production function.ppt

7/30/2019 Production Function.ppt

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Introduction & Meaning

Production is the transformation of inputs into

outputs. Inputs are the factors of production -land, labor,

capital raw materials and business services.

Meaning:The relationship between the quantities of inputs

and the maximum quantities of outputs produced is

called the "production function."

The maximum output that can be produced with agiven quantity of inputs (Land ,Labor, capital and

Machinery).It describes the productive capabilities of a

firm.


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Concept of ProductionFunction

Production function can be defined as the

specification of the minimum input requirements

needed to produce the maximum output. With

the given set of all technically feasiblecombinations of output and inputs.

This focus on the allocation efficiency ,making

allonative choices

How much of each input factor to use.

How much to produce

With the given cost (Purchase Price).


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Production Function as theEquation

Production Function in the form of Equation

Q = f( X1,X2,X3n)

Where

Q is the quantity

X1,X2,X3.n are the factor inputs


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Production Function as thegraph


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Stages of production

To simplify the interpretation of a production function, it is

common to divide its range into 3 stages.

In Stage 1 (from the origin to point B) the variable input is beingused with increasing output per unit, the latter reaching a maximum

at point B (since the average physical product is at its maximum atthat point). Because the output per unit of the variable input is

improving throughout stage 1, a price-taking firm will always operate

beyond this stage.

In Stage 2, output increases at a decreasing rate, and the averageand marginal physical product are declining. However the average

product of fixed inputs (not shown) is still rising, because output is

rising while fixed input usage is constant.
http://en.wikipedia.org/wiki/Marginal_physical_producthttp://en.wikipedia.org/wiki/Marginal_physical_product


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Contd

In this stage, the employment of additional variable inputs

increases the output per unit of fixed input but decreases the output

per unit of the variable input. The optimum input/output combination

for the price-taking firm will be in stage 2, although a firm facing a

downward-sloped demand curve might find it most profitable to

operate in Stage 1.

In Stage 3, too much variable input is being used relative to theavailable fixed inputs: variable inputs are over-utilized in the sense

that their presence on the margin obstructs the production process

rather than enhancing it. The output per unit of both the fixed and

the variable input declines throughout this stage. At the boundarybetween stage 2 and stage 3, the highest possible output is being

obtained from the fixed input.


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Total Product, In this example, output increases

as more inputs are employed up until point A.The maximum output possible with this production

function.


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Average Product , If there are 10 employees working

on a production process that manufactures 50 units per

day, then the average product of variable labor input is 5

units per day. It can be obtained by drawing a vector

from the origin to various points on the total product

curve. The continuous marginal product of a variable

input can be calculated as the derivative of quantity

produced with respect to the variable input employed.

The MPP curve obtained from the slope of the TPP.


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Total, Marginal and Average

Product

Units of

Input

TP

0 0

1 2000

2 3000

3 3500

4 3800

5 3900

MP

2000

1000

500

300

100

AP

2000

1500

1167

950


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Law of Diminishing Returns

The Law of diminishing returns states that when weadd additional input while holding the other inputs

constant. The marginal product of the each unit of input

will decline as the amount of that input increases. It

holds true to increase in each of other input .Law of Diminishing Returns express the relationship

between the variable input and the output, as the

variable input increases, the output also increases, but at

a decreasing rate.

For Example:

A farmer will find that a certain number of farm

laborers will yield the maximum output . If that number is

exceeded, the output per worker will fall.


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Inputs

Output

Here is a picture of the relationship between the

variable input and the output in the numerical example in the

above table. The curve slope gets flatter: as the variableinput Increases, output increases at a decreasing rate.

This is a visualization of the Law of Diminishing Returns.


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Short and Long Run

Some inputs can be varied flexibly in a relatively short

period of time. Labor and Raw Materials as "variableinputs". Other inputs require a commitment over alonger period of time.

Capital goods are thought of as "fixed inputs". A capitalgood represents a relatively large expenditure at a

particular time, with the expectation that the investment

will be repaid -- and any profit paid -- by producing goods

and services for sale over the useful life of the capitalgood. In this sense, a capital investment is a long-term

commitment. So capital is thought of as being variable

only in the long run, but fixed in the short run.


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Contd

Thus, we distinguish between the short run and the long

run as follows:

In the perspective of the short run, the number andequipment of firms operating in each industry is fixed.

In the perspective of the long run, all inputs are variableand firms can come into existence or cease to exist, so

the number of firms is also variable.

In the long run the firm have the various choices ofproduction function, whereas it is limited undershortrun.


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Returns to Scale

In microeconomics, diminishing returns as a

short run. In the long run, all inputs can be

increased or decreased in proportion.

Reductions in the marginal productivity of labor,due to increasing the labor input, can be offset

by increasing the tools and equipment the

workers have to work with. The returns to scale

concept is an inherently long run concept. In thelong run we define three possible cases:


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Increasing returns to scale

A production function for which any given

proportional change in all inputs leads to a more than

proportional change in output.

If an increase in all inputs in the same proportion (k)

leads to an increase of output of a proportion greater

than k, we have increasing returns to scale.

Example: If we increase the inputs to a software

engineering firm by 50% output increases by 60%, we

have increasing returns to scale in software engineering.This is also known as "economies of scale," since

production is cheaper when the scale is larger


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Decreasing returns to scale

A production function for which a proportional

change in all inputs causes a less than proportional

change in output

If an increase in all inputs in the same proportion k

leads to an increase of output of a proportion less than k,

we have decreasing returns to scale. Example: If we

increase the inputs to a dairy farm (cows, land, barns,

feed, labor, everything) by 50% and milk output

increases by only 40%, we have decreasing returns toscale in dairy farming. This is also known as

"diseconomies of scale," since production is less cheap

when the scale is larger.


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Constant returns to scale

A production function for which a

proportional change in all inputs causes output

to change by the same proportion.

If an increase in all inputs in the sameproportion k leads to an increase of output in the

same proportion k, we have constant returns to

scale. Example: If we increase the number of

machinists and machine tools each by 50%, andthe number of standard pieces produced

increases also by 50%, then we have constant

returns in machinery production.


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Least cost combination of Inputs

Firms minimize their cost of production.

It will strive to produce its output at the

lowest possible cost and thereby have

maximum amount of revenue. It applies

Perfect Competition

Monopolistic

Non profit organization.


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LeastCost Rule

To produce a given level of output at theleast cost, a firm should buy inputs until it hasequalized the marginal product spent on eachinput.

Marginal Product of L Marginal Product of A

Price of L Price of A

production function.ppt

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