process are called factors of production by economists. The myriad of possible inputs are usually grouped into five categories. These factors are:

In the “long run”, all of these factors of production can be adjusted by management. The “short run”, however, is defined as a period in which at least one of the factors of production is fixed.

A fixed factor of production is one whose quantity cannot readily be changed. Examples include major pieces of equipment, suitable factory space, and key managerial personnel.

A variable factor of production is one whose usage rate can be changed easily. Examples include electrical power consumption, transportation services, and most raw material inputs. In the short run, a firm’s “scale of operations” determines the maximum number of outputs that can be produced. In the long run, there are no scale limitations.

## Total, average, and marginal product

Total Product Curve

The total product (or total physical product) of a variable factor of production identifies what outputs are possible using various levels of the variable input. This can be displayed in either a chart that lists the output level corresponding to various levels of input, or a graph that summarizes the data into a “total product curve”. The diagram shows a typical total product curve. In this example, output increases as more inputs are employed up until point A. The maximum output possible with this production process is Qm. (If there are other inputs used in the process, they are assumed to be fixed.)

The average physical product is the total production divided by the number of units of variable input employed. It is the output of each unit of input. If there are 10 employees working on a production process that manufactures 50 units per day, then the average product of variable labour input is 5 units per day.

Average and Marginal Physical Product Curves. The input amount were the MPP is 0, is the same as for A in the Total Product Curve (image above).

The average product typically varies as more of the input is employed, so this relationship can also be expressed as a chart or as a graph. A typical average physical product curve is shown (APP). It can be obtained by drawing a vector from the origin to various points on the total product curve and plotting the slopes of these vectors.

The marginal physical product of a variable input is the change in total output due to a one unit change in the variable input (called the discrete marginal product) or alternatively the rate of change in total output due to an infinitesimally small change in the variable input (called the continuous marginal product). The discrete marginal product of capital is the additional output resulting from the use of an additional unit of capital (assuming all other factors are fixed). The continuous marginal product of a variable input can be calculated as the derivative of quantity produced with respect to variable input employed. The marginal physical product curve is shown (MPP). It can be obtained from the slope of the total product curve.

Because the marginal product drives changes in the average product, we know that when the average physical product is falling, the marginal physical product must be less than the average. Likewise, when the average physical product is rising, it must be due to a marginal physical product greater than the average. For this reason, the marginal physical product curve must intersect the maximum point on the average physical product curve.

## Diminishing returns

Diminishing returns can be divided into three categories:

1. Diminishing Total returns, which implies reduction in total product with every additional unit of input. This occurs after point A in the graph.
2. Diminishing Average returns, which refers to the portion of the APP curve after its intersection with MPP curve.
3. Diminishing Marginal returns, refers to the point where the MPP curve starts to slope down and travels all the way down to the x-axis and beyond.

Ordered by input, at first the marginal returns start to diminish, then the average returns, followed finally by the total returns.

## Diminishing marginal returns

These curves illustrate the principle of diminishing marginal returns to a variable input (not to be confused with diseconomies of scale which is a long term phenomenon in which all factors are allowed to change). This states that as you add more and more of a variable input, you will reach a point beyond which the resulting increase in output starts to diminish. This point is illustrated as the maximum point on the marginal physical product curve. It assumes that other factor inputs (if they are used in the process) are held constant. An example is the employment of labour in the use of trucks to transport goods. Assuming the number of available trucks (capital) is fixed, then the amount of the variable input labour could be varied and the resultant efficiency determined. At least one labourer (the driver) is necessary. Additional workers per vehicle could be productive in loading, unloading, navigation, or around the clock continuous driving. But at some point the returns to investment in labour will start to diminish and efficiency will decrease. The most efficient distribution of labour per piece of equipment will likely be one driver plus an additional worker for other tasks (2 workers per truck would be more efficient than 5 per truck).

Resource allocations and distributive efficiencies in the mix of capital and labour investment will vary per industry and according to available technology. Trains are able to transport much more in the way of goods with fewer "drivers" but at the cost of greater investment in infrastructure. With the advent of mass production of motorized vehicles, the economic niche occupied by trains (compared with transport trucks) has become more specialized and limited to long haul delivery.

P.S.: There is an argument that if the theory is holding everything constant, the production method should not be changed, i.e., division of labour should not be practiced. However, the rise in marginal product means that the workers use other means of production method, such as in loading, unloading, navigation, or around the clock continuous driving. For this reason, some economists think that the “keeping other things constant” should not be used in this theory.

## Many ways of expressing the production relationship

The total, average, and marginal physical product curves mentioned above are just one way of showing production relationships. They express the quantity of output relative to the amount of variable input employed while holding fixed inputs constant. Because they depict a short run relationship, they are sometimes called short run production functions. If all inputs are allowed to be varied, then the diagram would express outputs relative to total inputs, and the function would be a long run production function. If the mix of inputs is held constant, then output would be expressed relative to inputs of a fixed composition, and the function would indicate long run economies of scale.

Rather than comparing inputs to outputs, it is also possible to assess the mix of inputs employed in production. An isoquant (see below) relates the quantities of one input to the quantities of another input. It indicates all possible combinations of inputs that are capable of producing a given level of output.

Rather than looking at the inputs used in production, it is possible to look at the mix of outputs that are possible for any given production process. This is done with a production possibilities frontier. It indicates what combinations of outputs are possible given the available factor endowment and the prevailing production technology.

## Isoquants

Isoquant Curve/Isocost Curve
Two Isoquants (Interior and Corner Solutions)

An isoquant represents those combinations of inputs, which will be capable of producing an equal quantity of output; the producer would be indifferent between them. The isoquants are thus contour lines, which trace the loci of equal outputs. As the production remains the same on any point of this line, it is also called equal product curve. Let Q0 = f(L,K) be a production factor, where Q0 = A is a fixed level of production.

L = Labour

K = Capital

If three combinations of labour and capital A, B and C produces 10 units of product, then the isoquant will be like Figure 1.

Here we see that the combination of L1 labour and K3 capital can produce 10 units of product, which is A on the isoquant. Now to increase the labour keeping the production the same the organization has to decrease capital. In Figure 1 B is the point where capital decreases to K2, while labour increases to L2. Similarly, 10 units of product may be produced at point C on the isoquant with capital K1 and labour L3. Each of the factor combinations A, B and C produces the same level of output, 10 units.

## The marginal rate of technical substitution

Marginal Rate of Technical Substitution

Isoquants are typically convex to the origin reflecting the fact that the two factors are substitutable for each other at varying rates. This rate of substitutability is called the “marginal rate of technical substitution” (MRTS) or occasionally the “marginal rate of substitution in production”. It measures the reduction in one input per unit increase in the other input that is just sufficient to maintain a constant level of production. For example, the marginal rate of substitution of labour for capital gives the amount of capital that can be replaced by one unit of labour while keeping output unchanged.

To move from point A to point B in the diagram, the amount of capital is reduced from Ka to Kb while the amount of labour is increased only from La to Lb. To move from point C to point D, the amount of capital is reduced from Kc to Kd while the amount of labour is increased from Lc to Ld. The marginal rate of technical substitution of labour for capital is equivalent to the absolute slope of the isoquant at that point (change in capital divided by change in labour). It is equal to 0 where the isoquant becomes horizontal, and equal to infinity where it becomes vertical.

The opposite is true when going in the other direction (from D to C to B to A). In this case we are looking at the marginal rate of technical substitution capital for labour (which is the reciprocal of the marginal rate of technical substitution labour for capital).

It can also be shown that the marginal rate of substitution labour for capital, is equal to the marginal physical product of labour divided by the marginal physical product of capital.

In the unusual case of two inputs that are perfect substitutes for each other in production, the isoquant would be linear (linear in the sense of a function $y = a - bx$). If, on the other hand, there is only one production process available, factor proportions would be fixed, and these zero-substitutability isoquants would be shown as horizontal or vertical lines.