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Theory Of Topic - Production Function

Production Function is the relationship between the input and output during the process of production. It is a function which shows how output is a function of the inputs that go into production. The four main inputs used for production are land, labor, capital and organization. The quantity that is produced is simply a function of these four factors of production. Some of these factors mainly land is a fixed factor of production while other are variable. Output differs if there is any change in any of these factors.

Production Function is a mathematical and graphical representation of these relationships between input and output. Given that land is a fixed factor of production, labor and capital are majorly what defines the output of production. The production function is defined as follows:

Q=f(K,L)

Where, Q is the quantity produced from the production process

K is the amount of capital invested

And, L is the amount paid to laborers

It is used for determining the efficiency of the production process. It shows how much input is required to produce an optimal level of output. It also determines the optimal level of production. It is used to calculate marginal product which is basically the marginal quantity produced with increase in the variable input. Production function shows different combination of different factors of production so that any producer can choose the best combination and allocate resources accordingly in the production process.

Due to the advancement in technology, the capital part of the production function keeps fluctuating. There are many assumptions that go into the theory of production function. Production function depends on the long run or short run production process. In the short run, the factors other than land are variable. In the long run, all the factors are variables. A firm can increase production by changing its input in the long run while in the short run, it is difficult to do that, There are shifts in the production curve determined by the production function due to a change in the quantity produced and the inputs that go in.

**Other assumptions of the production function include the following:**

- The production function is only for a particular point of time.
- The technology used in the production remains constant.
- The producer is using the best technique for productions
- The factors of production are divisible into feasible units.

Due to these assumptions, there are a lot of limitations while using the production function in real life. These assumptions usually do not hold true from the producers' end and t is thus, considered more of a theoretical approach than a practical one.

Production function is still used by many producers and economists to determine the relationship between the factors of production so that they can arrive at the most optimal production combination of inputs and outputs and maximize their returns. It is used for calculating the total product, average product and marginal product for the process for production.

**Problems Encountered In Solutions To Production Function Problems**

The assumptions of production function are not always true. The students who try to solve production function often miss out on the assumptions and make a mistake. There are different formulas and calculation of Total product, average product and marginal product can be confusing and can lead to a lot of mistakes in calculating the perfect combination. Since it is also used to calculate producer's equilibrium, the calculations need to be more accurate and cannot have an error.

The calculations have to be accurate and thus require a lot of concentration while solving production function problems. It is a technical relation between the factors of production and thus, becomes complex and challenging.

There are different stages of the production which needs to be identified and it has to be figured out which stage occurs when in order to take the right decisions. The firm objectives might change in the long run as well. It might decide to maximum profit to constant profit as their motive. All these changes need to keep in mind while doing problems relating to production function.

All these reasons and factors make the problems of production function extremely challenging and students have a tough time figuring out the solutions for the problems of production function.

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