Production Analysis

• Production Function– Q = F(K,L)– The maximum amount of output that can be

produced with K units of capital and L units of labor.

• Short-Run vs. Long-Run Decisions• Fixed vs. Variable Inputs

Total, Average and Marginal Product of Labour

Labour Input

Total Product of Labour

Average Product of Labour

Marginal Product of Labour

0 0 --- ----

1 20 20 20

2 50 25 30

3 90 30 40

4 120 30 30

5 140 28 20

6 150 25 10

7 155 22 5

8 150 19 -5

Law of Variable Proportions OR Law of Diminishing Marginal Product

Q

L

Q=F(K,L)

IncreasingMarginalReturns

DiminishingMarginalReturns

NegativeMarginalReturns

MP

AP

Stages of Production

Law of Variable Proportions

Stage 1 Stage 2 Stage 3

TPP

APP

MPP

Y

X

Y

X

TotalPhysicalProduct

Average/MarginalProducts

Units of Variable Input (Labour)

Marginal Product of Labour

• MPL = Q/L

• Measures the output produced by the last worker.

• Slope of the production function

Average Product of Labour

• APL = Q/L

• This is the accounting measure of productivity.

Isoquant

• The combinations of inputs (K, L) that yield the producer the same level of output.

• The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.

L

Linear Isoquants• Capital and labor are perfect substitutes

Q3Q2Q1

Increasing Output

L

K

Leontief Isoquants• Capital and labor are perfect

complements• Capital and labor are used in

fixed-proportions

Q3

Q2

Q1

K

Increasing Output

L

Kinked Isoquants

Y

X

ab

dc

Iq

LabourO

Iq1

Iq2

Iq3

Iq4

Y

XO Labour

Isoquant Map

Isocost• The combinations of

inputs that cost the producer the same amount of money

• For given input prices, isocosts farther from the origin are associated with higher costs.

• Changes in input prices change the slope of the isocost line

K

LC1C0

L

KNew Isocost Line for a decrease in the wage (price of labor).

Y

Iq1

Iq2

Iq3

Least Cost Combination or Producer’s Equilibrium

Capital

LabourO

Isocost curve

LEAST COST COMBINATION OR

PRODUCER’S EQUILIBRIUM

X

Cost Minimization

Iq

L

K

Point of Cost MinimizationSlope of Isocost

= Slope of Isoquant

In economics, the Cobb–Douglas functional form of production functions is widely used to represent the relationship of an output to inputs. It was proposed by Knut Wicksell (1851–1926), and tested against statistical evidence by Charles Cobb and Paul Douglas in 1900–1928.

Cobb-Douglas Production Function

Y = ALαKβ or Y = ALαK1-α

where:•Y = total production (the monetary value of all goods produced in a year)•L = labor input•K = capital input•A = total factor productivity•α and β are the output elasticity of labor and elasticity of capital, respectively. These values are constants determined by available technology.•α > 0, β > 0, L > 0 and α+β = 1 (i.e., the sum of exponents is equal to unity)

Homogeneity of the Function

The Cobb-Douglas Production Function, Y = ALαKβ has two inputs, Labour and Capital.Therefore Q = f(L,K)Multiplying both sides by a constant, ‘λ’,

λQ = f(λL, λK)Then f(λL, λK) = A(λL) α (λK) β

= Aλα Lα λβKβ

= λα+β ALα Kβ

= λα+β Q = λQ (since Q = ALαKβ ) Therefore, it is proved that if inputs are increased by λ times, output is also increased by λ times.If α + β = 1, then the production will operate under constant returns to scale and the function is homogeneous of degree one (i.e., Linear Homogeneous Function).If α + β > 1, then the production will operate under increasing returns to scale.If α + β < 1, then the production will operate under decreasing returns to scale.

PROPERTIES OR FEATURES1.If the inputs (L and K) are increased by ‘λ’ times, the total output will also be increased by ‘λ’ times.2.The general form of Cobb-Douglas Production Function is homogeneous of degree (α+β). If α+β = 1, then the function turns into Linearly Homogeneous Function. But the function itself is not linear.3.If the P.F. is homogeneous of degree on (α+β = 1), then the production is operating under constant returns to scale. That is the value of (α+β) is the returns to scale.4.If the P.F. is a linear homogeneous P.F., then the elasticity of substitution between capital and labour is equal to unity, 1.5.Both inputs are essential factors in production process. That is, if one of the inputs is zero, other input will also be zero and, in turn, the output will also be zero.6.In the linear homogeneous P.F. (Q = ALαKβ) α and β represent the shares of labour and capital to the total output respectively.7.α and β represent the elasticity of output with respect to labour and capital respectively.8.The expansion path of Cobb-Douglas P.F. is linear homogeneous and it passes through the origin.9.Its Isoquants are sloping downwards.10.Its Isoquants are convex to the origin.11.Marginal products are proporitonal to Average Products.12.Marginal Product of Capital is α (Q/K) and the Marginal Product of Labour is β (Q/L).

SIGNIFICANCE OR IMPORTANCE OR USES OF COBB-DOUGLAS P.F.

Cobb-Douglas P.F. is the widely used function in Econometrics. Many economists are using this PF in different industrial and agricultural sectors. It provides important information regarding these sectors.

Useful to determine the factor prices.

Helps to verify the Marginal Productivity Theory. That is, with the help of the function we can determine whether the prices of factors of production are equal to their marginal productivity or not.

Helps to compute elasticity values for international or inter-sectoral comparisons.

Helps us to study the different laws of returns to scale.

Used to test laws of returns and substitutability of factors.

LIMITATIONS OR CRITICISMS OF COBB-DOUGLAS PRODUCTION FUNCTIONThis PF has been criticised by different economists. The main critics are K.J.Arrow, H.B.Chenery, B.s. Minhas and R.M. Solow. Following are the main criticisms.

1.The function has only two inputs, Labour and Capital. In other words, this is inapplicable for more than two inputs.2.This function assumes constant returns to scale.3.It assumes that technological conditions remain constant. But, the production changes due to change in technology. Thus, this function is based on the unrealistic assumption of stagnant technology.4.It assumes that ll inputs are homogeneous. In fact, all inputs are not homogeneous. For example, some labourers areefficient and others may not be.5.No upper limit to production is determined in this function.6.α and β of this function represent the share of labour and share of capital to the total output respectively. It is true only when there is perfect competition in the market. But, in the real world, there is no perfect competition. Even, if there is imperfect competition, the above relationship does not hold good.7.This considers only the positive marginal productivity of factors. That means, this function ignores the possibility of the negative3 marginal productivity of factors.8.It does not give any informatioin regarding inter-relations between the factors of production.

CES production function

The CES production function is a type of production function that displays constant elasticity of substitution. In other words, the production technology has a constant percentage change in factor (e.g. labour and capital) proportions due to a percentage change in marginal rate of technical substitution. The two factor (Capital, Labor) CES production function introduced by Arrow, Chenery, Minhas, and Solow is:

X = y [λC-α +(1-λ) N-α] d/α

WhereX = Output; C = Capital; N = Labour input; α = Substitution parameter;

y = Coefficient of technical efficiency; λ = Coefficient of Capital intensity1- λ = Coefficient of Labour intensityd = degree of homogeneity or the degree of returns to scale

Properties of CES P.F.The value of the elasticity of substitution depends upon the value of α.The marginal product is greater than ZeroThe marginal product curves are sloping downward and the marginal product of each factor will increase for increase in the other factor inputs.

AdvantagesRepresents a more general form of production technique than the Cobb-Douglas P.F. In the CES P.F., the elasticity of substitution is constant and not necessarily be equal to unity.The function has a number of important parameters than Cobb-Douglas P.F. Therefore, it has wider scope, substitutability and efficiency.The Cobb-Douglas P.F. is a special case of CES P.F. If we put α = 0 in the CES P.F., we can get the Cobb-Douglas P.F..The function is free from the difficulties nad unrealistic assumptions of Cobb-Douglas P.F.

LimitationsConsiders only two factors, labour and capital. It is not possible to consider more factors of production.Contains only one parameter, i.e., d, which affect by the scale of operation and technological change.Assumes that the elasticity of substitution changes in response to technology only and not in response to changes in factor proportions. But, really the elasticity of substitution also changes in response to changes in factor proportions.The capital intensity parameter of CES P.F. is not dimensionless.

23

The Explicit and Implicit costsThe explicit or accounting costs: are the actual out of pocket expenditures of the firm to purchase or hire inputs it requires in production. (i.e. wages to hire labour, interest on borrowed capital, rent on land and buildings and the expenditure on raw materials).

The Implicit costs: refers to the value of the inputs owned and used by the firm in its own production processes.

Cost Analysis• Types of Costs

– Fixed costs (FC)– Variable costs (VC)– Total costs (TC)– Sunk costs

Total and Variable CostsC(Q): Minimum total cost of producing alternative levels of output:

C(Q) = VC + FC

VC(Q): Costs that vary with output

FC: Costs that do not vary with output

$

Q

C(Q) = VC + FC

VC(Q)

FC

Fixed and Sunk Costs

FC: Costs that do not change as output changes

Sunk Cost: A cost that is forever lost after it has been paid

cost

Q

FC

C(Q) = VC + FC

VC(Q)

Some DefinitionsAverage Total Cost

ATC = AVC + AFCATC = C(Q)/Q

Average Variable CostAVC = VC(Q)/Q

Average Fixed CostAFC = FC/Q

Marginal CostMC = C/Q

Cost

Q

ATC

AVC

AFC

MC

Fixed Cost

Cost

Q

MC

ATC

AVC

Q0

AFC Fixed Cost

Q0(ATC-AVC)

= Q0 AFC

= Q0(FC/ Q0)

= FC

ATC

AVC

Variable Cost

Cost

Q

ATC

AVC

MC

AVC

Variable Cost

Q0

Q0AVC

= Q0[VC(Q0)/ Q0]

= VC(Q0)

$

Q

ATC

AVC

MC

ATC

Total Cost

Q0

Q0ATC

= Q0[C(Q0)/ Q0]

= C(Q0)

Total Cost

Economies of Scale

LRAC

$

Output

Economiesof Scale

Diseconomiesof Scale

Economies of Scale

Internal Economies

Internal economies of scale relate to the lower unit costs a single firm can obtain by growing in size itself. There are five main types of internal economies of scale.

External Economies

External economies of scale occur when a firm benefits from lower unit costs as a result of the whole industry growing in size.

Bulk-buying Economies

As businesses grow they need to order larger quantities of production inputs. For example, they will order more raw materials. As the order value increases, a business obtains more bargaining power with suppliers. It may be able to obtain discounts and lower prices for the raw materials.

Technical economies

Businesses with large-scale production can use more advanced machinery (or use existing machinery more efficiently). This may include using mass production techniques, which are a more efficient form of production. A larger firm can also afford to invest more in research and development.

Financial Economies

Many small businesses find it hard to obtain finance and when they do obtain it, the cost of the finance is often quite high. This is because small businesses are perceived as being riskier than larger businesses that have developed a good track record. Larger firms therefore find it easier to find potential lenders and to raise money at lower interest rates.

Marketing Economies

Every part of marketing has a cost – particularly promotional methods such as advertising and running a sales force. Many of these marketing costs are fixed costs and so as a business gets larger, it is able to spread the cost of marketing over a wider range of products and sales – cutting the average marketing cost per unit.

Managerial Economies

As a firm grows, there is greater potential for managers to specialize in particular tasks (e.g. marketing, human resource management, finance). Specialist managers are likely to be more efficient as they possess a high level of expertise, experience and qualifications compared to one person in a smaller firm trying to perform all of these roles.

Transport and communication links improve

As an industry establishes itself and grows in a particular region, it is likely that the government will provide better transport and communication links to improve accessibility to the region. This will lower transport costs for firms in the area as journey times are reduced and also attract more potential customers. For example, an area of Scotland known as Silicon Glen has attracted many high-tech firms and as a result improved air and road links have been built in the region.

Training and education becomes more focused on the industry

Universities and colleges will offer more courses suitable for a career in the industry which has become dominant in a region or nationally. For example, there are many more IT courses at being offered at colleges as the whole IT industry in the UK has developed recently. This means firms can benefit from having a larger pool of appropriately skilled workers to recruit from.

Other industries grow to support this industry

A network of suppliers or support industries may grow in size and/or locate close to the main industry. This means a firm has a greater chance of finding a high quality yet affordable supplier close to their site.

Diseconomies of scaleIncrease in long-term average cost of production as the scale of operations increases beyond a certain level. This anomaly may be caused by factors such as (1) over-crowding where men and machines get in each other's way, (2) greater wastage due to lack of coordination, or (3) a mismatch between the optimum outputs of different operations.

Diseconomies of scale occurs when Average Costs start to rise with increased output. Therefore there will be decreasing returns to scale

Diseconomies of scale can sometimes occur for the follow reasons

1.A specific process within a plant cannot produce the same quantity of output as another related process. For example, if in a product required both gadget A and gadget B, diseconomies of scale might occur if gadget B is produced at a slower rate than gadget A.

2. As output increases, costs of transporting the good to distant markets can increase enough to offset any economies of scale. For example, when a firm has a large plant capable of producing a large output located in one location, the more the firm produces, the more it needs to ship to distant locations.•Poor communication in a large firm•Alienation: Working in a highly specialized assembly line can be very boring, if workers become de motivated. In a large firm there is an increased gap between top and bottom e.g. call centres•Lack of control: when there is a large number of workers it is easier to escape with not working very hard because it is more difficult for managers to notice shirking.