Embed Size (px)
Citation preview
THE THEORY OF PRODUCTIONProduction theory forms the foundation for the theory of supply
Managerial decision making involves four types of production decisions:
1. Whether to produce or to shut down?2. How much output to produce?3. What input combination to use?4. What type of technology to use?
Production involves transformation of inputs such as capital, equipment, labor and land into output - goods and services
In this production process, the manager is concerned with efficiency in the use of the inputs
- technical vs. economical efficiency
The objective of efficiency will provide us with some basic rules about the manner in which firms should utilize inputs to produce goods and services
Technical vs. Economical efficiency
• Economic efficiency:– occurs when the cost of producing a given output
is as low as possible
• Technical efficiency:– occurs when it is not possible to increase output
without increasing inputs
The basic production theory is simply an application of the constrained optimization:
the firm attempts either to minimize the cost of producing a given level of outputOrto maximize the output attainable with a given level of cost.
Production Function
A production function shows the maximum amount of output that can be produced from any specified set of inputs, given the existing technology
x
QQ = output x = inputs
Production FunctionQ = f(X1, X2,…, Xk)
whereQ = outputX1,…,Xk = inputs
For economic analysis, let’s reduce the inputs to two, capital (K) and labor (L):Q = f(L, K)
Short-Run Production
• In the short run some inputs are fixed and some variable– e.g. the firm may be able to vary the amount of
labor, but cannot change capital– in the short run we can talk about factor
productivity
Relationship Between Total, Average, and Marginal Product: Short-Run Analysis
–Total Product (TP) = total quantity of Total Product (TP) = total quantity of outputoutput
–Average Product (AP) = total Average Product (AP) = total product/total inputproduct/total input
–Marginal Product (MP) = change in Marginal Product (MP) = change in quantity when one additional unit of input quantity when one additional unit of input usedused
The Marginal Product of LaborThe marginal product of labor is the increase in output obtained by adding 1 unit of labor but holding constant the inputs of all other factors
Marginal Product of L:MPL = Q/L (holding K constant)
= Q/LAverage Product of L:
APL = Q/L (holding K constant)
Law of Diminishing Returns(Diminishing Marginal Product)
Holding all factors constant except one, the law of diminishing returns says that:
• beyond some value of the variable input, further increases in the variable input lead to steadily decreasing marginal product of that inpute.g. trying to increase labor input without also
increasing capital will bring diminishing returns
Law of Diminishing Returns
• Sometimes referred to as variable factor proportions, law of diminishing returns states that as equal quantities of one variable factor are increased, while other factor inputs remain constant, ceteris paribus, a point is reached beyond which the addition of one more unit of the variable factor will result in a diminishing rate of return and the marginal physical product will fall.
Law of Diminishing Returns
• With nobody working on the land, output will be zero (point a). As the first farm workers are taken on, wheat output initially rises more and more rapidly.
• The assumption behind this is that with only one or two workers efficiency is low, since the workers are spread too thinly.
• With more workers, however, they can work together – each, perhaps, doing some specialist job – and thus they can use the land more efficiently.
• Output rises more and more rapidly up to the employment of the third worker (point b).
• The TPP curve gets steeper up to point b.
Law of Diminishing Returns
Law of Diminishing Returns
• After point b, however, diminishing marginal returns set• in: output rises less and less rapidly, and the TPP curve
correspondingly becomes less steeply sloped.• When point d is reached, wheat output is at a maximum: the
land is yielding as much as it can.• Any more workers employed after that are likely to get in
each other’s way.• Thus beyond point d, output is likely to fall again: eight
workers produce less than seven workers.
The short-run production function:average and marginal product
• In addition to total physical product, two other important concepts are illustrated by a production function: namely,
• average physical product (APP) and marginal physical product (MPP).
• the average physical product of labour when four workers are employed is 36/4 = 9 tonnes per year.
• Marginal physical product• This is the extra output (ΔTPP) produced by employing one
more unit of the variable factor.• Thus the marginal physical product of the fourth worker is 12
tonnes. • The reason is that by employing the fourth worker, wheat
output has risen from 24 tonnes to 36 tonnes: a rise of 12 tonnes.
• In symbols, marginal physical product is given by:MPP = ΔTPP/ΔQv
• Thus in our example:MPP = 12/1 = 12
Total Product
0
10
2030
40
50
60
0 1 2 3 4 5 6 7 8X
Q
Average and marginal poducts
-4
-2
0
2
4
6
8
10
12
14
0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 X
AP, MP
Average and Marginal Products
Three Stages of ProductionThree Stages of ProductionAP,MP
X
Stage I Stage II Stage III
APX
MPXFixed input grossly underutilized; specialization and teamwork cause AP to increase when additional X is used
Specialization and teamwork continue to result in greater output when additional X is used; fixed input being properly utilized
Fixed input capacity is reached; additional X causes output to fall
TOTAL PRODUCT MARGINAL PRODUCT AVERAGE PRODUCT
STAGE I INCREASES AT AN INCREASING RATE
INCREASES, REACHES ITS MAXIMUM & THEN
DECLINES TILL MP = AP
INCREASES & REACHES ITS
MAXIMUM
STAGE II INCREASES AT A DIMINISHING RATE TILL IT REACHES MAXIMUM
IS DIMINISHING AND BECOMES EQUAL TO ZERO
STARTS DIMINISHING
STAGE III STARTS DECLINING
BECOMES NEGATIVE CONTINUES TO DECLINE
Three stages
Three stages
FROM THE ABOVE TABLE ONLY STAGE II IS RATIONAL WHICH MEANS RELEVANT RANGE FOR A RATIONAL FIRM TO OPERATE.
IN STAGE I IT IS PROFITABLE FOR THE FIRM TO KEEP ON INCREASING THE USE OF LABOUR.
IN STAGE III, MP IS NEGATIVE AND HENCE IT IS INADVISABLE TO USE ADDITIONAL LABOUR.
Long run production In the long run all inputs become variable e.g. the long run is the period in which a firm can adjust all inputs to changed conditions in the long run we talk about returns to scale
Production in the Long-Run
All inputs are now considered to be variable (both L and K in our case)How to determine the optimal combination of inputs?
To illustrate this case we will use production isoquants.
An isoquant is a curve showing all possible combinations of inputs physically capable of producing a given fixed level of output.
AN ISOQUANT OR ISO PRODUCT CURVE OR EQUAL PRODUCT CURVE
An IsoquantGraph of Isoquant
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 X
Y
IMPORTANT ASSUMPTIONS
• The two inputs can be substituted for each other. For example if labour is reduced in a company it would have to be compensated by additional machinery to get the same output.
Types of Isoquant
1. Linear Isoquant2. Right-angle Isoquant3. Convex Isoquant
LINEAR ISOQUANTS
In linear isoquants there is perfect substiutabilty of inputs.
For example in a power plant equipped to burn oil or gas. Various amounts of electricity could be produced by burning gas, oil or a combination. I.E OIL AND GAS ARE PERFECT SUBSITUTES. Hence the isoquant would be a straight line.
Substituting InputsFrom above we can see that there exists From above we can see that there exists some degree of substitutability between some degree of substitutability between inputs.inputs.
Different degrees of substitution:Different degrees of substitution:
L
a) Perfect substitution b) Perfect Complementarity
All other ingredients
K
Q
Q
Capital
L1 L2 L3 L4
K1 K
2 K
3
K4
K
L
Right-angle isoquants
In right-angle isoquants there is complete non-substiutabilty between inputs.
For example two wheels and a frame are required to produce a bycycle these cannot be interchanged.
This is also known as leontief isoquant or input-output isoquant.
Convex Isoquants
In convex isoquants there is substiutabilty between inputs but it is not perfect.
For example
(1) a shirt can be made with large amount of labour and a small amount machinery.
(2) the same shirt can be with less labourers, by increasing machinery.
(3) the same shirt can be made with still less labourers but with a larger increase in machinery.
Unitsof K402010 6 4
Unitsof L 512203050
Point ondiagramabcde
a
Units of labour (L)
Uni
ts o
f ca
pita
l (K
)An isoquant yielding output (TPP) of 5000 units
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
Unitsof K402010 6 4
Unitsof L 512203050
Point ondiagramabcde
a
b
Units of labour (L)
Uni
ts o
f ca
pita
l (K
)
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
An isoquant yielding output (TPP) of 5000 units
Unitsof K402010 6 4
Unitsof L 512203050
Point ondiagramabcde
a
b
c
de
Units of labour (L)
Uni
ts o
f ca
pita
l (K
)
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
An isoquant yielding output (TPP) of 5000 units
Properties of Isoquants
1. An isoquant is downward sloping to the right. I.E NEGATIVELY INCLINED. This implies that for the same level of output, the quantity of one variable will have to be reduced in order to increase the quantity of other variable.
2. A higher isoquant represents larger output. That is with the same quantity of 0ne input and larger quantity of the other input, larger output will be produced.
Properties of Isoquants• No two isoquants intersect or touch each other. If the
two isoquants do touch or intersect that means that a same amount of two inputs can produce two different levels of output which is absurd.
• Isoquant is convex to the origin. This means that the slope declines from left to right along the curve. That is when we go on increasing the quantity of one input say labour by reducing the quantity of other input say capital, we see less units of capital are sacrificed for the additional units of labour.
ISOQUANT- ISOCOST ANALYSIS
• Isoquants
– their shape
– diminishing marginal rate of (technical) substitution
– Rate at which we can substitute capital for labour and still maintain output at the given level.
• Isoquants
– their shape
– diminishing marginal rate of (technical) substitution
– Rate at which we can substitute capital for labour and still maintain output at the given level.
MRTS = K / LSometimes just called Marginal rate of Substitution (MRS)
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
g
hK = -2
L = 1
isoquant
MRTS = -2 MRTS = K / L
Diminishing marginal rate of tech. substitution
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
g
h
j
k
K = -2
L = 1
K = -1
L = 1
Diminishing marginal rate of factor substitution
isoquant
MRTS = -2
MRTS = -1
MRTS = K / L
0
10
20
30
0 10 20
An isoquant mapU
nits
of
capi
tal (
K)
Units of labour (L)
Q1=5000
Substituting Inputs
• In case the two inputs are imperfectly substitutable, the optimal combination of inputs depends on the degree of substitutability and on the relative prices of the inputs
Substituting Inputs continued
MRTS = L/K
MRTS is when some of L is removed from the production and substituted by K to maintain the same level of output
Diminishing Marginal Rate of Technical Substitution:
Table 7.8 Input Combinationsfor Isoquant Q = 52Combination L K
A 6 2B 4 3C 3 4D 2 6E 2 8
L K MRTS
-2 1 2
-1 1 1 -1 2 1/2
0 2
Diminishing Marginal Rate of Technical Substitution continued
0
1
2
3
4
5
6
7
2 3 4 6 8 X
Y
X = 2Y = -1
X = 1
Y = -1
X = 1
Y =- 2
A
BC
D E
Returns to Scale
• Let us now consider the effect of proportional increase in all inputs on the level of output produced
• To explain how much the output will increase we will use the concept of returns to scale
Increasing returns to scale
• we are experiencing increasing returns to scale
• Also constant returns to scale and decreasing returns to scale are possible
Reasons for Increasing or Decreasing Returns to Scale:
• Often we can assume that firms experience constant returns to scale:
– for example doubling the size of a factory along with a doubling of workforce and machinery should lead to a doubling of output
– why could a greater (or smaller) than proportional increase occur?
0
1
2
3
4
0 1 2 3
Increasing Returns to Scale (beyond point b)Increasing Returns to Scale (beyond point b)U
nit
s o
f c
apit
al (
K)
Units of labor (L)
200
300
400
500
600
a
b
cR
700
0
1
2
3
4
0 1 2 3
Un
its o
f ca
pita
l (K
)
200
300
400
500
600
a
b
cR
Units of Labour
Constant Returns to Scale
0
1
2
3
4
0 1 2 3
Decreasing Returns to Scale (beyond point b)Decreasing Returns to Scale (beyond point b)U
nits
of c
ap
ital (
K)
Units of labor (L)
200
300
400
500
a
b
cR
Measurement of Returns to Scale continued
– Multiplying the coefficients of the production function:
If original production function isQ = f(X,Y)
and if the resulting equation after the multiplication of inputs by k is
hQ = f(kX, kY)
where h presents the magnitude of increase in production
Then, ifh>k, increasing returnsh=k, constant returnsh<k, decreasing returns
0
10
20
30
0 10 20
An isoquant mapU
nits
of
capi
tal (
K)
Units of labour (L)
Q1=5000
0
10
20
30
0 10 20
Q2=7000
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
An isoquant map
Q1
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
An isoquant map
Q1
Q2
Q3
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
An isoquant map
Q1
Q2
Q3
Q4
0
10
20
30
0 10 20
Q1
Q2
Q3
Q4
Q5
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
An isoquant map
ISOQUANT- ISOCOST ANALYSIS
• Isoquants
• E.g: Cobb-Douglas Production Function
Q=K1/2 L1/2
• We now turn to an important aspect of production, namely returns to scale.
• Isoquants
• E.g: Cobb-Douglas Production Function
Q=K1/2 L1/2
• We now turn to an important aspect of production, namely returns to scale.
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Suppose producing 5000 units with 10 units of capital and 5 units of labour
What happens now if we double the amount of capital and labour?
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Suppose producing 5000 units with 10 units of capital and 5 units of labour
What happens now if we double the amount of capital and labour?
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
What is the output level at this new isoquant?
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Suppose 20 K and 10 L gives 10,000 units
then we say there are constant returns to scale
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
If Q(K,L) =5000
Then Q(2K,2L)
= 2Q(K,L) =10,000
Q2=10,000
Constant Returns to Scale
Constant Returns to Scale
• For example the Cobb-Douglas Production Function: Q(K,L)= K1/2 L1/2
Q(2K,2L)= (2K)1/2(2L)1/2
=2 K1/2L1/2 =2Q(K,L)
A function such that Q(aK,aL)=aQ(K,L) for all a>0 (or a=0), is said to be HOMOGENOUS OF DEGREE 1 (sometimes: LINEAR HOMOGENOUS)
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
If Q(K,L) =5000
and Q(2K,2L)=15,000
>2Q(K,L)=10000
Then there is IRSQ2=15,000
Increasing returns to scale, IRS
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Increasing returns to scale:
“Isoquants get closer together”
Q2=15,000
Q2=10,000
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
If Q(K,L) =5000
and
Q(2K,2L)=7,000
< 2Q(K,L)=10000Q2=7,000
Decreasing returns to scale, DRS
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Q2=7,000
Q2=10,000
Decreasing returns to scale: “Isoquants get further apart”
ISOQUANT- ISOCOST ANALYSIS
• Isoquants– isoquants and marginal returns:
The Marginal Return measures the change in output when one variable is changed and the other is kept fixed.
– To see this, suppose we examine the CRS diagram again, this time with 3 isoquants,
– 5000, 10,000, and 15,000
• Isoquants– isoquants and marginal returns:
The Marginal Return measures the change in output when one variable is changed and the other is kept fixed.
– To see this, suppose we examine the CRS diagram again, this time with 3 isoquants,
– 5000, 10,000, and 15,000
0
10
20
30
0 10 20
Uni
ts o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5 15
Q2=10,000
Q3=15000
Isocost CurvesAssume PL=Rs100 and PK =Rs200
CombinationCombination laborlabor capitalcapital
AA 00 55
BB 22 44
CC 44 33
DD 66 22
EE 88 11
Optimal Levels of Inputs• The optimality conditions given in the previous
slides ensure that a firm will be producing in the least costly way, regardless of the level of output
• But how much output should the firm be producing?
• Answer to this depends on the demand for the product (like in the one input case as well)
Isocost Curve and Optimal Combination of L and K
5
10 L
KK
“Q52”
Isocost and Isoquant Curve for Inputs L and K
Un
its
of
cap
ita
l (K
)
O100
200
300
Expansion path
TC =£20 000
TC =£40 000
TC =£60 000
The long-run situation:both factors variable
Expansion Path
Optimal Combination of Inputs
How to determine the optimal combination of inputs As was said this optimal combination depends on the relative prices of inputs and on the degree to which they can be substituted for one another
This relationship can be stated as follows:
MPL/MPK = PL/PK
GM and Diminishing Returns to scale
• General Motors Company, also known as GM, is a United States based automaker with headquarters in Detroit, Michigan.
• Founded by :William C. Durant Founded in 1908• By sales, GM ranked as the largest U.S. automaker and the
world's second largest for 2008.• GM had the third highest 2008 global revenues among
automakers on the Fortune Global 500.• GM manufactures cars and trucks in 34 countries, recently
employed 244,500 people around the world, and sells and services vehicles in some 140 countries.
GM and Diminishing Returns to scale
• The unprecedented growth of GM would last into the early 1980s when it employed 349,000 workers and operated 150 assembly plants.
• GM previously led in global sales for 77 consecutive years (1931 to 2008), longer than any other automaker
GMSALES(in bl $)
Employees(thousands
Sales per employee(In thousand $)
GM 123.1 756 162.7
FORD 88.3 333 265.4
CHRYSLER 29.4 123 238.8
Total no of employees in 2009 : 235,000
Worker Days to produce Average car
GM 34
FORD 30
CHRYSLER 32
GM consolidated and reduced no of models from 89 to 75Centralised its marketing system, sales and service.Reducing manufacturing time from 34 to 30 days Reduced scale operations to increase its efficiency
GM and Diminishing Returns to scale
• On June 1, 2009 General Motors filed for Chapter 11 bankruptcy proceedings from which it emerged on July 10, 2009 in a reorganization in which a new entity acquired the most valuable assets.
• GM is temporarily majority owned by the United States Treasury and to a smaller extent the Canadian government, with the US government investing a total of US$57.6 billion under the Troubled Asset Relief Program.
• While no GM shares are currently available to the public, the company plans an initial public stock offering (IPO) in 2010.
GM and Diminishing Returns to scale
• GM plans to focus its business on its four core US brands — Chevrolet, Cadillac, Buick, and GMC. In Europe, following a period of negotiation to sell a majority stake in its Opel and Vauxhall brands, GM decided to retain full ownership of these operations.
• On January 26, GM announced that it had reached an agreement to sell SAAB to Spyker Cars NV.
• GM also has an agreement to sell its Hummer brand, awaiting Chinese regulatory approval, while winding down its Pontiac and Saturn brands as they remain under the old GM, now known as Motors Liquidation Company.
GM• On July 10, 2009, a new entity, NGMCO Inc. purchased the ongoing
operations and trademarks from General Motors Corporation.• The purchasing company in turn changed its name from NGMCO Inc. to
General Motors Company, marking the emergence of a new operation from the "pre-packaged" Chapter 11 reorganization
• Under the reorganization process, termed a 363 sale (for Section 363 which is located in Title 11, Chapter 3, Subchapter IV of the United States Code, a part of the Bankruptcy Code), the purchaser of the assets of a company in bankruptcy proceedings is able to obtain approval for the purchase from the court prior to the submission of a re-organization plan, free of liens and other claims.
GM
• It’s used in most Chapter 11 cases that involve a sale of property or other assets. This process is typical of large organizations with complex branding and intellectual property rights issues upon exiting bankruptcy. The new company plans to issue an initial public offering (IPO) of stock in 2010
GM
• GM's remaining pre-petition creditors' claims are paid from the remaining assets of Motors Liquidation Company, the new name of the former General Motors Corporation, although the directors of that company believe its debts far outweigh its assets. This means that while the former GM's bondholders may recover a small portion of their investment, former GM shareholders (now shareholders of Motors Liquidation Company) will likely not receive anything.
GM
• Also on July 10, 2009, GM announced plans to trim its U.S. workforce by 20,000 employees as part of its reorganization by the end of 2009 due to economic conditions.
GM current Scenario• President Barack Obama’s administration owns 60.8
per cent of GM’s common stock, the price of about 43 billion dollars in emergency funds that helped GM avoid collapse. GM separately received about 7 billion dollars in government loans that have since been returned.
• US media have speculated the stock sale would net the government about 16 billion dollars, which along with earnings for other stakeholders would make it the second-largest initial public offering in US history.
GM current Scenario
• The looming stock sale is a mark of GM’s renewed confidence after some of the most tumultuous years in its history. GM posted two straight quarters of profits for the first time since 2004, the result of a major restructuring effort after bankruptcy in June and July of last year.
• GM lost the title of world’s largest carmaker to Toyota as it shed loss-making brands, closed factories, fired workers and began a shift to greener vehicles, all in a bid to remain a viable company.
A comparison (estimates) of the new GM and the old GM
Old GM (before July 10, 2009) New GM (after July 10, 2009)
Buick, Cadillac, Chevrolet,
GMDaewoo (48.2%), GMC,
Holden, Hummer, Oldsmobile,
Opel, Pontiac, Saab, Saturn,
Vauxhall
Brands Buick, Cadillac, Chevrolet,
GMDaewoo (70.1%), GMC,
Holden, Opel, Vauxhall
5,900 US Dealerships 3,600
Common shareholders,
bondholders and secured
creditors
Ownership TThe United States Treasury,
the Crown in Right of Canada, Old
GM bondholders, and UAW union
47 US Plants 34
US$94.7 B Debt[41] US$17 B
91,000 US employees 68,500
