Production Function, Total Product ,Marginal Product ,Average Product and Law of diminishing marginal product.

Production is the process by which inputs (raw materials) are transformed into outputs or products for consumers. Production is carried out by producers or firms, to acquire inputs a firm has to pay for them. This is called the cost of production. Once output has been produced, the firm sell it in the market and earns revenue. The difference between the revenue and cost is called the firm’s profit. 

 

The production function of a firm is a relationship between used inputs and produced outputs by the firm. For various quantities of inputs used, it gives the maximum quantity of output that can be produced

Explicit costs are those incurred which paid to other economic entity. These include wages, expenditures for raw materials, taxes, machinery, and so on.

Implicit costs are those opportunity costs which cost in using all the resources that belong to the firm. These include depreciation, the depletion of business assets, and the opportunity cost of a firm’s capital.Such as Machines, building and office equipment depreciate with time.

Sunk costs are costs that have already been incurred and cannot be reversed back.

Production in short run 
In the short run, at least one of the factor – labour or capital remain fixed or constant.

Therefore in short run firms can only vary their output  by changing the amount of labor they employ as a factor of production.

In below table I am considering an assumed data to explain concept of Total Product, Marginal product and Average Product.

Production by a  Firm (Table1)

Labour(L)	Total product(Q)	Marginal product(MP)	Average Product (AV)
1	0	0	---
2	15	15	7.5
3	20	5	6.66
4	26	6	6.5
5	30	4	6
6	38	8	6.33
7	49	11	7
8	56	7	7
9	68	12	7.55
10	75	7	7.50
11	80	5	7.27
12	72	-8	6
13	68	-4	5.23
14	54	-14	3.86
15	48	-6	3.20

Marginal product is the change in output that results from altering in labor input. You can notice that when employment of labour rises from 9 to 10, output grows from 68 to 75 . Marginal product is therefore 7 at this point. Contrary to that when employment of labor rises from 11 to 12 output start declining from 80 to 72. so marginal product is -8.
Marginal product is calculated by dividing the change in output "𝛁Q" by the change in labor "𝛁L". The delta "𝛁" symbol is used to denote change. Thus, marginal product (MP) is equal to 𝛁Q/𝛁L; it is the change in output that results from adding extra labor

 

Average product (AP) is computed by dividing total output by the number of labors employed to produce that output (Q/L)
                                                    or
Average product is defined as the output per unit of variable input (Q/L)

To understand more concepts plot the data in table 1, placing labour on the X-axis and product(output) on the Y-axis, we get the curves shown in the diagram below. 

 If you will observe the above plot you can see that Total Product(TP) increases as employment of labour increases. But the rate at which it increases is of varying nature at input of 2 output is of 15 whereas at input level 3 output is 20. This variation can be observe in Marginal Product (MP).

since the rate at which TP increase is shown by the MP. Oberve that the MP first increases upto 9 units of labour and then begins to decline. This tendency of the marginal product (MP) to first increase and then fall is called the law of variable proportions or the law of diminishing marginal product. Law of variable proportions say that the marginal product of a factor input initially rises with its employment level. But after reaching a certain level of employment, it starts falling.

As firm hold one factor fixed and keep increasing the other, the factor proportions change. Initially, as we increase the amount of the variable input, the factor proportions become more and more suitable for the production and marginal product increases. But after a certain level of labor input, the production process becomes too crowded with the variable inputs (labour) and the marginal product begins to fall.