Production Cost Firm

8/10/2019 Production Cost Firm

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Production, Cost & Organisation

Bino Paul, Tata Institute of Social Sciences



Firm & Production

• Transformation of input into output

•Output: Final commodity, Intermediate product, Service

• Production is a flow (rate of output over a given period of time)



Value Addition and

Production Function

X = Q – R

X = value addition, Q = Output, R = Raw Materials

Q = f (K, L, LA, O, R)

K = Capital, L = Labour, LA = Land,O = Organization, R = Raw material

X = f (K, L, LA, O)



Inputs

Factor Inputs Non Factor Inputs

K

L

LA

O

R



Law of Return

X = f (L);

X = Net Value Added

L = Labour

Other factors are kept constant.

TP = Total ProductMP = TP/ L

AP = TP/L

Labour TP MP AP

1 10 10

2 22 12 11

3 36 14 12

4 48 12 12

5 57 9 11.4

6 63 6 10.5

7 67 4 9.57

8 67 0 8.38

9 65 -2 7.22



-10

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10

T P , M

P , A P

Units of Labour

TP

MP

API

II

III

AP = MP

MP = 0



Output Elasticity & Returns

Relation Between

AP and MP

Output Elasticity

=( TP/ TP)/( L/L)

= ( TP/ L)/ (TP/L)

= MP/AP

MP > AP > 1

[INCREASING RETURNS]

MP = AP 1

[CONSTANT RETURNS]

MP < AP < 1

[DIMINISHINGRETURNS]



Technical Change

TP

L

TP1

TP2

TECHNICALPROGRESS



Technical Change

TP

L

TP2

TP1

TECHNICALREGRESS



Process

A process is a way of

combining of factor inputs.In formal language, it is a

vector of inputs

Process 1 Process 2 Output

Column (1)* Column (2)*

Capital (K) 5 3 100 units

Labour (L) 2 4 100 units



Process & Technical Efficiency

Technical efficiency (TE) of

a process implies that

minimum use of inputs for

a given output.

Processes 1 and 2 are

technically efficient, but

process 3 is inefficient,

and it is inferior to other

processes

Technical Efficiency and a Comparison of

Processes

Process

1

Process

2

Process

3

Output

Capital

(K)

5 3 6 100

units

Labour

(L)

2 4 5 100

units



Technical efficiency

A is Technically efficient.

B is technically inefficient.

A

B

TP

L



ISO-QUANT and Total Product Map

K

6 10 22 29 34 38 39

5 12 26 34 38 40 38

4 12 26 34 38 38 34

3 10 22 31 34 34 30

2 7 17 26 28 28 261 3 8 12 14 14 12

L 0 1 2 3 4 5 6



Iso-Quant

• ISO-Quant is a set oftechnically efficientprocesses.

• On Iso-Quant, TP

remains same (i.e. TP

= 0)

L

TP

K

K

LK

L

TP

TP

K

L

Convex Iso-Quant

LP Iso-QuantInput-Output Iso-Quant

Linear Iso-Quant

TP



Properties of Technology

•

Monotonic

• Convex



Monotonic function

If the amount of at least one input is increased,it should be possible to produce at least as much

output as produced originally.



Convex Technology

Let processes (K 1, L1 ) and (K 2, L2 ) generate 1 unit

of output apiece.

So, (100 K 1, 100 L1 ) 100 (100 K 2, 100L2 )



Convex Technology

Weighed average of processes produce 100 units

2L 4L

10 K

5K

(0.25 * 5K + 0.75 *10K),

(0.25 * 2L + 0.75 *4L)



Marginal Products

Let Y = f(X 1, X 2 )

Y/X 1 = {f(X 1+X 1, X 2 ) – f(X 1, X 2 )} /X 1

Y/X 1 = Marginal Product of Factor 1 =MP1

Y/X 2 = {f(X 1, X 2 +X 2 ) – f(X 1, X 2 )} /X 2

Y/X 2 = Marginal Product of Factor 2=MP2



Technical Rate of Substitution (TRS)

Y = MP1 X 1 + MP2 X 2 = 0

TRS =X 2/X 1 = MP1/MP2

Diminishing TRS



The long run and the short run

• In the short run, there will be at least one factor

of production that is fixed at pre determined

level

•

In the long run, all the factors of production vary.



Returns to Scale

Scale: Increase all inputs by a constant

Let Y = f(X 1, X 2 ). Increase X 1 and X 2 by 2 each; f( 2X 1, 2X 2 ).

Supposing we get 2Y = f( 2X 1, 2X 2 ), Constant Returns to Scale


Supposing we get 1.5Y = f( 2X 1, 2X 2 ), Diminishing Returns to Scale


Supposing we get 4Y = f( 2X 1, 2X 2 ), Increasing Returns to Scale



Cobb Douglas Production Function

Let Y = Value Added, X 1 and X 2 are factor inputs

Y = f ( X 1, X 2 ) = A X 1a X 2

b

A = Scale of Production

a, b

How much output we would get if we

used one unit of each input

How the amount of output responds to

change in input



Measuring Capital (K)

It = K t-K t-1; K t = It + K t-1; I = Investment, d = rate of depreciation

K 1 = I1 + K 0 (1-d)

K 2 = I2 + K 1 (1-d) = I2 + (I1 + K 0(1-d)) (1-d)

= I2 + I1 (1-d) + K 0 (1-d)2

K 3 = I3 + K 2 (1-d)

= I3 + [I2 + I1 (1-d) + K 0 (1-d)2 ](1-d)

= I3 + I2 (1-d) + I1 (1-d)2 + K 0 (1-d)3

K 4 = I4 + K 3 (1-d)= I4 + [I3 + I2 (1-d) + I1 (1-d)2 + K 0 (1-d)3 ] (1-d)

= I4 + I3 (1-d) + I2(1-d)2 + I1(1-d)3 + K 0 (1-d)4



Marginal Products (MP)

Y = f( X 1, X 2 ) = A X 1a X 2

b

MP1 = δ Y/δX 1 = a A X 1a-1 X 2

b

MP 2 = δ Y/δX 2 = b A X 1a X 2b-1



TRS

Y =A X 1a

X 2b

X 1

X 2 TRS = MP1/MP2 = (a A X 1

a-1 X 2b )/(b A X 1

aX 2b-1 )

=(a/b) (X 2/X 1 )



An exercise

Year

Number of

Persons

Investment

at constant

prices depeciation Capital

Output at

Constant

Prices

Output

Index

Capital

Index

Labour

Index lnoutput lncapital lnlabour

1.00 5.00 0.05 10.00 0.70 100.00 100.00 100.00 4.61 4.61 4.61

2.00 5.00 1.50 0.05 11.00 1.20 171.43 110.00 100.00 5.14 4.70 4.61

3.00 7.00 1.30 0.05 11.75 1.40 200.00 117.50 140.00 5.30 4.77 4.94

4.00 8.00 1.70 0.05 12.86 1.50 214.29 128.63 160.00 5.37 4.86 5.08

5.00 10.00 2.00 0.05 14.22 1.55 221.43 142.19 200.00 5.40 4.96 5.30

6.00 12.00 2.10 0.05 15.61 1.67 238.57 156.08 240.00 5.47 5.05 5.48

7.00 15.00 2.20 0.05 17.03 1.80 257.14 170.28 300.00 5.55 5.14 5.70

8.00 16.00 2.50 0.05 18.68 1.90 271.43 186.77 320.00 5.60 5.23 5.77

9.00 17.00 2.70 0.05 20.44 2.00 285.71 204.43 340.00 5.65 5.32 5.83

10.00 18.00 2.80 0.05 22.22 2.50 357.14 222.21 360.00 5.88 5.40 5.89

11.00 19.00 3.00 0.05 24.11 2.65 378.57 241.10 380.00 5.94 5.49 5.94

12.00 20.00 3.40 0.05 26.30 2.80 400.00 263.04 400.00 5.99 5.57 5.99

13.00 21.00 3.30 0.05 28.29 2.83 404.29 282.89 420.00 6.00 5.65 6.04

14.00 21.00 4.80 0.05 31.67 2.96 422.86 316.74 420.00 6.05 5.76 6.04

15.00 22.00 4.95 0.05 35.04 3.30 471.43 350.41 440.00 6.16 5.86 6.09

16.00 23.00 5.00 0.05 38.29 3.45 492.86 382.89 460.00 6.20 5.95 6.13

17.00 24.00 5.40 0.05 41.77 3.56 508.57 417.74 480.00 6.23 6.03 6.17

18.00 25.00 4.80 0.05 44.49 3.57 510.00 444.86 500.00 6.23 6.10 6.21

19.00 25.00 5.60 0.05 47.86 3.89 555.71 478.61 500.00 6.32 6.17 6.21

20.00 26.00 5.90 0.05 51.37 4.50 642.86 513.68 520.00 6.47 6.24 6.25

21.00 27.00 8.00 0.05 56.80 4.60 657.14 568.00 540.00 6.49 6.34 6.29

22.00 28.00 8.20 0.05 62.16 4.70 671.43 621.60 560.00 6.51 6.43 6.33



Ordinary Least Square (OLS)Regression of Production Function

Y = f( K, L) = A K a Lb

In Y t = In A + a In K t + b In Lt + ut

Dependent Variables: Y (output),

Independent Variables: K (capital), L (Labour)Random Variable: u (error)

Parameters/Coefficients: A (factor that explains variation emanating neither from capital nor from labour);a (proportionate change in Output divided by proportionate change in Capital);b (proportionate change in Output divided by proportionate change in Labour)

ln: Natural Logarithm; Subscript ‘t’ : Time

From the data: ln Y t = 0.86 + 0.56 In K

t + 0.33 In L

t Y = 2.4 K 0.56 L 0.33

All the coefficients/parameters are statistically significant



Cost

C = w 1X 1 + w 2X 2, C = Cost, w 1= Unit compensation to X 1 w 2= Unit compensation to X 2

Slope = maxX 2/maxX 1= w 1/w 2

X 1

X 2

If X 1= 0,

then

max X 2 =C/w 2



Equilibrium

Y =A X 1a

X 2b

X 1

X 2 TRS = MP1/MP2 = (a/b) (X 2/X 1 )

MP1/MP2=(a/b) (X 2/X 1 ) = w 1/w 2MP1/w 1=MP2/w 2

C= w 1x1+w 2x2



Returns to Scale

Let f(X 1, X 2 ) = A X 1aX 2

b becomes f( 2X 1, 2X 2 ) = A (2X 1 )a (2X 2 )

b

= 2a+b A X 1a X 2

b

= 2a + b Y

a + b = ? Returns to Scale

1 Constant Returns to Scale

>1 Increasing Returns to Scale

< 1 Diminishing Returns to Scale



Profit Function

Set of Outputs = {y 1……y n}

Set of Inputs = {x1……xn}

Set of Prices = {p1……pn}Price of Inputs = {w 1…… w n}

π = ∑i =1….n pi y i - ∑ i =1….n w i x i ; π = Economic Profit

Value all inputs and outputs at their opportunity costs



Organization of Firms

Firm

Proprietorship

Partnership

Corporation

(independence between owner andmanager)

Maximizing the present vale of the stream of

profits the firm generates

Should firm

outsource or

internalise



Fixed and Variable Factors

If the input varies with the

output

Type of inputs

NO (input remains fixed evenat zero output)

Fixed

YES Variable

NO except at zero output Quasi Fixed



Short run vs. Long run

Long Run When all the factors of

production vary

Short Run When at least one factor ofproduction is fixed



Short run profit maximisation

Let Set of Outputs = {y}; Set of Inputs = {x1,x*2}; Set of Prices = {p};

Price of Inputs = {w 1, w 2}; π = Economic Profit

x1 = Variable factor x*2 = Fixed Factor

π = py – (w 1x1+w 2x*2 )

π/p = y – (w 1x1/p) – (w 2x*2/p) ; y = π/p + (w 1x1/p) + (w 2x*2/p)In the above equation, while y and x1 are variables, rest are constants.

Therefore, there will be different combinations of y and x1 that correspond to a

fixed π .

RevenueCost



Profit maximizing output (Short run)

Given y = f(x1, x*2 )

y = π/p + (w 1x1/p) + (w 2x*2/p)

Production function/Technology

Iso Profit

Iso Profit

Production function/Technology

Y

X1

Profit maximizing

output



Comparative statics

Slope of Iso profit = Y/X 1 = w 1/p

Slope of production function = Y/X 1 = Marginal Product of X 1. At the equilibrium = w 1/p = Marginal Product of X 1.

What happens if w 1 increases …..

Higher w 1

Lower w 1



Comparative statics

Slope of Iso profit = Y/X 1 = w 1/p

Slope of production function = Y/X 1 = Marginal Product of X 1. At the equilibrium = w 1/p = Marginal Product of X 1.

What happens if p increases …..

Lower p

Higher p



Long run profit maximization

Let Set of Outputs = {y}; Set of Inputs = {x1,x2}; Set of Prices = {p};

Price of Inputs = {w 1, w 2}; π = Economic Profit

x1 = Variable factor x2 = Variable Factor

π = py – (w 1x1+w 2x2 )

Since y = f(x1, x2 ), π = pf(x1, x2 ) – (w 1x1+w 2x2 )

δ π/ δx1 = p ( δy/ δx1 )- w 1 = 0δ π/ δx2 = p δy/ δx2 )- w 2 = 0

p MP1 = w 1

p MP2 = w 2



Cost

Cost {C(y)}; C(y) = F + C v (Y)

Fixed Cost

F

Variable Cost

C v (Y)



Average Cost

Average Cost {AC(y)};

AC(y) = (F/Y) + (C v (Y)/Y)

Average Fixed Cost

F/Y

Average VariableCost

C v (Y)/Y



AFC, AVC, and AC

Y

AFC

Y

AVC AC=

AFC+AVC

Y



Marginal Cost (MC)

MC (y) =C(y)/ Y

=(c(Y+ Y) – c(Y))/ Y

MC(y)

=C v

(Y)/ Y

= [C v (Y+ Y)- C v (Y)]/ Y

C v = Variable Cost

MC(1) = [C v (1) + F – C v (0) – F]/1 = C v (1)/1 = AVC(1)

MC(2) = [C v (2) + F – C v (1)-F)/1

MC(3) = [C v (3) + F – C v (2)-F)/1



Average Cost (AC), Average Variable Cost (AVC)

and Marginal Cost (MC)

AC

AVCMC

AC, AVC,

MC

Y



Relation between Average Cost (AC) andMarginal Cost (MC)

Let C = Total Cost and Y = Output

Supposing AC reaches minimum

d(C/Y)/dY = [Y (dC/dY) – C]/Y 2

= 0; Y 2

not equal to Zero

dC/dY = C/Y ; dC/dY = MC; C/Y = AC

AC = MC



Long Run Average Cost

AC

Y

Long run AC

Short run AC



Profit Maximizing Output

For an output to be profit maximizing:

Necessary condition: Marginal Revenue (MR) = Marginal Cost (MC)

Sufficient Condition: MC/ Y exceeds MR/ Y



Revenue and Market Structure

Market

Structure

Average

Revenue (AR)

Marginal

Revenue (MR)

PerfectCompetition

(pY)/Y = p;p is determined by marketforces. Firm has only negligiblestake in price determination

(pY) = p Y + Y p

(pY) / Y = p + Y ( p/ Y)

Since

p = 0,

(pY) /

Y = p

MR = AR

ImperfectCompetition(Monopoly, Monopolisticcompetition, Oligopoly)

(pY)/Y = p;p is determined by the firm onthe basis of demand. Forexample, p = a - b Y

(pY) = p Y + Y p

(pY) / Y = p + Y ( p/ Y)

AR tends to exceed MR since( p/ Y) carries negative sign



Decision making in perfect competition

P r i c e

Demand/Supply

A v e r a g e C o s t

( A C ) / M a r g i n

a l C o s t

( M C )

Output

AC

MC

Average

Revenue =Marginal

Revenue= Price



Decision making in imperfect competition

(monopoly)

AR = Average Revenue

MR = Marginal Revenue

AC= Average Cost

MC = Marginal Cost

AR=Price

AR

MR

MC

AC

AR,

MR,

AC, MC

Output

Super

normal Profit



Adam Smith….

• Division of Labor

• Scale of Production

• Self Interest as a coordinating force

• Exchange in an Economy



Stigler….

• Disintegration of activities

• Integration of activities

Process 2

Process 1

Process 3

Process 4

Output

AverageCost

Can Process 3 be

transformed to a new

industry?



Coordination in Economy

There are two major coordinating forces

Price

Entrepreneur

These forces direct resources, goods

and so on.

Price & Entrepreneur



Price & Entrepreneur

Price

Capital Labour

Land

CapitalLabour

Land

Entrepreneur



Firm

Coase (1937)

Firm = f (Cost of Using Price Mechanism)

Let

F = Likelihood of firm,

C = Cost of Using Price Mechanism

F = f (C)

F

C



Cost of Using Price Mechanism

Cost of

Using

Price

Mechanism

Discovering

Relevant

Prices

Cost of

Contract

= +



Two Relations

Desirability of

Specifying

Expectations

Duration

of

Contract

Likelihood

Of Firm

Desirability of

Long Term

Contract



Firm and its Size

Volume of Organizing the Transaction

Marginal Cost ofOrganizing

Transaction(MCO) /Marginal Cost ofExchange throughMarket (MC)

Firm’s Size

MCO

MC



Efficiency & Organization

Efficiency in

Terms of

Factor Use

Volume of Organizing Transaction



A review of “The modern corporation: origins,

evolution, attributes” by Oliver E Williamson



Theory of firms and markets

Firm as a production function

Ronald Coase (1937): Transaction cost

Arrow (1969): cost of running economic system



Organization Theory

Herbert Simon (1947): Bounded rationality

Cognitive limits

Memory

Non Standard Business practices



p

Is the non standard business practices anti competitive oreconomising of resources?



Business History

Lance Davis and North (1971)

Institutional change

Chandler (1962, 1977)

Organisational form and performance



Transaction cost

Ex ante cost : negotiating and writing

Ex post cost: executing, policing and remedying

Production function frame work may cover cost of planning,adapting and monitoring under alternative governance structures



Transaction cost: behavioural assumptions

Bounded rationality

Opportunism ( moral hazard )

“assess alternative governance structures in terms of their capacities

to economise on bounded rationality while simultaneouslysafeguarding transactions against opportunism”

Is transaction important in economics of



Is transaction important in economics of

organizations

Frequency of transaction

Uncertainty to which transactions are subject to

Specific investments to support transactions



Asset Specificity

Site specificity: to economise inventory and transportationcost

Physical asset specificity: special inputs to producecomponents

Human asset specificity: learning-by-doing



Asset specificity

Lock in

Organisational design:



three principles

Asset-specificity principle

Externality Principle ( free riding )

Hierarchical decomposition principle



Advantages of procurement through market

If firm needs are small in relation to small

(static economies of scale)

Market can aggregate uncorrelated demands

(risk pooling benefits)

Economies scope



Asset specificity principle

“recurring transactions for technologically separable goods and services will be efficiently

mediated by autonomous market contracting is progressively weakened as assetspecificity increases”

Asset specificity Less transferable to other uses



Situation Nature of Assetspecificity

Classical market Assets non specific to

partnersBilateral or obligationalmarket contracting

Semi specific

Internal organisation High specific



Externality Principle

In the distributional stage, there is information asymmetry onquality (enhancement or debasement)

Autonomous contracting will be replaced by obligational

contracting (franchising)



Heirarchical Decomposition

Operating Parts (high frequency; short run dynamics)

Strategic Parts (Low frequency; long run dynamics)



19th Century Corporation

Rail road

Forward Integration



Integrationclass

Economies ofscope

externalities AssetSpecificity

none considerable negligible negligible

minor some some Negligible

wholesale uncertain Some Some

Retail Negligible some considerable

20 h i



20th century corporation

Unitary structure

(less integration)

versus

M form (du Pont and Sloan) [Multi-divisional structure]

(semi-autonomous units; miniature capital markets)

Conglomerates, Multi National Enterprises

Level Frequency Purpose



q y

(Years)

p

Embeddedness,

Informal Institutions, Traditions,Norms, Religion

102 to 103

Often non calculative,

spontaneous

Institutional Environment;Formal rules of the game-

especially property (polity,judiciary, bureaucracy)

10 to 102 Get the institutionalenvironment right. 1st order

economizing

Governance: play of thegame – especially contractaligning governancestructures with transactions

1 to 10

Get the governancestructures right: 2nd ordereconomizing

Resource allocation andemployment (prices &quantities; incentivealignment)

Continuous Get the marginal conditionsright. 3rd order economizing

Social Theory

Economics of Property

Rights, Positive PoliticalTheory

Transaction Cost Economics

Neoclassical Economics



Simple contracting Schema

Unassistedmarket

h=0

Unrelievedhazards

h > 0 & s = 0

h > 0 & s > 0

Credible Commitment Integration

h = Contractual hazard, s = Safeguard



Thanks

Production Cost Firm

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