# Production function notes. 3 Types Of Production Functions: Cobb Douglas, Leontief, CES 2022-12-17

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A production function is a mathematical representation of the relationship between the inputs used in the production process and the output produced. It specifies the maximum output that can be produced for a given set of inputs. The inputs used in the production process are known as factors of production and can include labor, capital, land, and materials. The output produced is typically measured in terms of the quantity of goods or services produced.

There are several types of production functions, including the short run production function and the long run production function. The short run production function represents the relationship between the inputs used in the production process and the output produced, taking some inputs as fixed and others as variable. The long run production function represents the relationship between the inputs used in the production process and the output produced, taking all inputs as variable.

One important concept in production function analysis is the law of diminishing returns. This states that as more units of a variable input are added to a fixed amount of other inputs, the marginal product of the variable input will eventually decline. This occurs because the fixed inputs are being used more efficiently as the variable input increases, and at some point, the additional units of the variable input will not be used as efficiently as the previous units.

Another important concept in production function analysis is the concept of returns to scale. This refers to the relationship between the percentage change in the inputs used in the production process and the percentage change in the output produced. If the percentage change in output is greater than the percentage change in inputs, then there are increasing returns to scale. If the percentage change in output is equal to the percentage change in inputs, then there are constant returns to scale. If the percentage change in output is less than the percentage change in inputs, then there are decreasing returns to scale.

In conclusion, the production function is a useful tool for understanding the relationship between inputs and output in the production process. It allows firms to analyze the efficiency of their production process and make decisions about how to allocate resources in order to maximize output. Understanding the concepts of diminishing returns and returns to scale is also important in production function analysis, as they can help firms to identify opportunities for improving efficiency and increasing output.

## What is Production Function?

In the production function, the variation in total output is due to the variation in input quantity. Note that there may be many other factors as well but we have assumed two-factor inputs here. We may note, at the outset, that in this func­tional form, both inputs are necessary to produce any output at all. It assumes strict complementarity of factors of production. One important problem in the empirical anal­ysis of a production function is to determine what happens to output when all inputs are increased pro­portionately. Marginal Cost : Marginal cost MC is the change in total cost associated with a finite small change in output.

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## Production Function: Short Run and Long Run Production Functions

In order to understand the input invested and how much of it is required to gain a certain amount of output, economists establish production functions that show the relationship between inputs and output. Total revenue is at its highest when marginal revenue is zero, and when marginal revenue becomes negative, TR begins to fall. Any pricing de­cision is based on cost explicitly or implicitly. Technological change has been most spectacular in the computer industry in recent years. So, its labor-to-capital ratio is 6:1. Relation between MC and AC: i when AC falls, MC AC. Answer: Returns to a factor is used to explain the short-run production function.

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## Production function

Input Input means factors of production such as land, labour, capital and enterprise. The Cobb-Douglas form will enable us to esti­mate the following: 1. Because of the law of variable proportion, AVC is U-shaped. Where Y is output, a and b are constants and x is variable input. It is a homothetic production function, which implies that it has a straight-line expansion path, i. Basi­cally, this is a measure of elasticity since it reflects the percentage change in output in response to a given percentage change in the level of usage of both the inputs.

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## Concept of Production Function Class 11 Economics Notes

So when units of variable factor are employed, it leads to optimum utilization of fixed factor. Exogenous progress, in its turn, can be of two types. They vary directly with the output. Again, the longer the dura­tion of abnormal demand, the greater the likelihood that some fixed costs will actually be varied. Average product or Average return to an input: It is per unit total product of variable factors. The vertical distance between the AC curve and the AVC curve, on the other hand, continues to decrease, but these two curves never intersect because the average fixed cost is never zero.

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## Production and Production Function

Time-series data may con­tain a series of observations for outputs and inputs for a given firm or given industry over an extended period of time. Think about it, as an additional worker adds less to the overall production, the average product produced will also drop. Microeconomics Class 12 Chapter 3 Notes prepared by the experts at Vedantu will not only enhance the knowledge of the students but will also help them in undergoing a thorough and well-rounded learning of the chapter. Similarly, AP curve first rises, reaches its maximum and then declines taking the shape of an inverted U. Production function example Let's say there is a farming company that plants apples. The coefficient b is supposed to capture all those quantitative effects of any force for which they did not have quantitative data. The boundary between stage II and III shows the level at which all resources are fully utilised.

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## Production Function: Definition & Formula

The marginal product of an input is the increase in the quantity of output when one more unit of that input is used. Introduction In economics, it is sometimes necessary to relate input with output. Total product or Total physical product: - Total product is the sum of the final units of output produced by a firm using a given amount of inputs over a given time period. This is evident from the fact that no single commodity can be produced without the help of one of these four factors of production. To see how such an estimation can be used, let us now turn to a few examples. Relation between TR, AR and MR when more quantity by sold at the lower price or there is monopoly or monopolistic competition in the market.

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## What is Production Function? Meaning, Definition, Factors

This distinction is extremely relevant in microeconomics. So, the labor-to-capital ratio or the short-run production function will decrease when capital is increased. Or, the labourer might turn out to be much more efficient than expected by the entrepreneur. Types of Production Function: There are two types of Production Function. Suppose we are to draw a production function for this company. Then we will get a function where the outcome of the function will only vary depending on only changing capital.

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## Production Function

Schedule Unit of land Unit of labour TP MP Returns of variable factors Stage of production 1 1 2 2 TP increases at increasing rate so MP also increases Increasing returns to a factor. The increasing returns to scale is due to the economies of scale and decreasing returns to scale is due to the diseconomies of scale. In other words, we can say that production function is an indicator of the physical relationship between the inputs and output of a firm. This is due to technological progress. The long run production function studies the effect on output due to change in all the factors inputs. The law of variable proportion states that as we increase the quantity of only one input, keeping other inputs fixed, the total product increases at an increasing rate convex shape in the beginning, then increases at diminishing rate concave shape and after a level of output ultimately falls.

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## Production

Production function can be classified into short term and long term based on the variables used. In the short run, fixed factors like plant, machinery, building etc. It is calculated by dividing the total Product by the units of variable factor. As all the variables change, the ultimate outcome of the production function may have an incremental or detrimental effect. There are two kinds of the production function, short run production function and long run production function.

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## Production Function and Returns to a Factor Class 11

It is illustrated in column 8 of Table 15. Various factors explain why the number of working hours required to produce each unit of output declines as more units of the product are produced. Technology in the production function means a technological process enables firms to increase production without changing the quantities of inputs. Notice that the total apples produced do not increase as much as before when the number of workers increases. The law of returns to a factor is an example of such a production function.

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