## Note on Concept of Total Product, Average Product and Marginal Product And Production Function

• Note
• Things to remember

### Concept of Total, Average and Marginal Product

There are three concepts of a product. They are:

Total Product (TP): It refers to the total amount of commodity produced by the combination of all inputs in a given period of time. It is calculated in two ways:

• Multiplying the average product with the total units of the inputs employed, i.e. TP = AP×N; where, TP= Total Product, AP= Average Product, N= Total units of inputs employed
• Summation of marginal products, i.e. TP=∑MP
where, TP= Total Product, MP= Marginal Product

Average Product (AP): An average product is the outcome of the total product divided by the total units of the input employed. It refers to the output per unit of the input.

Mathematically, AP= TP/N

where,

AP= Average Product

TP= Total Product

N= Total units of inputs employed

Marginal Product (MP): It is the addition made to the total product by employing one more unit of the input. In other words, it is the ratio of the change in the total product with the change in the units of the input. It is expressed as

MP = ΔTP/ΔN
where,

MP= Marginal Product

ΔTP= Change in total product

ΔN= Change in units of input

It is also expressed as

MP = TP(n) – TP(n-1)

where,

MP= Marginal Product

TP(n)= Total product after employing one more unit (nth unit)

TP(n-1)= Total product before employing one more unit

Derivation of TP, AP, and MP

 Units of inputs TP AP MP 1 0 8 8 2 20 10 12 3 30 12 16 4 48 12 12 5 56 11.2 8 6 56 9.3 0 7 48 6.9 -8

### Production Function

The production process involves the use of various inputs or factor services to produce output. In other words, business firm transforms inputs into output. Inputs are the means of producing the goods and services demanded by society. There are four factors of production: land, labor, capital and organization.

According to A. Koutosoyianis, “The production function is purely a technical relation which connects factors inputs and output.”

The functional relationship between inputs (as an independent variable) and output (as a dependent variable) is usually referred to as production function.

In other words, production function refers to the functional relationship between the quantity of goods produced and a factor of production. For example, a wheat farm takes land, labor, seed, fertilizer, spades, and tractors to produce wheat. In short, it is a schedule indicating the amount of the output obtained from a different combination of inputs, given the state of technology and in a given period of time. Mathematically, it is expressed as Q= f(N)

where, Q=output, f=function, N=Inputs

Basic concepts

There are some basic concepts of production function

• Production function establishes a functional relationship between inputs (as an independent variable) and output (as a dependent variable).
• The production function is a flow of inputs resulting in a flow of output over some specified period of time.
• It expresses a physical relation because both inputs and outputs are expressed in physical terms.
• It describes a purely technological relation between input and output.

#### Types of production function

The production function is of two types. They are:

1. Short run production function

The short run is defined as a period in which at least one input of the factors of production is constant. Market supply cannot be changed according to the change in the market demand. In a short run, usually factory facilities, equipment, and machinery which includes land are fixed and the market supply can be altered by changing the demand for labor, raw material, and other factory components.

In a short run, inputs can be classified into fixed inputs and variable inputs. Fixed inputs are those inputs which cannot be varied as required. For example, land, building, permanent staffs, etc. But variable inputs are those inputs which can be varied as required. For example, raw materials, delivery workers, etc.

• Fixed Costs: The cost of production of the investment which is utilized by the firm is called fixed cost. The fixed cost does not vary despite the production output. Examples are overhead cost, property tax, rent of offices and buildings, amortization and interest.
• Variable Cost: This shows cost associated with direct labor, raw materials, supplies, and materials. The variable cost is connected in the production of goods.

The short run production function refers to the functional relationship between the units of variable factors and the output. In short run production function, we study the effect of a change in the quantity of one variable input on the output by keeping all other inputs constant. It is also called single variable production function. Algebraically written as:

Q= f(Nvf)K’
where, Q=Output, f=function, Nvf=Quantity of variable factors, K’=Constant units of fixed inputs

2. Long run production function

Long run is a period in which market supply can be changed according to the change in market demand. It is because the producer has sufficient time to adjust all the inputs as required. In fact, all of the inputs are variable and elastic in a long run. In the long run, firms can hire a greater quantity of labor as well as capital. With large employment of factor inputs, the scale of production rises higher. Therefore, in a long run, production of a commodity can be increased by employing more units of all the inputs. In the long run, the function relationship between factor inputs and output generated with changing scales is explained clearly under laws of returns to scale. The laws of returns to scale are usually explained through isoquant technique in economics.

Thus, long run production function refers to the functional relationship between the quantities of all inputs and output. In long run production function, we study the effect on the output with the variation of all inputs, say, land, labor, capital and entrepreneur. Therefore, the long run production function is also termed as a multivariable production function. Algebraically, it is expressed as:

Q=f(W,L,K,M,T)
where, Q=output, f=function, W=Land, L=Labor, K=Capital, M=Management, T=Technology

Long run production function is also depicted as production function with two variable inputs, i.e. Q=f(L, K)

where, Q=output, F=function, L=Labor, K=Capital

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan

• Total Product refers to the total amount of commodity produced by the combination of all inputs in a given period of time.
• An average product is the outcome of the total product divided by the total units of the input employed.
• Marginal Product is the addition made to the total product by employing one more unit of the input.
• The short run production function refers to the functional relationship between the units of variable factors and the output.
• The long run production function refers to the functional relationship between the quantities of all inputs and output.

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##### aastha

what are the relationship between MP and MC?