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Production analysis

Production is an activity

that transforms inputs into output.

that increases consumers usability of goods andservices

Technology:

A firms production behaviour is fundamentallydetermined by the state of technology.

Existing technology sets upper limit for the production ofthe firm, irrespective of the nature of output, size of thefirm or the kind of management.

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Inputs

Time period of production

The production function:

Technological relationship which expresses the relationbetween output of a good and the different combinationsof inputs used in its production.

It indicates the maximum amount of output that can beproduced with the help of each possible combination ofinputs

Assumptions:

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1. Technology is invariant2. Firms utilizes their inputs at the maximum level of

efficiency

Short run analysis of production function1. Case of one variable input

If all factors of a firm are fixed except amount of labourservices, then any decrease or increase in output isachieved with the help of changes in the amount of labourservices used.When firm changes the amount of labour services only, italters the proportion between the fixed input and variable

input.As firm keeps on altering this proportion by changing theamount of labour, it experiences the law of variableproportion or diminishing marginal returns.

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Law of variable proportions:(Law of diminishing marginal returns)

As more and more of the factor input is employed, all otherquantities remaining constant, a point will eventually bereached where additional quantities of varying input will yielddiminishing marginal contributions to total product.

Find Marginal and Average ProductLabour Input Total product AverageProduct Marginalproduct.

1 1002 210

3 3304 4305 5206 600

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Column four shows that the marginal physical product startsdeclining from 4th unit of labour onward. If labour unit

employed beyond 10 the MPP will become zero and laterbecomes negative.

The stage from where MPP starts declining shows the law of

diminishing returns or law of variable proportions.MP begins to fall before the AP does.

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Reason: AP attributes the increase in TP equally to allthe units of the variable factor whereas the MP attributes the

increase in TO to the marginal unit of the variable factor.

If MP > AP : AP risesIf MP

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Stage2 :- Initially TPP increases more than proportionately

until X units of labour are employed; Between X units andY units of labour used, the TPP rises with every additionalunit of labour but the increase is less than proportionate( MPP and APP are declining)

Stage 3

- TPP decreasing-Additional units of labour makes MPP negative

NO firm will choose to operate in stage 1 or stage 3

In stage I MPP is rising- profitable to keep on increasing theuse of labour

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In stage III MPP is negative inadvisable to use more labour.Even if the cost of labour is zero it is not advised to use

additional labour.Stage II is the only relevant range.

Exact number of labour units hired can be found only whenthe corresponding data on wage rates is available.

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TPP MPP APP

Stage IIncreases at anIncreasing Rate Increases and

reaches itsmaximum

Increases (butslower than MPP)

Stage IIIncreases at adiminishing rate andbecomes maximum

Starts diminishingand becomes equalto zero

Starts diminishing

Stage III

Reaches itsmaximum, becomesconstant and thenstarts declining.

Keeps on decliningand becomesnegative.

Continues to

diminish butmust always begreater thanzero.

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Stage I Stage II Stage IIIFixed inputs grosslyunderutilized,specialization andteamwork causeAPP to increase

when additional X isused.

Specialization andteamwork continueand result in greateroutput whenadditional X is used,

fixed input is beingproperly utilized.

Fixed inputscapacity is reached ,additional X causesoutput to fall.

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Isoquant:

Isoquants are a geometric representation of the production function.

It is also known as the ISO PRODUCT curve.

Assuming continuous variation in the possible combination of labour andcapital, we can draw a curve by plotting all the alternative combinations for agiven level of output.

This curve which is the locus of all possible combinations is called Isoquantsor Iso-product curve.

Each Isoquants corresponds to a specific level of output and shows differentways all technologically efficient, of producing that quantity of outputs.

Different types of isoquants1. Smooth curvature2. Perfect substitutes3. Perfect compliments

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Properties of Isoquants

1. Iso-quants are downward sloping and convex to the origin.

2. Higher Isoquants show higher level of out put.

3. Isoquants do not touch the axis

4. No two iso-quants intersect each other.

5. Slope of an iso-quant indicates the rate at which factors can be

substituted for each other while a constant output is maintained.

Budget Line (Iso-cost Line):

Locus of various combinations of inputs that a producer can purchase with

his budget.

Example:Suppose the price of one unit of labour is $10 and one unit of capital is$2.5

a. Use this information to determine the iso cost equationcorresponding to a total cost of $200 and $500.

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b. Plot these two iso-cost lines on the graphc. If the price of labour falls from $10 per unit to $8 per

unit , determine the new $500 iso-cost line and plot it

on the same diagram used in part (b)

Marginal Rate of technical substitution

Marginal rate of technical substitution of labour for capital may be definedas the number of units of capital which can be replaced by one unit of

LABOUR, the level of output remaining unchanged.

MRTS of labour for capital= K/ L = SLOPE

Factor combination units of labour unit of capital MRTS of Lfor KA 1 12B 2 8C 3 5D 4 3E 5 2

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Optimal Factor combination:

Theory of production can be viewed from two angles which are dual toeach other

A firm may decide to produce a particular level of output and thenattempt to minimize the cost of inputs

OrIt may attempt to maximize its output subject to a cost constraint.

A firm spends money on two inputs say labour and capital.It decides its budget and knows the price of each of the inputs which

remains constant.

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Slope of budget line is negative

Slope of budget line is equal to the price ratio of the two inputs.The budget line of the firm has been superimposed on its isoquant map.

The firm will be at equilibrium at the point where isoquant is tangent tothe budget line AB i.e. point E

At equilibrium the firm produces on the isoquant Q2 and uses OX1 unitsof labour and OY1 units of capital

At point E,

Slope of Isoquant= Slope of budget line

Or, MRTS= ratio of prices of two inputs.

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Thus to minimize production costs ( or to maximize output for a givencost outlay), the extra output or marginal product spent on labourmust be equal to the marginal product per unit spent on capital.

Expansion Path

Economic region of production ( Ridge Lines)

Long run production function:

Situation where all inputs are subject to variation is a caseof Long period production function.

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In short period fixed inputs sets the upper limit forproduction. In long run by definition such limitations do not

exist.Let us consider labour and capital. These can change in

two ways-a.Both K and L change in same proportion ( K/L

remaining same i.e. technology remaining same)b.L and K change in different proportion ( K/L ratio or

technique of production varies with change in

output.The percentage increase in output when all inputs vary in

the same proportion is known as returns to scale.

Returns to scale relate to greater use of inputs maintainingthe same technique of production.

When returns to scale occurs , three alternative situations

are possible:1. Constant returns to scale2. Increasing returns to scale3. Decreasing returns to scale.

Units of Units of Percentag Total Percentag Returns to

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labour capital e increasein labour

andcapital

product e increasein total

product

scale

1 100 - 100 02 200 100 220 1203 300 50 350 594 400 33.33 500 42.95 500 25 625 25

6 600 20 750 207 700 16.66 860 14.668 800 14.29 940 9.39 900 12.5 1000 6.4

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Causes for increasing returns to scale

1. Specialisation2. Dimensional advantages

Causes for decreasing returns to scale1Co-ordination and control become increasingly difficult.2. Distortion of information