 # Production Technology in Economics

What is the meaning of production technology in Economics? Are you stranded in the production theory and are looking for an easy entry to the topic? This article will help you focus on the essential concepts of production theory you will not easily find in many microeconomic and macroeconomic textbooks.

## Introduction to Production Technology in Economics

In many economic books, you will find chapters dealing with the production theory. Consequently, some literature will discuss production theory as the theory of the firm in detail. On the other hand, others will focus on maximizing profits and minimizing costs in great depth. The only issue the literature does not mention is production technology as a concept in economics on its own. But how do we connect production technology with the production function? These issues are facultatively relevant for closely understanding production technology as an economic concept.

### Defining Production Technology as an Economic Concept

So what is a production technology? Production technology is the sum of all knowledge and capabilities of the society to combine scarce resources to produce final goods for consumption. This definition implies that the production technology also covers all industrial processes, interexchange, and intra-exchange of intermediate inputs in the value chain of final consumption goods.

### Production functions in Microeconomics and Macroeconomics

In your introductory economics courses, you should first invest some effort in understanding some technicalities of how economists describe production technologies using production functions at both microeconomic and macroeconomic levels. Consequently, the production function is the mathematical interpretation of the production technology in economics. Without some mathematical background, you will have some difficulty interpreting the concepts of production theory. Therefore, make sure you have reintroduced yourself to derivation rules, integration rules, and other mathematical concepts.

Let us assume for now that we face a Cobb-Douglas Production technology defined as follows:

Y=F(L,K)=K^\alpha \cdot L^{(1-\alpha)}

Why does your textbook describe such technology as one with constant returns to scale? We will understand this shortly by looking a the production technology in microeconomics and macroeconomics.

## Production Technology in Microeconomics

Economists use the production technology at the microeconomic level to describe the knowledge and capabilities of a firm in an economy. They assume that only one firm exists in an economy in most cases. The assumption is contrary to the existence of many firms in reality. By doing this, economists want you to focus on the behavior of a firm within an economic order. Firms are economic subjects that make production (or output), profit, and cost decisions in the economy. First, the output level is how much we need to cover the needs of final consumers. Secondly, profit is the income that firms should generate for their owners. Lastly, the costs are the incomes of those resources (or inputs) firms hire to work for them.

### Weaknesses of Microeconomics Literature

Surprisingly, It does not matter which microeconomic textbook you pick. You will experience some technical dilemmas in text, mathematics, and graphical representation of the knowledge. You will also find these problems in other microeconomic subtopics, such as household theory, welfare economics, and different economic fields.

### How to connect production technology with the production function

A simple way to understand the production technology is to first learn the technology’s essential characteristics from a mathematical and economic perspective. The vital features of production technology also apply in macroeconomics, as we will discuss later. In mathematical terms, the production function captures the output-input relationship to explain the knowledge and capabilities of the production technology in a firm or an economy. We can assume that each firm has its unique technology or that an economy has a unique technology shared by local firms. You will find enough literature working around this assumption.

## Three Essential Economic Concepts of Production Theory

In any output-input relationship you will discover in microeconomics, economists will describe the production technology using three concepts of economics; the return to scale, the marginal product of inputs, and the change of marginal productivity. Read more about the scarce resources in economics as production technology inputs.

The concept of return to scale describes how the simultaneous change of all inputs affects the output levels within a production technology. Most of the microeconomic literature will introduce you to four types of production technology depending on the kind of return to scale. There are three general forms of return to scale of inputs;

To distinguish between the three forms of return to scale, you will need to understand the following two concepts; the marginal product of inputs and the change of marginal productivity.

\lambda^{r}F(L,K)=F(\lambda K, \lambda L)=\lambda^{r}Y \\ \Rightarrow [(\lambda K)^{\alpha} \cdot (\lambda L)^{(1-\alpha)}= \lambda^{1} \cdot K^\alpha \cdot L^{(1-\alpha)}]

The Cobb-Douglas Production function above is of homogeneity of grade one and, therefore, depicts the constant return to scale of all inputs. That means that when we increase all inputs with factor $\lambda$, we will increase the output by a factor $\lambda$.

### The Concept of Marginal Productivity of Inputs

The concept of marginal productivity of inputs describes the slope of the production function concerning a resource, e.g., labor, capital, raw materials, or human capital. In mathematical terms, we describe the slope of the production function using the first derivative of the production function. Economically, the marginal productivity of inputs quantifies the extra units of output gained by increasing the inputs by one.

\frac {\partial F(K,L)}{\partial L}=(1-\alpha) \cdot \Biggl (\frac{K}{L}\Biggr)^\alpha
\frac {\partial F(K,L)}{\partial K}=\alpha \cdot \Biggl (\frac{L}{K}\Biggr)^{(1-\alpha)}

### The Concept of Change of Marginal Productivity of Inputs

The concept of change of marginal productivity of inputs describes, on the other hand, the change in slope of the marginal productivity of a resource, e.g., labor, capital, raw material, or human capital. Mathematically speaking, we use the second derivative of the production function to describe the slope change. In economic terms, the change in marginal productivity captures the curvature of the production function. Consequently, the curvature will help us distinguish between the three general forms of return to scale of inputs. We can therefore identify three economically relevant types of marginal productivity;

• The constant marginal productivity of inputs
• The Increasing marginal productivity of inputs
• The decreasing marginal productivity of inputs

In simple terms, the constant marginal productivity implies no change in the marginal productivity of an input and a constant return to an input’s scale. Consequently, the increasing/decreasing marginal productivity suggests a positive/negative change in the marginal productivity and an increasing/decreasing return to an input’s scale.

\frac {\partial F(K,L)}{\partial^{2} L}=-\alpha(1-\alpha) \cdot \Biggl (\frac{K}{L}\Biggr)^{\alpha} \cdot \frac{1}{L}
\frac {\partial F(K,L)}{\partial^{2} K}=-\alpha(1-\alpha) \cdot \Biggl (\frac{L}{K}\Biggr)^{(1-\alpha)} \cdot  \frac{1}{K}

## Opportunity Costs of Production using Inputs

We need the three essential concepts of production theory to build on them and extend our analysis to the opportunity costs of production. The first extension will introduce the isoquant, and secondly, introduce the slope of the isoquant. On the one hand, the isoquant demarcates all input combinations that lead to the same output level. On the other hand, the slope of the isoquant quantifies the opportunity costs of producing the same output level using different amounts of inputs combinations. Economists will then introduce the marginal rate of technical substitution in microeconomics, which measures opportunity costs of production. The marginal rate of technical substitution also describes the slope of the isoquant.

## Production Technology in Macroeconomics

The concepts developed in the section above flow in understanding the production technology in macroeconomics. At the macroeconomic level of the economy, economists focus on explaining the production technology of an economy as a whole and not of a single firm. The latter would be a microeconomic analysis of individual agents in an economy. The neoclassical theorists love introducing production technology in their economic models. So you might consider expanding your knowledge about production functions in macroeconomics. For example, the general growth theory introduces the Solow-Model of capital accumulation in basic and advanced levels of macroeconomics.

## Literatur

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