Managerial economics

Managerial Economics

Prepared by : - Amit Maisuriya

Stages of the law of Variable Proportions

1. Stage of Increasing Returns 2. Stage of diminishing returns 3. Stage of Negative returns : -

Addition of more and more units of variable factors are added to a fixed factor, beyond a certain point, output increases at a diminishing rate and ultimately turns out to be negative.

E.g.. Overdose of Fertilizers.

Behavioral Pattern of TP,AP,MP during 3 Stages

Stage Total Product Marginal Product Average Product

Stage – I Increases of an increasing rate

Increases and reaches its maximum

Increases, but at a lower rate than marginal product and reaches its maximum

Stage – II Increases at diminishing rate and becomes maximum

Start diminishing and become zero

Starts diminishing

Stage – III Reaches its maximum, becomes constant, and than start falling

Continues to decline and become negative

Continues to decline but not up to zero level

Conclusion

• Economic efficiency rises during stage - 1 • During 2 stage average product and marginal product

decline but total product continue to increase.• In 3 stage is ruled out as all the three outputs,

namely total product, marginal product and average product are decline marginal product becomes negative.

Return to scale

• It mean the behavior of production scale or returns when all the factors are increased or decreased simultaneously in the same proportion.

• The percentage or proportionate increase in output when all inputs are changed in the same proportion is known as return to scale.

• Return to scale due to the increase in the scale of operations namely increase in size, additional technical and management personnel.

Phases of return to scale

1. Increasing returns to scale: - Indivisibility of the factors Division of labor leading to specialization Dimensional economics2. Constant return to scale:-

Increase in same proportion as increase in input.

3. Diminishing returns to scale: - Out put increase in smaller

proportion than increase in all inputs.

Internal Economies They arise within or inside the firm They arise due to improvement in internal factors They arise due to specific efforts of one firm They are particular to a firm an enjoyed by only one firm They arise due to an increase in the scale of production. They are dependent on the size of the firm They can be effectively controlled by the management of

a firm They are called as “ Business Secrets” of a firm.

External Economies

• The following imp. Aspects of external economies…1. They arise out side the firm2. They arise due to improvements in external factors3. They arise due to collective efforts of an industry4. They are general, common and enjoyed by all firms5. They arise due to over all development expansion and

growth of an industry or a region.6. They are dependent on the size of industry7. They are beyond the control of management of the firm8. They are called as open secrets of the firm.

Production function with two variable Inputs

• In this chapter, we shall study production function when two factors are taken as variables factors and which are substitutes for each other.

• This technique is known as iso-quants or iso-product curve which are similar to indifference curve technique of the theory of consumption.

What are Iso-quants? An Iso-quants may be defined as a curve representing various

combinations of two inputs that produce the same level of output.

An iso-quant is also known as an iso-product curve or an equal product curve or production indifference curve.

On an indifference curve shows the same level of satisfaction to the consumer

Similarly every point on an iso-quant would indicate the same amount of output.

“An Iso-quants may be defined as a curve which shows the different combinations of the two inputs producing the same level of output.”

Illustration of iso-quant with the help of table and curve

Combination Units of labour

Units of Capital

Total output (in units)

A 1 12 100

B 2 8 100

C 3 5 100

D 4 3 100

E 5 2 100

Iso-quant Schedule

Iso-quant curve

1 2 3 4 50

2

4

6

8

10

12

14

ISO-QUANT

UNITS OF CAPITAL

A

B

C

DE

CAPITAL

LABOUR

Iso-quant Map

An iso-quant map is a set of iso-quants representing different levels of output.

A higher iso-quant indicates higher level of output.

Iso-quant map

100120

140

Iso-quant map

An Iso-quant map is a set of iso-quant representing different levels of output. A higher iso-quant indicates higher level of output.

Each combination on the same iso-quant gives the same level of out put.

however a higher iso-quant represent higher level of output.

Types of Iso-quant

• Iso-quant may be different shapes depending on the degree of elasticity of substitutability of inputs.

1. Linear iso-quant 2. Input output iso-quant3. Kinked iso-quant4. Smooth convex iso-quant

Linear iso-quant

Q1 Q2 Q3

Natural Gas

Diesel

Electrical Power

y

X

Linear iso-quant

• This type of iso-quant assumes perfect substitutability between different factors of production. Thus, for example, a given output, say 100 units, may be produced by using only labour capital. The shape of such an iso-quant shall as on the left side.

Input output iso-quants

iso-quantsUNITOFCAPITAl

Units of labor

Zero Substitutability

This type of Iso-Quant assumes perfect complementary or zero substitutability between the inputs. When there is only one method of production for any product, its Iso-quant is of right-angled shape. This type of iso-quant is also known as Leontief iso-quant.

Kinked Iso-Quant

A1A2

A3

A4

Iso-quant UNITOFCAPITAl

Units of labor

Linear Programming Iso-Quant

• This is also known as linear programming iso-quant. • It assumes limited substitutability of labour and capital.• As there are only a few processes which are available for producing any commodity ( say A1, A2, A3, A4) substitutability of factors is possible only at kinks. This can be illustrated as on the left side.

Smooth Convex Iso-QuantConvex Iso-Quant

UNITOFCAPITAl

Units of labor

Imperfect substitutability

X

Y It assumes continuous substitutability of labour and capital only over a certain range, beyond which factors cannot be substituted for each other. This iso-quant appears as a smooth curve convex to origin.

Marginal Rate of Technical substitution

• The Principles of marginal rate of technical substitution is based on the production function where two factors can be substituted in Variable proportions in such a way as to produce a constant level of output.

• Marginal rate of technical substitution indicates the rate at which factors can be substituted at the margin without any change in the level of output.

Conti…

• For Example.. The marginal rate of technical substitution of labour for capital is the number of units of capital which can be replaced by one unit of labour without changing the level of output.

• The concept of marginal of technical substitution can be easily understood from the table given below

Marginal rate of technical substitution

Factor Combination Units of Labour Units of Capital Marginal rate of technical substitution of labour for capital

A 1 12 --

B 2 8 4:1

C 3 5 3:1

D 4 3 2:1

E 5 2 1:1

Conti… It will be seen from the above table that the marginal rate

of technical substitution shows a decline. E.G. In factor combination B, 4 units of capital can be

replaced by 1 unit of labour without change in output. So, 4:1 is the marginal rate of technical substitution at this

stage. In factor combination c, 3 units of capital can be replaced

by 1 unit of labour without any loss of output and as such the marginal rate of technical substitution is 3:1.

Similarly, the marginal rate of technical substitution for combinations D and E is 2:1 and 1:1 respectively.

Conti…

Marginal rate of Technical Substitution = Labour Units

Capital Units

Conti..

A

B

cD

E

UNITOFCAPITAl

Units of labor

Iso-Quant

A small movement downwards the iso-quant curve from A to B in the figure given below say K is substituted by an amount of labour say L without any loss of output. The slope of the iso-quant curve Q1 at point A, Therefore, equal to K

L

Conti…

UNITOFCAPITAl

Units of labor

The marginal rate of technical substitution is equal to the ratio of a marginal physical products of the two factors. since the definition, output remains the same on an iso-quant curve, the loss in physical output from a small reduction in units of capital will be equal to the gain in physical output from increase in the units of labour. Thus, the loss in output is equal to the marginal physical product of capital multiplied by the amount of reduction in capital. likewise, the gain in output is equal to the marginal physical product of labour multiplied by increase in labour.

MRTS = K = MPL

L MPk

Why the marginal rate of technical substitution diminishes?

• It will be seen from the above table and diagram that the marginal rate of technical substitution diminishes and this is its one important feature.

• in other words, a salient characteristic of the marginal rate of technical substitution is that it diminishes as more and more units of labour are substituted for capital.

• Thus, as the quantity of labour used is increased and the quantity of a capital employed decreased,

• The units of capital that are required to be substituted by an additional unit of labour diminishes.

• This is known as the principle of diminishing marginal rate of technical substitution

• As a more and more units of labour are used to compensate for the loss of the units of capital to maintain the same level of out put.

Conti…

• The marginal physical productivity of labour diminishes and the marginal physical productivity of capital increases and therefore less and less units of capital will be required to replace one units of labour to maintain the same level of output.

• Thus, the marginal rate of technical substitution diminishes as labour is substituted for capital.

• It means that the iso-quant must be convex to the origin at every point.

Properties of Iso-quants

1. An Iso-Quant curve like a an indifference curve is a downward sloping curve towards the right

2. A Higher Iso-Quant represents large output3. No two Iso-Quant can intersect each other4. Iso-Quant are convex to the origin5. In between two iso-quants there may be

number of iso-quants6. Units of output shown on iso-quant are purely

arbitrary

An Iso-Quant curve like a an indifference curve is a downward sloping curve towards the right

• That means, it has a negative slope.• This implies that if more of one factor is used,

less of other factor is needed for producing the same output.

• Thus, when the quantity of say labour is increased, the quantity of other factor , say capital must be reduce so as to keep the output constant on a given iso-quant.

Conti…• The downward slope of an iso-quant follows from a valid assumption

that the marginal physical products of factors are positive, that is, the use of additional units of a factors give positive increments in output.

• And so, when one factor is increased yielding positive marginal products, the other factor must be reduced to hold the level of output constant or else the total output will increase and we will be switching over to a higher iso-quant.

• It would be interesting to note here that if iso-quants do not have a negative slope, certain logical absurdities would follow.

• Thus for example, if the iso-quant slops upwards to the right • This means that inspite of having used more units of both labour and

capital, the total output remains the same which is just not ppossible.

Conti…

• In this diagram factor combination T on the iso-quant curve shows more units of both labour and capital and therefore, it will give more output than combination P where less units of labour and capital are used.• As such, point P and T on the iso-quant curve cannot indicate equal product.• As said earlier, every point on iso-quant curve shows the same level of output.• An upward sloping iso-quant curve cannot indicate the same level of output.

Conti..

• Likewise, Suppose iso-quant of labour is combined with more units of capital or less units of capital; in that case iso-quant cannot be a constant product curve.

Conti…

• Similarly, if iso-quant is horizontal to x-axis which means that a given amount of capital is combined with more units of labour or less units of labour; and in this case too iso-quant cannot be a constant product curve.• The iso-quant curve, therefore, cannot be equal product curve.• From the above discussion, it would be clear that iso-quant curve must slope downwards to right.

The higher iso-quant represents large output

That is, higher the iso-quant, Greater the output and vice versa.

In the diagram the combination T on iso quant curve, shows large output (200 units) than point P on iso-quant curve (100 units). Thus, the combination of OA capital and OB of labour produces 100 units o output, while OC units of capital and OD units of lobar produce 200 units. As such IQ1 which lies above IQ2 to the right represents a large level of output.

No two iso-quant can intersect each other

if two iso-quant intersect of touch each other, this means that there will be a common point on the two curve as shown in the diagram. This implies that the same factor combination.(labour and capital) which can produce say 100 units of output at one iso-quant can also produce 150 units of output at the other iso-quant. This is quite absurd because the same factor combination cannot produce two different of output.

Iso-Quant are convex to the origin The convexity of an iso-quant curve implies that the slope of the iso-quant curve moves downwards from let to right along the curve. thus, foe example, as more and more units of labour are employed to produce 100 unites of the product, lesser and lesser units of capital are used. this is because the marginal rate of technical substitution between two factors diminishes.

In between two iso-quants there may be a number of iso-quants

• it showing various levels of output which the combination of two factors can give.

• Thus, for example in between 100 units and 200 units of output shown on IQ and IQ1 respectively ,

• There may be iso-quant showing 120,135,150,175 units of output.

Units of output shown on iso-quant are purely arbitrary

• Thus, for example the various units of output like 100,150,220,300 etc. shown on isoquant map are arbitrary.

• Instead of these units any other number of units of output say like 10,25,35,45, or 1000,1500,2000 etc. can also be assumed.

Difference between iso-quant and Indifference curve

• As said earlier, iso-quants are very much similar to indifference curves of the theory of demand in the sense that :

1. Just as indifference curves assume two commodities, iso-quant also consider two factors or inputs, say like labour capital

2. All points or combinations on indifference curve show equal level of satisfaction to the consumer, likewise all combination on an iso-quant show equal level of production.

3. The main properties of indifference curve are also similar to the properties of iso-quants.

However, there are certain difference also between these two techniques:

1) An indifference curve indicates satisfaction to consume, which however, cannot be measured in physical units, while in the case of an iso-quant the product can be measured in physical units.

2) in difference map only indicates that a higher indifference curve gives more satisfaction than a lower one; but it does not say how much more or how much less satisfaction the consumer would derive. On the other hand, in the case of an iso-quant map one can say how much output is more on an iso-quant as compared to lower iso-quant.

3) As satisfaction on indifference curves cannot be measured In physical units, we give arbitrary numbers say like 1,2,3,4 etc on the other hand, on iso-quants we can indicates physical units say like 100,200,250,300 etc. to indicate the level of output to which each curve corresponds.

Iso-Cost Curve• Having discussed the properties of iso-quants, we turn to the prices of

the two inputs as represented on the iso-quant map by the iso-cost curves.

• As iso-cost curve is also known as the price line or outlay line showing the price of the actor in terms of another factor.

• each iso-cost curve represents the different combination of two inputs which a firm can buy for a given amount of money at the given price of each input.

• In other words, the iso-cost curves represent the locus of all combination of the two input factors which result in the same total cost.

• E.G. if the unit cost of labour (L) is P and the unit cost of a capital C is q, then the ,

Total cost (TC) = pL + qC

Iso-cost line • The combination of the factors , say labour and capital – with

which a firm produces a given output depends on the prices of the factors and the amount of money which a firm is willing to spend.

• An iso-quant line indicates the prices of factors and the total sum of money which a firm wants to spend.

• Each iso-quant line shows various combination of two inputs which can be purchased with a given amount of money.

• An iso-quant line may, therefore, be defined as the locus of various combinations of factors which a firm can buy with a constant outlay.

• As said earlier , the iso-quant is also known as price line or outlay line.

Conti…

• E.G. A firm has Rs. 1000/- to spend and the price per unit of a labour and capital is Rs. 50/- and Rs. 100/- respectively.

• Now, if the firm spends the entire amount on labour it has a combination of 20 units of labour + Zero (0) capital.

• Alternatively, if it spend the entire amount on capital its has a combination of zero (0) labour + 10 units of capital.

• There are many possible combination of these two factors representing equal expenditure.

Conti…

Combination Units of Labour

Units of Capital

Total expenditure

A 20 +

0 Rs. 1000-00

B 10 +

5 Rs. 1000-00

C 00 +

10 Rs. 1000-00

Conti… in this diagram plotting the points. A,B,C etc. we get a line AC which is budget line or an iso-cost line. every point on the budget line iso-cost curve shows the same amount of expenditure. if the total outlay ( expenditure) of the firm and the prices of the two factors are given . an iso-cost curve indicates all possible combinations of the two factors which the firm can have. Clearly the budget line or an iso-cost is the counter-part of the price-line in indifference curve analysis.

Conti… Now, if the firm decides to increase the total expenditure on two factors to Rs. 2000/- it can purchase more of both the factor. Thus, as a result of the increase in total outlay to Rs. 2000/- the iso-cost line will shift towards the right. Likewise, with a total outlay being increased to Rs. 3000/- the iso-cost line will further move to the right. The diagram on the left side shows the shift in iso-cost line from AB to CD TO EF resulting from increase in outlay or total cost.The slope of the iso-cost line is the ratio of the price of a unit of labour to the price of unit of capital. in case, the price of any of the input changes, ,there would be corresponding changes In the iso-cost curve and the equilibrium position too would shift.

Least Cost - Combination of Factors

The firm tries to attain equilibrium position by working for the most economical or least cost combination of the factors of production.

Just as a consumer when faced with making a choice between different combination of two commodities aims at achieving maximum profits.

And for this purpose, the firm has to choose the factor combination in a most economic or optimum manner, that is, the firm would try to attain least cost combination of the factorof production.

Conti…

• In other words, it may be said that in order to produce a given output, there are various combinations of the factors of production and the firm

• Naturally would choose that combination of factors which minimizes its cost of production, for only then that the firm can get maximum profits.

• Thus, the firm will try to produce a given level of output with least cost combination of factors.

• This least cost combination will be the optimum point for the firm.

Returns to scale: Iso-Quant• Return to scale, i.e. increase in scale of operation of the firm• we have to vary not only the variable factor (s) but also fixed factor (s).• if all factors are increased in same proportion and output increase in

the same proportion,• we have a case of constant returns to scale • If output increases more than proportionately • we have a case of increasing returns to scale and• If output increases less than proportionately, we have a case of

diminishing returns to scale.• when increasing returns to scale are available , the firm is realizing

certain advantages of large scale operation; in the opposite case there are disadvantages.

Conti…

• When advantages and disadvantages of scale are balanced, there are constant returns to scale.

• This can be explained by the technique of iso-quants.• An iso-quant is an equal quantity curve on which all

points show the same level of output.• A higher iso-quant shows the higher level of output and

lower level iso-quant lower level of output.• In the diagram IQ1,IQ2,IQ3 etc. are iso-quants, showing

for example, 1000 units, 2000 units, and 3000 units of output.

• Line OP shows the output at different levels on various iso-quant curves.

Increasing Returns to Scale

IN Figure. MN<LM, which means that with less increase in inputs, same quantity of output can be achieved In other words, of factors of production are doubled the output will be more than doubled. The returns to scale increase. The firm enjoys increasing returns to scale

Diminishing Returns To Scale

In figure. OP is the scale line. In this case MN>LM Which shows that the inputs, are rising faster, but the increase in output is the same. In other words, the doubling factors will result in less than double the amount of output.

Constant Returns to Scale

If the factor of the production vary in the same proportion and output also varies in the same proportion, there are constant returns to scale. in Figure MN = LM indicating that increase in input is the same at every stage , and the consequent increase in output is in, the same proportion. Thus, if the factors are doubled output also is doubled. This is known as the operation of the lay of constant returns.

Conti…

• If may be noted that increasing returns to scale are due to internal economies accruing to the firm on account of increase in the scale of operation of the firm.

• diminishing returns are due to internal diseconomies which is nothing but increasing inefficiency in operation beyond and optimum size of the firm.

• Similarly, if internal economies and diseconomies are balanced, we have a case of operation if constant returns to scale.

Expansion Path

The indifference curve analysis and the Iso-quant/iso-cost analysis come to identical conclusions.

A consumer attains equilibrium when the marginal ratio of substitution between two commodities is equal to the price of the two commodities.

Similarly, the firm attains equilibrium when Marginal rate of technical substitution between two factors is equal to the price ratio of the two factors.

This is the condition of equilibrium of a consumer and firm.

Conti… Now let us explain the expansion path of a firm with the help of iso-

quant/iso-cost curves. “ Expansion Path is a line or a curve on which every point is an

equilibrium point i.e. minimum cost combination of two factors at various level of output.

As the firm tries to expand its output, it will try to see that it attains equilibrium at the lowest cost at that output.

This is nothing but the concept of minimizing cost an maximizing profit.

we assume that the prices of two factors are given and the map of iso-quants (i.e., equal quantity curves) is also given.

Each higher iso-cost line shows higher level of cost (i.e. outlay) but the prices of two variable factors (i.e. X and Y or labour & Capital) remain constant.

Conti…

The between iso-cost and iso-quant indicates equilibrium which shifts as the firm moves form lower to higher level of production.

A firm receiving maximum profit will produce at one or the other point on expansion path, because any other point, outside will mean less than maximum profit.

Conti… In this above diagram, iso-quants are given as IQ1, IQ2, IQ3 etc. and iso-costs are presented as AB, CD, EF etc. The slopes of iso-costs are constant because the prices of two factors remain constant. Iso-quants are indicated by figures 100,200,300 etc. points P,Q and R show equilibrium positions of the firm at different level of output. As the firm expands its output, the combination of factors will change as indicated by points on the expansion path. it may be noted here that the expansion path shown above is based on the assumption that the prices of two factors remain constant . if the price of any one factor changes or if both the prices change, in different proportions The expansion path too will change. Here the shape of expansion is not necessarily the same shown above.

Conti..

similarly, if the iso-quants are more or less convex to the origin than what they are shown In the above diagram

the tangency points will change and hence the expansion path too will change.

The shape of iso-quants depend on the degree of substitutability or complementarities between the two factors.

Economic Region and Ridge - Lines

We are familiar with the shape of a an iso-quant.

it is generally convex to the origin But there may be exceptional iso-quant,

which may bend backwards at the upper end and slope upwards at the lower end.

As shown beside …..

Conti… In this diagram iso-quant is abnormal beyond A1 and B1. Between these two points it is normal i.e. convex toe the origin. the firm will produce only between A1 and B1. If the firm uses more of both the factors, it will produce less than the output indicated by the IQ1 i.e. 100 Units.

Conti… In this diagram we have different iso-quants indicating different levels of output. In this diagram OA and OB are called Ridge lines. Ridge lines show the limits within which the firm will operate for production because outside the ridge lines, production will be uneconomic. It may be noted that the area within the ridge lines is the area wherein the iso-quant are normal i.e. convex to the origin. outside his area, the iso-quants are not convex the area between the ridge lines i.e. OA and OB is called the economic region. In the economic region, certain units of labour and capital can be employed to produce 100,200,300 units as shown by respective iso-quants. Any point out side the economic region is called uneconomic because less output will be produced by a combination of two factors one o=r both of which are more than required for production.

Conti…

This is clearly waste and therefore the firm will always try to remain in the economic region which lies within the two Ridge-lines.

Obviously the firm will not produce at any point above OA or below OB lines.

The above analysis shows relevance of that portion of the iso-quants which the firm would always like to keep in mind while taking production decisions.