managerial economics | unit 2

Managerial Economics

1

Session I

Demand: Concept and Types2

The process to satisfy human wants/ needs/desires.Want: having a strong desire for somethingNeed: lack of means of subsistenceDesire: an aspiration to acquire something

Demand: effective desireDemand is that desire which backed by willingness and ability to buy a particular commodity. Things necessary for demand:TimePrice of the commodity Amount (or quantity) of the commodity consumers are willing to purchase at the price

3

Type

s of

Dem

and

Direct or Autonomous and Derived DemandDirect demand is for the goods as they are such as Consumer goodsDerived demand is for the goods which are demanded to produce some other

commodities; e.g. Capital goodsRecurring and Replacement DemandRecurring demand is for goods which are consumed at frequent intervals such

as food items, clothes.Durables are purchased to be used for a long period of time

4

Type

s of

Dem

and

Complementary and Competing DemandSome goods are jointly demanded hence are complementary in

nature, e.g. software and hardware, car and petrol.Some goods compete with each other for demand because they are

substitutes to each other, e.g. soft drinks and juices.Demand for Perishable and Durable Goods Durables: Last for a relatively long time and can be consumed

multiple times Demand can be postponed

Non-durables: Perishable, Non-perishable.Individual and Market DemandIndividual demand: Demand for an individual consumerMarket demand: Demand by all consumers

5

Session II Demand: Determinants6

Det

erm

inan

ts o

f Dem

and

Price of the product Single most important determinantNegative effect on demand

Income of the consumer Normal goods: demand increases with increase in consumer’s income Inferior goods: demand falls as income rises

Price of related goods Substitutes If the price of a commodity increases, demand for its substitute rises.

Complements If the price of a commodity increases, quantity demanded of its complement falls.

7

Det

erm

inan

ts o

f Dem

and

Tastes and preferencesVery significant in case of consumer goods

Expectation of future price changes Gives rise to tendency of hoarding of durable goods

PopulationSize, composition and distribution of population will influence demand

AdvertisingVery important in case of competitive markets

Contd…

8

Session III Demand: Function9

Dem

and

Func

tion

Interdependence between demand for a product and its determinants can be shown in a mathematical functional form

Dx = f(Px, Y, Py, T, A, N) …….. [Multivariate fx] Independent variables: Px, Y, Py, T, A, N Dependent variable: Dx

Px: Price of x Y: Income of consumerPy: Price of other commodityT: Taste and preference of consumerA: AdvertisementN: Macro variable like inflation, population growth, economic growth

10

Law

of D

eman

d A special case of demand function which shows relation between price and demand of the commodity

Dx = f(Px) Dx = f(Px)

Reasons Substitution Effect Income Effect

11

Dem

and

Sch

edul

e an

d In

divi

dual

D

eman

d C

urve

Point on Demand Curve

Price (Rs per cup)

Demand (‘000 cups)

a 15 50b 20 40c 25 30d 30 20e 35 10

e

b

a

c

10 20 30

15

20

30

35

5040

25

Quantity of coffee

Pric

e of

Cof

fee

O

d

12

Mar

ket D

eman

dMarket: interaction between sellers and buyers of a good (or service) at a mutually agreed upon price.

Market demand Sum total of the quantities of a commodity that all buyers in the market are

willing to buy at a given price and at a particular point of time (ceteris paribus)

Market demand curve: horizontal summation of individual demand curves

13

Session IVShifting Demand & Exceptions 14

Change in DemandOr Demand Shifting

D1

D2

D0

Price

Quantity0

Shift in demand curve from D0 to D1 More is demanded at same price

(Q1>Q)

Increase in demand caused by: A rise in the price of a substitute A fall in the price of a complement A rise in income A change in tastes that favours the

commodity

Shift in demand curve from D0 to D2 Less is demanded at each price (Q2<Q)

P

Q1QQ2

15

Exc

eptio

ns to

the

Law

of D

eman

d

Law of demand may not operate due to the following reasons: Giffen Goods: Sir Robert Giffen, IrelandSnob Appeal: Veblen Goods, Thorstein VeblenDemonstration Effect: FashionFuture Expectation of Prices (Panic buying)AddictionNeutral goods Life saving drugsSalt

16

Goods with no substituteAmount of income spent

Match box

Session V Elasticity of Demand17

Elas

ticity

of D

eman

d “Elasticity” is a standard measure of the degree of responsiveness (or sensitivity) of one variable to changes in another variable.

price of the commodity, price of the other commodities, income, taste, preferences of the consumer and other factors.

Elasticity of Demand

Mathematically, it is the percentage change in quantity demanded of a commodity to a percentage change in any of the (independent) variables that determine demand for the commodity.

Four major types of elasticity:◦ Price elasticity,

◦ Income elasticity,

◦ Cross elasticity

◦ Advertising (or promotional) elasticity.

ceteris paribus

Price Elasticity of Demand

Price is most important among all the independent variables that affect the demand for any commodity.

Hence price elasticity of demand (“ep”) is considered to be the most important of all types of elasticity of demand.

Perfectly elastic demand ep=∞ (in absolute terms). Horizontal demand curve Unlimited quantities of the commodity can be sold at the prevailing price

A negligible increase in price would result in zero quantity demanded

Perfectly inelastic demand ep=0 (in absolute terms) Vertical demand curve Quantity demanded of a commodity remains the same, irrespective of any change in the price

Such goods are termed neutral.

Degrees of Price Elasticity Price

Quantity O

P D

Q1 Q2

Price

Quantity O

P1

P2

D

Q1

Degrees of Price ElasticityHighly elastic demand

Proportionate change in quantity demanded is more than a given change in price

ep >1 (in absolute terms) Demand curve is flatter

Unitary elastic demand Proportionate change in price brings about an equal proportionate change in quantity demanded

ep =1 (in absolute terms). Demand curves are shaped like a rectangular hyperbola, asymptotic to the axes

Relatively inelastic demand Proportionate change in quantity demanded is less than a proportionate change in price

ep <1 (in absolute terms) | Demand curve is steep

Price

Quantity O

D

D

Q2

P2

Q1

P1

Price

Quantity O

D

D

Q1

P1

Q2

P2

Price

Quantity O

Q1

P1

Q2

P2

D

D

Contd.

Ratio (or Percentage) Method◦ The most popular method used to measure elasticity◦ Elasticity of demand is expressed as the ratio of proportionate change

in quantity demanded and proportionate change in the price of the commodity

◦ It allows comparison of changes in two qualitatively different variables◦ It helps in deciding how big a change in price or quantity is

ep=

◦ where Q1= original quantity demanded, Q2= new quantity demanded, P1= original price level, P2= new price level

Met

hods

of M

easu

ring

Elas

ticity

Xcommodity of pricein change ateProportionXcommodity of demandedquantity in change ateProportion=ep

112

112

/)(/)(PPPQQQ

Point Elasticity Method◦ Elasticity measured at a point of demand curve is referred as point

elasticity of demand.

For nonlinear demand curve we need to apply calculus to calculate point elasticity. As changes in price become smaller and approach zero, the ratio becomes equivalent to the first order derivative of the demand function with respect to price

Point elasticity can be expressed as:

ep = =

PdPQdQ

//

dPdQ

QP.

dPdQ

PQ

Met

hods

of M

easu

ring

Ela

stic

ity

Arc Elasticity Method ◦ Used when the available figures on price and quantity

are discrete, and it is possible to isolate and calculate the incremental changes.

◦ It is used to find the elasticity at the midpoint of an arc between any two points on a demand curve, by taking the average of the prices and quantities.

◦ This method finds wider applications, as it reflects a movement along a portion (arc) of a demand curve

ep = /

=

2/)( 21

12

QQQQ

2/)( 21

12

PPPP

21

12

QQQQ

.

12

21

PPPP

Met

hods

of M

easu

ring

Ela

stic

ity

Total Outlay Method (Marshall)

◦ Elasticity is measured by comparing expenditure levels before and after any change in price, i.e. whether the new expenditure is more than, or less than, or equal to the initial expenditure level.

◦ Helps a seller in taking a decision to raise price only if:◦ Reduction in quantity demanded does not reduce total revenue or◦ Reduction in price increases the quantity demanded to the extent that total revenue also increases.

◦ Degrees◦ When demand is elastic, a decrease in price will result in an increase in the revenue (sales).◦ When demand is inelastic, a decrease in price will result in a decrease in the revenue (sales).◦ When demand is unit-elastic, an increase (or a decrease) in price will not change the revenue (sales)

Met

hods

of M

easu

ring

Ela

stic

ity

Nature of commodity ◦ Necessities are relatively price inelastic, while luxuries are relatively

price elastic

Availability and proximity of substitutes ◦ Price elasticity of demand of a brand of a product would be quite

high, given availability of other substitute brands

Alternative uses of the commodity◦ If a commodity can be put to more than one use, it would be

relatively price elastic

Determinants of Price Elasticity of Demand

Proportion of income spent on the commodity◦ The greater the proportion of income spent on a commodity, the more sensitive would the

commodity be to price◦ Reason is income effect

Time◦ Demand for any commodity is more price elastic in the long run

Durability of the commodity◦ Perishable commodities like eatables are relatively price inelastic in comparison to durable

items

Items of addiction◦ Items of intoxication and addiction are relatively price inelastic

Determinants of Price Elasticity of Demand

Revenue and Price Elasticity of Demand

For relatively inelastic demand, a change in price would have a greater effect on revenue than a change in quantity demanded AR is same as the price of the product

◦Demand curve is also the AR curve of the firm. Marginal Revenue is the revenue a firm gains in producing one additional unit of a commodity

Till ep>1 MR is positive and TR is rising At the midpoint of the demand curve, ep=1 and MR is equal to 0 and TR is at its peak When ep<1, MR is negative and TR is falling. MR= AR [1- MR= AR [1- eepp] ]

TR

Price, Revenue

OQuantity

MR

Revenue and Price Elasticity of Demand

Income Elasticity of Demand (ey) ey measures the degree of responsiveness of demand for a good to a given change in income, ceteris paribus.

Degrees:◦ Positive income elasticity

◦ Demand rises as income rises and vice versa◦ Normal good

◦ Negative income elasticity◦ Demand falls as income rises and vice versa◦ Inferior good

consumer of incomein change ateProportionXcommodity of demandedquantity in change ateProportion=ey

Y1)/Y1-(Y2Q1)/Q1-(Q2=ey

Zero income elasticityNo impact of incomeNeutral good

Cross Elasticity of Demand ec measures the responsiveness of demand of one good to changes in the price of a related good

Degrees◦ Negative Cross Elasticity◦ Complementary goods

◦ Positive Cross Elasticity ◦ Substitute goods

Ycommodity of pricein change ateProportionXcommodity of demandedquantity in change ateProportion=ec

Promotional/Advertising Elasticity of Demand

Advertising (or promotional) elasticity of demand (ea) measures the effect of incurring an “expenditure” on advertising, vis-à-vis an increase in demand, ceteris paribus. Some goods (like consumer goods) are more responsive to advertising than others (like heavy capital equipment).

Degrees◦ea>1 | Firm should go for heavy expenditure on advertisement. ◦ea <1 | Firm should not spend too much on advertisement

X of eexpenditur gadvertisinin change ateProportionXcommodity of sales)(or demandedquantity in change ateProportion=ea

Importance of Elasticity

Determination of price◦ Elasticity is the basis of determining the price of a product keeping its possible effects on the

demand of the product in perspective

Basis of price discrimination◦ Products having elastic demand may be sold at lower price, while those having inelastic

demand may be sold at high prices

Determination of rewards of factors of production◦ Factors having inelastic demand are rewarded more than factors that have relatively elastic

demand.

Government policies of taxation◦ Goods having relatively elastic demand are taxed less than those having relatively inelastic

demand.

Session VIDemand Forecasting

35

“An estimate of sales in dollars or physical units for a specified future period under a proposed marketing plan.”

- American Marketing Association

Demand forecasting is the scientific and analytical estimation of demand for a product (service) for a particular period of time. It is the process of determining how much of what products is needed when and where.

Meaning of Demand Forecasting

Categorization of Demand Forecasting

By Level of Forecasting Firm (Micro) level: forecasting of demand for its product by an individual firm.

◦ decisions related to production and marketing. Industry level: for a product in an industry as a whole.

◦ insight in growth pattern of the industry ◦ in identifying the life cycle stage of the product ◦ relative contribution of the industry in national income.

Economy (Macro) level: forecasting of aggregate demand (or output) in the economy as a whole. ◦ helps in various policy formulations at government level.

Categorization of Demand Forecasting

By nature of goods Capital Goods: Derived demand

◦demand for capital goods depends upon demand of consumer goods which they can produce.

Consumer Goods: Direct demand◦durable consumer goods: new demand or replacement demand◦Non durable consumer goods: FMCG

Techniques of Demand Forecasting Subjective (Qualitative) methods: rely on human judgment and opinion.◦ Buyers’ Opinion◦ Sales Force Composite◦ Market Simulation◦ Test Marketing◦ Experts’ Opinion

◦ Group Discussion◦ Delphi Method

Quantitative methods: use mathematical or simulation models based on historical demand or relationships between variables.Trend ProjectionSmoothing TechniquesBarometric techniquesEconometric

techniques

Subjective Methods of Demand Forecasting

Consumers’ Opinion Survey Buyers are asked about future buying intentions of products, brand preferences and quantities of purchase, response to an increase in the price, or an implied comparison with competitor’s products. ◦ Census Method: Involves contacting each and every buyer◦ Sample Method: Involves only representative sample of buyers

Merits◦ Simple to administer and comprehend.◦ Suitable when no past data available.◦ Suitable for short term decisions regarding product and promotion.

Demerits• Expensive both in terms of resources and time.• Buyers may give incorrect responses.


Sales Force Composite Salespersons are in direct contact with the customers. Salespersons are asked about estimated sales targets in their respective sales territories in a given period of time.

Merits◦ Cost effective as no additional cost is incurred on collection of data.◦ Estimated figures are more reliable, as they are based on the notions of salespersons in

direct contact with their customers.

Demerits◦ Results may be conditioned by the bias of optimism (or pessimism) of salespersons.◦ Salespersons may be unaware of the economic environment of the business and may

make wrong estimates.◦ This method is ideal for short term and not for long term forecasting

Contd…


Experts’ Opinion Methodi) Group Discussion: (developed by Osborn in 1953) Decisions may be taken with the help of brainstorming sessions or by structured discussions.

ii) Delphi Technique: developed by the Rand Corporation at the beginning of the Cold War, to forecast impact of technology on warfare. ◦ Way of getting repeated opinion of experts without their face to face interaction. ◦ Consolidated opinions of experts is sent for revised views till conclusions converge on a point.

Merits◦ Decisions are enriched with the experience of competent experts.◦ Firm need not spend time, resources in collection of data by survey.◦ Very useful when product is absolutely new to all the markets.

Demerits◦ Experts’ may involve some amount of bias.◦ With external experts, risk of loss of confidential information to rival firms.

Contd…


Market Simulation Firms create “artificial market”, consumers are instructed to shop with some money. “Laboratory experiment” ascertains consumers’ reactions to changes in price, packaging, and even location of the product in the shop. ◦ Grabor-Granger test (1960s)

Merits◦ Market experiments provide information on consumer behaviour regarding a change in

any of the determinants of demand.◦ Experiments are very useful in case of an absolutely new product.

Demerits◦ People behave differently when they are being observed.

Contd…..


Test Marketing Involves real markets in which consumers actually buy a product without the consciousness of being observed.

Product is actually sold in certain segments of the market, regarded as the “test market”. Choice and number of test market(s) and duration of test are very crucial to the success of the results.

Merits◦ Most reliable among qualitative methods.◦ Very suitable for new products. ◦ Considered less risky than launching the product across a wide region.

Demerits ◦ Very costly as it requires actual production of the product, and in event of failure of the product the entire cost of

test is sunk.◦ Time consuming to observe the actual buying pattern of consumers.

Contd….

Quantitative Methods of Demand Forecasting

Trend ProjectionStatistical tool to predict future values of a variable on the basis of time series data.

Time series data are composed of:◦ Secular trend (T): change occurring consistently over a long time and is relatively

smooth in its path. ◦ Seasonal trend (S): seasonal variations of the data within a year ◦ Cyclical trend (C): cyclical movement in the demand for a product that may have a

tendency to recur in a few years◦ Random events (R): have no trend of occurrence hence they create random

variation in the series.

Quantitative Methods: Methods of Trend Projection

Graphical method◦ Past values of the variable on vertical axis and time on horizontal axis and line is plotted. ◦ Movement of the series is assessed and future values of the variable are forecasted◦ simple but provides a general indication and fails to predict future value of demand

020406080

100120140160180200

2001 2002 2003 2004 2005

Year

Dem

and

for m

obile

s (in

lakh

s)

Contd…

Quantitative Methods : Smoothing Techniques

Moving Average: forecasts on the basis of demand values during the recent past.

Dn= where Di= demand in the ith period, n= number of periods in the moving average

Weighted Moving Average: forecast the future value of sales on the basis of weights given to the most recent observations. The formula for computing weighted moving average is given as:

Dn= where Di= demand in the ith period, wi= weight for the ith period, n= number of periods in the

moving average.

n

Dn

ii

1

n

iiiDw

1

Quantitative Methods : Smoothing Techniques

Exponential Smoothing: assign greater weights to the most recent data, in order to have a more realistic estimate of the fluctuations. Weights usually lay between zero and one

Ft+1=aDt+(1-a)Ft

where Ft+1= forecast for the next period, Dt=actual demand in the present period, Ft=previously determined forecast for the present period, and a=weighting factor, termed as smoothing constant.

New forecast equals old forecast plus an adjustment for the error that had occurred in the last forecast

Ft+1=aDt+ a(1-a)Dt-1+ a(1-a)2Dt-2+ a(1-a)3Dt-3+...+a(1-a)t-1D1+ a(1-a)2Dt-2+ a(1-a)tF1)

Contd…

Quantitative Methods : Barometric Techniques

Barometric Technique alerts businesses to changes in the overall economic conditions.

Helps in predicting future trends on the basis of index of relevant economic indicators especially when the past data do not show a clear tendency of movement in a particular direction.

Indicators may be◦ Leading indicators: economic series that typically go up or down ahead of

other series

◦ Coincident indicators: move up or down simultaneously with the level of economic activities

◦ Lagging series : which moves with economic series after a time lag.

Contd….

Quantitative Methods

Simple (or Bivariate) Regression Analysis: ◦ deals with a single independent variable that determines the value of a dependent variable. ◦ Demand Function: D = a+bP, where b is negative. ◦ If we assume there is a linear relation between D and P, there may also be some random variation

in this relation.

Nonlinear Regression Analysis◦ Log linear function log D =A + B log P + e

where A and B are the parameters to be estimated and e represents errors or disturbances. ◦ Linear form of log linear function D* = a + b P* + e

where D*= log D and P*=log P

Contd…..

Quantitative MethodsMultiple Regression Analysis:D = a1+a2.P+a3.A+e

(where A = advertising expenditure incurred).

D^ = a^1 + a^2P + a^3A,

(where a1, a2 and a3 are the parameters and e is the random error term (or disturbance), having zero mean).

Similar to simple regression analysis, multiple regression analysis would aim at estimation of the parameters a1, a2 and a3.

Choose such values of the coefficients that would minimize the sum of squares of the deviations.

Contd…..

Quantitative MethodsSimultaneous Equations Method Based on the fact that in any economic decision every variable influences every other variable.

Incorporates mutual dependence among variables. It is a simultaneous and two way relationships,

A typical simultaneous equation model may comprise of: ◦ Endogenous variables: included in the model as dependent variables◦ Exogenous variables: given from outside the model◦ Structural equations: which seek to explain the relation between a particular endogenous

variable and other variables ◦ Definitional equations: which specify relationships that are considered to be true by definition

Limitations of Demand Forecasting

Change in Fashion

Consumers’ Psychology

Lack of Experienced Experts

Lack of Past Data◦ Accurate

◦ Reliable

Session VI Supply54

Supply

Indicates the quantities of a good or service that the seller is willing and able to provide at a price, at a given point of time, Ceteris Peribus.

Supply of a product X (Sx) depends upon:◦ Price of the product (Px)◦ Cost of production (C)◦ State of technology (T)◦ Government policy regarding taxes and subsidies (G)◦ Other factors like number of firms (N)

Hence the supply function is given as:

55

Sx = (Px, C, T, G, N)

Law of Supply Law of Supply states that other things remaining the same, the higher the price of a commodity the greater is the quantity supplied.Price of the product is revenue to the supplier; therefore higher price means greater revenue to the supplier and hence greater is the incentive to supply. Supply bears a positive relation to the price of the commodity.

Point on Supply Curve

Price (Rs. Per cup)

Supply (‘000 cups per month)

a 15 10b 20 20c 25 30d 30 45e 35 60

Supply Schedule

56

c

e

d

Supply Curve

3010 20 605040

1520

30

35

25

Pric

e of

Cof

fee

Quantity of Coffee0

ba

Change in Supply

Shift in the supply curve from S0 to S1 More is supplied at each price

(Q1>Q) Increase in supply caused by:

Improvements in the technology

Fall in the price of inputs Shift in the supply curve from S0

to S2 Less is supplied at each price

(Q2<Q) Decrease in supply caused by:

A rise in the price of inputs Change in government policy

(VAT) 57

S2

S1

S0

Price

Quantity O

Q2

P

Q0 Q1

Equilibrium occurs at the price where the quantity demanded and the quantity supplied are equal to each other.

Market Equilibrium

Price(Rs)

Supply (‘000 cups/

month)

Demand (‘000 cups/

month)

15 10 50

20 15 40

25 30 30

30 45 15

35 70 10

58

D

S

Quantity

Price

O

25 E

30

For prices below the equilibrium◦ Quantity demanded exceeds quantity supplied (D>S) ◦ Price pulled upward

For prices above the equilibrium◦ Quantity demanded is less than quantity supplied (D<S)◦ Price pulled downward.

Market Equilibrium

Price(Rs)

Supply (‘000 cups/

month)

Demand (‘000 cups/

month)

15 10 5020 15 4025 30 3030 45 1535 70 10

59

D

S

Quantity

Price

O

25 E

30

20

30

4515

Changes in Market Equilibrium(Shifts in Supply Curve)

The original point of equilibrium is at E, the point of intersection of curves D1 and S1, at price P and quantity Q

An increase in supply shifts the supply curve to S2

Price falls to P2 and quantity rises to Q2, taking the new equilibrium to E2

A decrease in supply shifts the supply curve to S0. Price rises to P0 and quantity falls to Q0 taking the new equilibrium to E0

Thus an increase in supply raises quantity but lowers price, while a decrease in supply lowers quantity but raises price; demand being unchanged

Q2

P2

E2

S2

S2

Q

PE

D1

D1

S1

S1

Price

QuantityO

E0P0

Q0

S0

S0

60

The original point of equilibrium is at E, the point of intersection of curves D1 and S1, at price P and quantity Q

An increase in demand shifts the demand curve to D2

◦ Price rises to P1 and quantity rises to Q1 taking the new equilibrium to E1

A decrease in demand shifts the demand curve to D0

◦ Price falls to P* and quantity falls to Q* taking the new equilibrium to E2.

Thus, an increase in demand raises both price and quantity, while a decrease in demand lowers both price and quantity; when supply remains same.

Q1

P1E1

D2

D2

Q*

P* E2

Changes in Market Equilibrium(Shifts in Demand Curve)

D0

D0

D1

D1S1

S1

Price

QuantityO

EP

Q

61

Change in Both Demand and Supply

P2

Q2

E2

S2

S2

D1

D1

Quantity

Price

O

S1

S1D2

D2

Q1

P1 E1

Whether price will rise, or remain at the same level, or will fall, will depend on: the magnitude of shift and the shapes of the demand and

supply curves. Therefore, an increase in both supply

and demand will cause the sales to rise, but the effect on price can be: Positive (D increases more than S) Negative (S increases more than

D) No change (increase in

D=increase in S) 62

Session VII Production63

ProductionThe process of transformation of resources (like land, labour, capital and entrepreneurship) into goods and services of utility to consumers and/or producers. The process of creation of value or wealth through the production of goods and services that have economic value.process of adding value may occur by change in form (input to output, say steel into car), or by change in place (supply chain, say from factory to

dealers/retailer), orby changing hands (exchange, say from retailer to consumer).

Factors of Production 5 factors of production

Land Gift of nature and not the result of human effort

Reward is called as rent

Labour Physical or mental effort of human beings - Skilled as well as unskilled.

Reward is called as wages

Capital Wealth used for further production as machine/ equipment/

Reward is called as interest

Enterprise The ability and action to take risk for uncertain economic gains

Reward is called as profit

Organization Managerial aspect of business.

Reward is called as salary

Production Function

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

It can be said that production function is:Always related to a given time periodAlways related to a certain level of technologyDepends upon relation between inputs. Normally a production function is written as:

Q = f (L,K,I,R,E) Where, Q is the maximum quantity of output, and L=labour; K=capital; I=land; R=raw material; E= efficiency parameter.

Production Function with One Variable Input

Also termed as variable proportion production functionIt 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: here Q = output, L = labour and K = fixed amount of capitalTotal product is a function of labour:

Average Product (AP) is total product per unit of variable input Average product of labour (APL) is:

Marginal Product (MP) is the addition in total output per unit change in variable input Marginal product of labour (MPL) is:

),( KLfQ

),( LKfTPL

LTPAPL

LTPMPL

Labour (’00

units)

Total Product (’000 tonnes)

MP AP Stages

1 20 - 20 Increasing returns2 50 30 25

3 90 40 304 120 30 30 Diminishing

returns5 140 20 286 150 10 257 150 0 21.58 130 -20 16.3 Negative

returns9 100 -30 11.1

Law of Variable Proportions

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.

First stage Increasing Returns to the Variable

FactorMP>0 and MP>AP

Second stageDiminishing Returns to a Variable

FactorMP>0 and MP<AP

Third StageNegative ReturnsMP<0 while AP is falling but positiveTechnically inefficient stage of

productionA rational firm will never operate in

this stage

Law of Variable Proportions

Labour

Total Output

OMPL

APL

Labour

Total Output

O

TPL

A*

A

Stage I

B*

B

Stage II

C

C*

Stage III

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

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

Represented as:

Capital (Rs. crore)

Labour (’00 units)

40 6

28 7

18 8

12 9

8 10

),( KLfQ 05

1015202530354045

6 7 8 9 10

Labour ('00 units)

Capi

tal (

Rs. C

rore

)

Characteristics of Isoquants

Downward sloping Convex to the origin A higher isoquant represents a higher output Two isoquants do not intersect

O Labour

Capital

Q0

B

Q1

A

C

Q2

B Q1

OLabour

Capital

C

Q2

A

Iso-Cost Lines

•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.

rw

wCr

C

LKSlope

rKwLC Total Cost is sum of Labour cost (wL) and Capital cost (rK) where wage (w) and interest (r)

The (absolute) slope of this line is equal to the ratio of the input prices.

B1

A1

B2

A2

Labour

Capital

O B

A

Producer’s Equilibrium

Necessary condition for equilibriumSlope of isoquant = Slope of

isocost line

Maximization of output subject to cost constraint

AB is the isocost lineAny 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 capitalQ3 is beyond reach of the firmPoints 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.

Labour

Capital

O

A

B

Q2Q3

Q0Q1

CE

L*

K*

D

Producer’s Equilibrium

B2

A2

B

A

B1

A1

L

K

OLabour

Capital

Q

Minimization of cost for a given level of output

Firm has decided the level output to be produced shown by the isoquant Q

Will be indifferent between output combinations shown by R, S, E on isquant Q.

Has to ascertain that combination of inputs Labour and Capital which minimizes the cost of production

Hence a map of isocost lines will be prepared

The isocost lines are parallel to each other because price of the inputs is given.

A1B1 line is not feasible It will use OK and OL of capital and

labour respectively, at point E which is also on AB, the lowest possible isocost line.

R, S are not desirable because they are on higher cost line A2 B2.

Necessary condition for equilibriumSlope of isoquant = Slope of

isocost line

E

R

S

Returns to Scale

Constant Returns to Scale : (Panel a)

Increasing Returns to Scale : (Panel b).

Decreasing Returns to Scale : (Panel c).

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.

Labour

Capital

O50Q

100QA

B200Q

C

Panel a

Labour

Capital

O50Q

125QA1

B1

90Q

C1

Panel c

LabourO50Q

150QA2

B2

C2

400Q

Capital

Panel b

Cobb-Douglas Production Function

Proposed by Wicksell and tested against statistical evidence by Charles W. Cobb and Paul H. Douglas in 1928

where α, β are constants. A is the technological parameter, α is the elasticity of output with respect to capital, and β is the elasticity of output with respect to labour.

LAKQ

PropertiesHomogeneous of degree (+)The returns to scale is immediately revealed by the sum of the two

parameters and Constant Returns to Scale: ( +) = 1 Increasing Returns to Scale: ( +) > 1 Decreasing Returns to Scale: ( +) < 1

Isoquants are negatively sloped and convex to the origin Elasticity of substitution is equal to 1

77

Cobb-Douglas Production Function

Managerial Economics

78

There are different types of costs. Invariably, firms believe costs are too high and try to lower them.

The Costs of Production

Fixed Costs, Variable Costs, and Total Costs

Costs of Production

The sum of the variable and fixed costs are total costs.

TC = FC + VC

Fixed Costs, Variable Costs, and Total Costs

Average Total Cost, Average Fixed Cost, and Average Variable Cost Average costs are costs per unit of output

Costs of Production: Average Costs

Average total cost (often called average cost) equals total cost divided by the quantity produced.

ATC = TC/Q

Average Costs

Average fixed cost equals fixed cost divided by quantity produced.

AFC = FC/Q Average variable cost equals variable cost

divided by quantity produced.

AVC = VC/Q

Average total cost can also be thought of as the sum of average fixed cost and average variable cost.

ATC = AFC + AVC

Average Costs

Marginal cost is the increase (decrease) in total cost of increasing (or decreasing) the level of output by one unit.

In deciding how many units to produce, the most important variable is marginal cost.

Marginal Cost

Determinants of cost:◦ Price of inputs◦ Productivity of inputs◦ Technology◦ Level of output

Mathematically we can express the cost function as:

C= f(Q, T, Pf) where C=cost; Q=output; T=technology; Pf = price of inputs.

Mathematical expression of Cost

Accounting Costs/ Explicit Costs/ Out of Pocket Costs◦ Which can be identified, measured and accounted for; e.g. cost of raw

materials, wages and salary and capital costs like cost of the factory building.

Real Costs◦ More or less social and psychological in nature and non quantifiable in

money terms; e.g. cost of sacrificing leisure and time. Opportunity Costs

◦ Help in evaluation of the alternative uses of an input other than its current use in production

Kinds of Costs Kinds of Costs

Implicit Costs◦ Do not involve cash outflow or reduction in assets, or increase in liability; e.g. owner

working as manager in own building

Direct Costs◦ Which can be attributed to any particular activity, such as cost of raw material, labour, etc.

Indirect Costs◦ Costs which may not be attributable to output, but are distributed over all activities are

indirect costs – Also known as overheads.

Kinds of CostsKinds of Costs

Replacement costs◦ Current price or cost of buying or replacing any input at present. Like buying new

machines for old plant. Social Costs

◦ Costs to the society in general because of the firm’s activities. E.g. pollution caused by industrial wastes and emissions.

Controllable Costs and Uncontrollable Costs◦ Controllable Costs are subject to regulation by the management of a firm; e.g. fringe

benefits to employees, costs of quality control. ◦ Uncontrollable Costs are beyond regulation of the management; e.g. minimum wages

are determined by government, price of raw material by supplier.

Kinds of CostsKinds of Costs

Fixed Costs◦ Do not vary with output; e.g. plant,

machinery, building.◦ Total Fixed Cost (TFC) curve is a straight

line, parallel to the quantity axis, indicating that output may increase to any level without causing any change in the fixed cost.

◦ In the long run plant size may increase hence FC curve may be step like, where each step showing FC in a particular time period.

Costs in Short Run

O

Costs

QuantityCosts

O Quantity

TFCC

TFC

Costs in Short Run

TVCTC

TFC

O

Costs

Quantity

Variable Costs Costs that vary with level of output

and are zero if no production; e.g. cost of raw materials, wages.

Normally TVC is like a straight line starting from origin.

TVC may be an inverse S shaped upward sloping curve, due laws of variable proportions.

Total cost (TC) Sum of TFC and TVC Slope of TC curve is determined

by that of the TVC.

TFC

Costs

O Quantity

TVCTC

All costs are variable in the long run since factors of production, size of plant, machinery and technology can be varied in the long run. The long run cost function is often referred to as the “planning cost function” and the long run average cost (LAC) curve is known as the “planning curve”. As all costs are variable, only the average cost curve is relevant to the firm’s decision making process in the long run. The long run consists of many short runs, therefore the long run cost curve is the composite of many short run cost curves.

Costs in Long Run Costs in Long Run

Costs in Long RunCosts in Long Run

MC2 SAC2MC3

SAC3

q0 q1 q2

MC1SAC1

LAC

AC, MC

QuantityO

o In the long run the firm may increase plant size to increase output.

o It shows scalloping curve as the plant costs are not smoothened.

Break Even Analysis

Breakeven point is the point where total cost just equals the total revenue, in other words it is the no profit no loss point.

Plot cost and revenue on the Y axis and output on the X axis.

TC is a straight line because AVC is assumed to be constant

Total revenue is proportional to output and the TR is a straight line through the origin.

Point of intersection of TR and TC (E) is the Break Even point, i.e. no profit no loss at output Q*◦ Prior to E is loss zone ◦ After E is the profit zone.

Shows the profit (or loss) resulting from each level of sales by the firm.

FC

TC

TR

O Output

Cost, Revenue

E

Q*

VC

Profit

Loss

managerial economics | unit 2

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