Theory of Production

Production Theory

• Types of Inputs

• Factors of Production

• Long run and Short run

• Law of Production Functions

• Law of Return Scales

• Concept of Production

• Marginal and Average Products

• Isoquants

• Isocost

• Producer’s Equilibrium

Production

The process of transformation of resources (like land, labour, capital and entrepreneurship) into goods and services of utility to consumers and/or producers.

Services include all intangible items, like banking, education, management, consultancy, transportation.

Goods includes all tangible items such as furniture, house, machine, food, car, television etc.

Inputs : Fixed Inputs and Variable Inputs

Fixed inputs Remains the same in the

short period.

At any level of output, the amount remains the same.

The cost of these inputs are called Fixed Cost

Examples:- Building, Land etc.

Variable inputs

In the long run, all factors of production varies according to the volume of outputs.

The cost of variable inputs are called Variable Cost

Example:- Raw materials, labor, etc.

Factors of Production

Land Anything which is gift of nature

and not the result of human effort, e.g. soil, water, forests, minerals

Income is called as rentLabour

Physical or mental effort of human beings that undertakes the production process. Skilled as well as unskilled.

Income is called as wages/ salary

Capital Wealth which is used for

further production as machine/ equipment/intermediary good

It is outcome of human efforts Income is called as interest

Enterprise/Entrepreneur The ability and action to take

risk of collecting, coordinating, and utilizing all the factors of production for the purpose of uncertain economic gains

Income is called as profit

Long Run and Short Run:

• The Long Run is distinguished from the short run by being a period of time long enough for all inputs, or factors of production, to be variable as far as an individual firm is concerned

• The Short Run, on the other hand, is a period so brief that the amount of at least one input is fixed

• The length of time necessary for all inputs to be variable may differ according to the nature of the industry and the structure of a firm

Production Function

A production function is a table or a mathematical equation showing the maximum amount of output that can be produced from any specified set of inputs, given the existing technology. The total product curve for different technology is given below:

Q

x

Q = output x = inputs

Q = f(X1, X2, …, Xk)

Where

Q = outputX1, …, Xk = inputs

For our current analysis, let’s reduce the inputs to two, capital (K) and labor (L):

Q = f(L, K)

Production Function ..continuation

A technological relationship between physical inputs and physical outputs over a given period of time.

shows the maximum quantity of the commodity that can be produced per unit of time for each set of alternative inputs, and with a given level of production technology.

Normally a production function is written as:

Q = f (L,K,I,R,E) where Q is the maximum quantity of output of a good being

produced, and L=labour; K=capital; l=land; R=raw material; E=efficiency parameter.

Production Function ..continuation

Production Function with One Variable InputAlso termed as law of variable proportion It is the short term production function Shows the maximum output a firm can produce when only

one of its inputs can be varied, other inputs remaining fixed: where Q = output, L = labour and K = fixed amount of capital

Total product is a function of labour:Average Product (AP) is total product per unit of variable

inputMarginal Product (MP) is the addition in total output per

unit change in variable input

11.1-301009Negative returns

16.3-201308

21.501507

25101506

28201405

Diminishing returns

30301204

3040903

2530502

Increasing returns

20-201

StagesAPMPTotal Product (’000 tonnes)

Labour (’00

units)

-50

0

50

100

150

200

1 2 3 4 5 6 7 8 9

Labour

Out

put

Total Product(’000 tonnes)

MarginalProduct

AverageProduct

As the quantity of the variable factor is increased with other fixed factors, MP and AP of the variable factor will eventually decline.

Therefore law of variable proportions is also called as law of diminishing marginal returns.

Law of Variable Proportion

Production Function with Two Variable Inputs

All inputs are variable in long run and only two inputs are used

Firm has the opportunity to select that combination of inputs which maximizes returns

Curves showing such production function are called isoquants or iso-product curves.

An isoquant is the locus of all technically efficient combinations of two inputs for producing a given level of output

05

1015202530354045

6 7 8 9 10

Labour ('00 units)

Capi

tal (R

s. Cr

ore)

Stages of Law of Production

Second Stage: Diminishing return TP increase but at diminishing rate and it reach at highest at the end of the

stage. AP and MP are decreasing but both are positive. MP become zero when TP is at Maximum, at the end of the stage MP<AP.

Third Stage: Negative return TP decrease and TP Curve slopes downward As TP is decrease MP is negative. AP is decreasing but positive.

First Stage: Increasing return

TP increase at increasing rate till the end of the stage.

AP also increase and reaches at highest point at the end of the stage.

MP also increase at it become equal to AP at the end of the stage.

MP>AP

Laws of Return Scales

- Long run production function with all inputs factors are variable

Explain long run production function when the inputs are changed in the same proportion.

Production function with all factors of productions are variable.. Show the input-out put relation in the long run with all inputs are

variable.

“Return to scale refers to the relationship between changes of outputs and proportionate changes in the in all factors of

production ”

Returns to Scale

Constant Returns to Scale : When a proportional increase in all inputs yields an equal proportional increase in output

Increasing Returns to Scale : When a proportional increase in all inputs yields a more than proportional increase in output

Decreasing Returns to Scale : When a proportional increase in all inputs yields a less than proportional increase in output

Returns to Scale show the degree by which the level of output changes in response to a given change in all the inputs in a production system.

Various concept of production

In the short run, capital is held constant.

Total Product

Average product is total product divided by the number of units of the input

Marginal product is the addition to total product attributable to one unit of variable input to the production process fixed input remaining unchanged.

MP = TPN – TPN-1

Marginal and Average Product:

• Marginal product at any point is the slope of the total product curve

• Average product is the slope of the line joining the point on the total product curve to the origin.

• When Average product is maximum, the slope of the line joining the point to the origin is also tangent to it.

P: Maximum Average Product

Q & R : Same Average Product

Both AP and MP first rise, reach a maximum and then fall.

MP = AP when AP is maximum.

MP may be negative if Variable input is used too intensively.

Law of diminishing marginal productivity states that in the short run if one input is fixed, the marginal product of the variable input eventually starts falling.

Isoquants and the Production Function

Isoquant is a curve that shows the various combinations of two inputs that will produce a given level of output

Slope of an isoquant indicates the rate at which factors K and L can be substituted for each other while a constant level of production is maintained.

The slope is called Marginal Rate of Technical Substitution (MRTS)

Properties of Isoquants There is a different isoquant for every

output rate the firm could possibly produce with isoquants farther from the origin indicating higher rates of output

Along a given isoquant, the quantity of labor employed is inversely related to the quantity of capital employed isoquants have negative slopes

Isoquants do not intersect. Since each isoquant refers to a specific rate of output, an intersection would indicate that the same combination of resources could, with equal efficiency, produce two different amounts of output

Isoquants are usually convex to the origin any isoquant gets flatter as we move down along the curve

Isocost Lines Isocost lines show different combinations of inputs which

give the same cost

At the point where the isocost line meets the vertical axis, the quantity of capital that can be purchased equals the total cost divided by the monthly cost of a unit of capital TC / r

Where the isocost line meets the horizontal axis, the quantity of labor that can be purchased equals the total cost divided by the monthly cost of a unit of labor TC / w

The slope of the isocost line is given by

Slope of isocost line = -(TC/r) / (TC/w) = -w / r

“The isocost line represents the locus of points of all the different combinations of two inputs that a firm can procure, given the total

cost and prices of the inputs.”

Maximization of output subject to cost constraint

Necessary condition for equilibrium

Slope of isoquant = Slope of isocost line

AB is the isocost line Any point below AB is feasible but not

desirable

E is the point of tangency of Q2 with isocost line AB Corresponds to the highest level of output

with given cost function. Firm would employ L* and K* units of labour

and capital

Q3 is beyond reach of the firm

Points C and D are also on the same isocost line, but they are on isoquant Q1, which is lower to Q2. Hence show lower output.

E is preferred to C and D, which is on the highest feasible isoquant.

Producer’s Equilibrium

SOURCES:

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