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2. The Theory of the Firm

3. Meaning of function
The word function is derived from mathematics. It establishes the relationship between two variables. It explains the extent to which one variable depends upon another. For example demand and price ,output and input, expenditure and income.

4. Production Function

5. Meaning of Production Function
Production function analyses the physical relationship between input and output.
Production function means functional relationship between physical inputs of factors of production and physical output of a firm. It indicates maximum rate of output that can be obtained from different combinations of productive factors during a certain period of time and for a given state of technical knowledge.
“The production function is a technical or engineering relationship between output and input. As long as the natural laws of technology remain unchanged, the production function remains unchanged.”
Prof. L.R.Klein

6. Production Function States the relationship between inputs and outputs
Inputs – the factors of production classified as:
Land – all natural resources of the earth
Price paid to acquire land = Rent
Labour – all physical and mental human effort involved in production
Price paid to labour = Wages
Capital – buildings, machinery and equipment not used for its own sake but for the contribution it makes to production
Price paid for capital = Interest

7. Production Function Mathematical representation of the relationship:
Q = f (K, L, La)
Output (Q) is dependent upon the amount of capital (K), Land (L) and Labour (La) used

8. Production Function Product or service generated – value added Inputs
Process
Output
Land
Product or
service
generated
– value added
Labour
Capital

9. Characteristics
It establishes relationship between physical quantities of output and inputs
This is an engineering problem
No change in technology
Production function should be considered with a particular period of time
Inputs can be easily substituted
It can be related to short period or long period
Divisibility or indivisibility of factor should be taken into account.

10. Kinds of production function
One variable and two variable production function
Production function for a firm and for an industry
Short run and long run PF
Homogeneous and Heterogeneous PF
PF= production function

11. Analysis of Production Function: Short Run
In the short run only one or two factors can be changed by keeping other factors constant.
Reflects ways in which firms respond to changes in output (demand)
Can increase output up to a certain level.
It is associated with law of variable proportions.

12. Analysing the Production Function: Long Run
The long run is defined as the period of time taken to vary all factors of production
By doing this, the firm is able to increase its total capacity – not just short term capacity
Associated with a change in the scale of production
The period of time varies according to the firm and the industry
In electricity supply, the time taken to build new capacity could be many years; for a market stall holder, the ‘long run’ could be as little as a few weeks or months!

13. Analysis of Production Function: Long Run
In the long run, the firm can change all its factors of production thus increasing its total capacity. In this example it has doubled its capacity.

15. The Production function expresses a functional relationship between quantities of raw materials and output. It shows how and to what extent output changes with variations in raw materials during a specified period. In the words of Stigler “The production function is the name given to the relationship between rates of input of productive services and the rate of output of product. It is economist’s summary of technical knowledge.” It is expressed as follows.                         __ Q =F (L,M,N,C,T), where Q stands for the output of a good per Unit of time, L for labour, M__ for management of organisation, N for land or natural resources, C for Capital and T for given technology and F refers to the functional relationship.

16. Basic concepts related to production or law of returns
Short run
Long run
Fixed factors
Variable factors
Levels of production
Scale of production

17. Total product, Average Product and Marginal Product
The total product of a factor identifies the total volume of goods produced by a given amount of factors of production during a certain period. 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 units of input are increased after this point, TP starts to decrease.

18. Average and Marginal product
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.
The marginal physical product of a variable input is the change in total output due to a one unit change in the variable input.

19. Average and Marginal Physical Product Curves

20. Mutual relationship between TP, AP and MP
As the quantity of variable factor of production is increased, TP also increased
TP is maximum when MP is zero.
TP and AP never can be zero
If the quantity of variable factors of production is increased after MP has become Zero, it will not increase TP rather it will start to decline.
At the initial stage TP increases at increasing rate and at the ultimate stage TP increases at a diminishing rate.

21. Laws of returns or Law of Variable of Proportions
Production of a commodity is the result of combined efforts of various factors of production. These factors of production can be classified as fixed and variable factors. To increase the quantity of production, quantity of the factors of production will have to be increased. But the increase in production in response to a given increase in factor of production is not always same. Such behavior if production is explained by Laws of Returns.

22. If one input is variable and all other raw materials are fixed the concern’s production function exhibits the law of variable proportions. If the number of units of a variable factor is increased, keeping other factors constant, how output changes is the concern of this law.  As per Leftwich “The law of variable proportions states that if a variable quantity of one resource is applied to a fixed amount of other input, output per unit of variable input will increase but beyond some point the resulting increases will be less and less with total output reaching a maximum before it finally begins to decline.”

23. Postulations This law is based on the below postulations.
It is feasible to alter the proportions in which the a range of factors are collective
Only one factor is erratic while others are held invariable
All units of the changeable factor are standardized
There is no variation in expertise
It presumes a short run condition
The produce is calculated in physical units, in quintals, tons etc.
The price of the produce is specified invariable

24. Types of laws of returns
Prof. Marshall propounded three types of laws of returns-
Law of increasing returns
Law of constant returns
Law of diminishing returns

25. Law of increasing returns
When increase in output is in greater proportion than increase in input, it is known as law of increasing returns. In other words –
When proportionate change in production is more than the proportionate change in the quantity of variable factors of production by keeping the fixed factors constant, it is called the law of increasing returns.
Units of labour TP AP MP 1 10 2 24 12 14 3 45 15 21 4 68 17 23 5 95 19 27

26. Causes to apply laws of increasing returns
Economies of division of labor and specialization
Saving of time and improvement in the technique of production
Economies of the use of Specialized Machinery
Economies of Buying and Selling

27. Law of constant returns
Law of constant returns states the situation when increase in production is just equal to the increase in input so, AP and MP remain constant.
Units of labour TP AP MP 1 10 2 20 3 30 4 40 5 50

28. Law of diminishing returns
Law of diminishing returns occupies an important place in economic theory. This law explains the stage of production in which the quantity of one input of production is increased with a fixed quantity of other inputs and the resulting increase in production decreases after a certain point
Law of diminishing returns states the situation when increase in production is less than increase in input so, AP and MP will eventually decline.

29. Law of diminishing returns
Units of labour TP AP MP 1 10 2 19
9.5 9 3 27 8 4 33 6 5 37
7.4

30. Assumptions Technology remains same
Organizational structure and managerial efficiency of the firm remain unchanged
It is also assumed that there are some inputs which quantity may be kept fixed and the quantity of other inputs may be changed, as required. This law will not apply if all the factors of production are proportionately changed.
All the units of variable factors are homogenous
This law is related to the physical quantity not with its value
It is essential for the operation of this law that the optimum combination of resources of production must have already been achieved because this law applies only after this stage.

31. Causes of the operation
Fixity of one or more factors of production
Scarcity of productive resources
Going beyond the optimum combination
Factors of production are not perfect substitute for one another

32. Significance Universal application
Base of Malthusian population theory
Base of Marginal Productivity Theory
Base of Determination of Standard of living
Responsible for migration of population

33. Explanation of the Law
To explain this law more clearly, let us construct a sketch.
           
          

34.   The TP curve first rises at an enhancing rate upto point A where its slope is highest. From point A upwards, the total product increases at a diminishing rate till it reaches its highest point C and then is starts falling. Point A where the tangent touches the TP curve is called the inflection point upto which the total product increases at an increasing rate and from where it starts increasing at a diminishing rate.
            The average product curve AP and the marginal product curve MP also raise with TP. The MP curve reaches its maximum point D when the slope of the TP curve is the maximum at point A.
            The maximum point on the AP curve is E where it coincides with the MP curve. This point also coincides with point B on the TP curve from where the total product starts a gradual rise.
            When the TP curve reaches its maximum point C, the MP curve becomes zero at point F. When the TP starts declining the MP curve becomes negative, i.e. is below X axis.
            The rising, the falling and the negative phases of the total, marginal and average products are in fact the different stages of the law of variable proportions which are discussed below.

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