5 Production Analysis

Production AnalysisProduction Analysis

A process of converting inputs into output is termed as A process of converting inputs into output is termed as production.production.

In eIn e conomic terms, production is an act of creating conomic terms, production is an act of creating value or utility that can satisfy the wants of individuals. value or utility that can satisfy the wants of individuals.

The production process is dependent on a number of The production process is dependent on a number of inputs, such as raw materials, labor, capital, technology, inputs, such as raw materials, labor, capital, technology, and time. These inputs are also known as factors of and time. These inputs are also known as factors of production.production.

Factors of production include:Factors of production include: Land Land Labor Labor Capital Capital EnterpriseEnterprise

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Concept of Production Concept of Production

Production function is the mathematical representation of relationship Production function is the mathematical representation of relationship between physical inputs and physical outputs of an organization. between physical inputs and physical outputs of an organization.

Production function represents the maximum output that an Production function represents the maximum output that an organization can attain with the given combinations of factors of organization can attain with the given combinations of factors of production (land, labor, capital, and enterprise) in a particular time production (land, labor, capital, and enterprise) in a particular time period with the given technology. period with the given technology.

In the long-run, the organization can increase labor and capital both In the long-run, the organization can increase labor and capital both for increasing the level of production. Thus, production function in for increasing the level of production. Thus, production function in long run=long run=

In short-run, the supply of capital is inelastic. This implies that capital In short-run, the supply of capital is inelastic. This implies that capital is constant. Thus, production function in short run = is constant. Thus, production function in short run =

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Production Function Production Function

Production Functions

Properties of Production Functions Determined by technology, equipment and input

prices. Discrete functions are lumpy. Continuous functions employ inputs in small

increments.

Returns to Scale and Returns to a Factor Returns to scale measure output effect of increasing

all inputs. Returns to a factor measure output effect of

increasing one input.

Total, Marginal, and Average Product Total Product (TP)

Total product is whole output.

Marginal product is the change in output caused by increasing any input X. (MP)

If MPX=∂Q/∂X> 0, total product is rising. If MPX=∂Q/∂X< 0, total product is falling (rare).

Average product (AP) APX=Q/X.

Law of Diminishing Returns to a Factor

Returns to a Factor Shows what happens to MPX as X usage

grows.• MPX> 0 is common.

• MPX< 0 implies irrational input use (rare).

Diminishing Returns to a Factor Concept MPX shrinks as X usage grows, ∂2Q/∂X2< 0.

If MPX grew with use of X, there would be no limit to input usage.

Law of diminishing returns explains thatLaw of diminishing returns explains that when more and when more and more units of a variable input are employed on a given more units of a variable input are employed on a given quantity of fixed inputs, the total output may initially quantity of fixed inputs, the total output may initially increase at increasing rate and then at a constant rate, increase at increasing rate and then at a constant rate, but it will eventually increase at diminishing rates.but it will eventually increase at diminishing rates.

Assumptions:Assumptions: Assumes labor as an only variable input, while capital is Assumes labor as an only variable input, while capital is

constant constant Assumes labor to be homogeneousAssumes labor to be homogeneous Assumes that state of technology is givenAssumes that state of technology is given Assumes that input prices are givenAssumes that input prices are given

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Law of Diminishing Returns Law of Diminishing Returns

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Stages of production in law of Stages of production in law of diminishing returns diminishing returns

Stage I: Refers to the stage of Stage I: Refers to the stage of production in which the total production in which the total output increases initially with output increases initially with the increase in number of the increase in number of labor.labor.

Stage II: Refers to the stage Stage II: Refers to the stage in which total output increases in which total output increases but marginal product starts but marginal product starts declining with the increase in declining with the increase in number of workers. number of workers.

Stage III: Refers to the stage Stage III: Refers to the stage in which the total product in which the total product starts declining with an starts declining with an increase in number of workersincrease in number of workers

In long run production function, the In long run production function, the relationship between changing input and relationship between changing input and output is studied in the laws of returns to output is studied in the laws of returns to scale, which is based on production scale, which is based on production function and isoquant curve. function and isoquant curve.

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Laws of Returns to Scale Laws of Returns to Scale

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Isoquant MapsIsoquant Maps

An An isoquantisoquant is a curve that shows the is a curve that shows the various combinations of inputs that will various combinations of inputs that will produce the same (a particular) amount of produce the same (a particular) amount of output.output.

An An isoquant mapisoquant map is a contour map of a is a contour map of a firm’s production function.firm’s production function. All of the isoquants from a production function All of the isoquants from a production function

are part of this isoquant map.are part of this isoquant map.

Points Input combinations Output

  K + L  

A OK4 + OL1 200

B OK3 + OL2 200

C OK2 + OL3 200

D OK1 + OL4 200

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Isoquant curveIsoquant curve

Input Combination Choice

Production Isoquants Show efficient input combinations. Technical efficiency is least-cost production.

Isoquant shape shows input substitutability. Straight line isoquants depict perfect

substitutes. C-shaped isoquants depict imperfect

substitutes. L-shaped isoquants imply no substitutability.

Marginal Rate of Technical Substitution (MRTS) is the Marginal Rate of Technical Substitution (MRTS) is the quantity of one input (capital) that is reduced to increase quantity of one input (capital) that is reduced to increase the quantity of the other input (Labor), so that the output the quantity of the other input (Labor), so that the output remains constant.remains constant.

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Marginal Rate of Technical SubstitutionMarginal Rate of Technical Substitution

Combination Input L Input K Output MRTS of L for K

P 1 15 150  

Q 2 11 150 4:1

R 3 8 150 3:1

S 4 6 150 2:1

T 5 5 150 1:1

Marginal Rate of Technical Substitution

Marginal Rate of Technical Substitution Shows amount of one input that must be

substituted for another to maintain constant output.

For inputs X and Y, MRTSXY=-MPX/MPY

Rational Limits of Input Substitution Ridge lines show rational limits of input

substitution. MPX<0 or MPY<0 are never observed.

Elasticity of factor substitution (σ) refers to the ratio Elasticity of factor substitution (σ) refers to the ratio of percentage change in capital-labor ratio to the of percentage change in capital-labor ratio to the percentage change in MRTS. It is mathematically percentage change in MRTS. It is mathematically represented as follows:represented as follows:

σ = percentage change in capital labor σ = percentage change in capital labor ratio/percentage change in MRTS ratio/percentage change in MRTS

Or, Or, σ = [(∆K/∆L) /∆MRTS] * [MRTS/ (K/L)] σ = [(∆K/∆L) /∆MRTS] * [MRTS/ (K/L)]

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Elasticity of Factor Substitution Elasticity of Factor Substitution

Iso-cost line represents the price of factors Iso-cost line represents the price of factors along with the amount of money an along with the amount of money an organization is willing to spend on factors. organization is willing to spend on factors.

For example, a producer wants to spend For example, a producer wants to spend Rs. 300 on the factors of production, Rs. 300 on the factors of production, namely X and Y. The price of X in the namely X and Y. The price of X in the market is Rs. 3 per unit and price of Y is market is Rs. 3 per unit and price of Y is Rs. 5 per unit.Rs. 5 per unit.

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Iso-cost Lines

Iso-cost Lines

A producer can attain equilibrium by applying the least A producer can attain equilibrium by applying the least cost combination of factors of production to attain cost combination of factors of production to attain maximum profit.maximum profit.

The producers try to use ratios of factors in such a way The producers try to use ratios of factors in such a way so that maximum output can be obtained, while keeping so that maximum output can be obtained, while keeping the cost as low as possible.the cost as low as possible.

The producer equilibrium would be attained when the The producer equilibrium would be attained when the output produced by spending an additional unit of money output produced by spending an additional unit of money (marginal rupee) on A is equal to the output produced by (marginal rupee) on A is equal to the output produced by spending an additional unit of money on B.spending an additional unit of money on B.

The producer equilibrium can be represented as follows:The producer equilibrium can be represented as follows:

MPa/Pa = MPb/Pb = ……. = MPn/PnMPa/Pa = MPb/Pb = ……. = MPn/Pn

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Producer’s Equilibrium

Producer’s equilibrium can be obtained Producer’s equilibrium can be obtained with the help of isoquant and iso-cost line.with the help of isoquant and iso-cost line.

For attaining equilibrium, a producer For attaining equilibrium, a producer needs to obtain a combination that helps needs to obtain a combination that helps in producing maximum output with the in producing maximum output with the least price.least price.

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Determination of Producer’s Equilibrium

Determination of Producer’s Equilibrium

Expansion Path

The law of returns to scale explains the proportional The law of returns to scale explains the proportional change in output with respect to proportional change in change in output with respect to proportional change in inputs.inputs.

The degree of change in output varies with change in the The degree of change in output varies with change in the amount of inputs. For example, an output may change amount of inputs. For example, an output may change by a large proportion, same proportion, or small by a large proportion, same proportion, or small proportion with respect to change in input.proportion with respect to change in input.

Law of returns can be classified into three categories:Law of returns can be classified into three categories: Increasing returns to scaleIncreasing returns to scale Constant returns to scale Constant returns to scale Diminishing returns to scaleDiminishing returns to scale

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Returns to ScaleReturns to Scale

If the proportional change in the output of an If the proportional change in the output of an organization is greater than the proportional change organization is greater than the proportional change in inputs, the production is said to reflect increasing in inputs, the production is said to reflect increasing returns to scale.returns to scale.

In Figure, a movement from a to b indicates that the In Figure, a movement from a to b indicates that the amount of input is doubled. Now, the combination of amount of input is doubled. Now, the combination of inputs has reached to 2K+2L from 1K+1L. However, inputs has reached to 2K+2L from 1K+1L. However, the output has increased from 10 to 25 (150% the output has increased from 10 to 25 (150% increase), which is more than double. Similarly, when increase), which is more than double. Similarly, when input changes from 2K+2L to 3K + 3L, then output input changes from 2K+2L to 3K + 3L, then output changes from 25 to 50(100% increase), which is changes from 25 to 50(100% increase), which is greater than change in input.greater than change in input.

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Increasing Returns to Scale

IRS

The production is said to generate constant returns to scale when the proportionate change in input is equal to the proportionate change in output.

In Figure, when there is a movement from a to b, it indicates that input is doubled. Now, when the combination of inputs has reached to 2K+2L from 1K+1L, then the output has increased from 10 to 20. Similarly, when input changes from 2K+2L to 3K + 3L, then output changes from 20 to 30, which is equal to the change in input.

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Constant Returns to Scale

CRS

Diminishing returns to scale refers to a situation when the Diminishing returns to scale refers to a situation when the proportionate change in output is less than the proportionate proportionate change in output is less than the proportionate change in input.change in input.

In Figure, when the combination of labor and capital moves In Figure, when the combination of labor and capital moves from point a to point b, it indicates that input is doubled. At from point a to point b, it indicates that input is doubled. At point a, the combination of input is 1K+1L and at point b, the point a, the combination of input is 1K+1L and at point b, the combination becomes 2K+2L. However, the output has combination becomes 2K+2L. However, the output has increased from 10 to 18, which is less than change in the increased from 10 to 18, which is less than change in the amount of input. Similarly, when input changes from 2K+2L to amount of input. Similarly, when input changes from 2K+2L to 3K + 3L, then output changes from 18 to 24, which is less than 3K + 3L, then output changes from 18 to 24, which is less than change in input. change in input.

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Diminishing Returns to Scale

DRS

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Capitalper week

4

A

q = 10

3

2

1Laborper week1 2 3

(a) Constant Returns to Scale40

Capitalper week

4

A

3

2

1

Laborper week

1 2 3

(c) Increasing Returns to Scale

40

Capitalper week

4

A

3

2

1

Laborper week1 2 3

(b) Decreasing Returns to Scale

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Isoquant Maps showing Constant, Isoquant Maps showing Constant, Decreasing, and Increasing Returns to Decreasing, and Increasing Returns to

ScaleScale

q = 10 q = 10

q = 20

q = 20q = 20

q = 30q = 30

q = 30q = 40

q = 40

Returns to Scale

Returns to scale show the output effect of increasing all inputs. Output elasticity is εQ = ∂Q/Q ÷ ∂Xi/Xi where

Xi is all inputs (labor, capital, etc.)

Output Elasticity and Returns to Scale εQ > 1 implies increasing returns.

εQ = 1 implies constant returns.

εQ < 1 implies decreasing returns.

Production Functions

In economics, a “production function" describes an empirical relationship between specified output and inputs. A production function can be used to represent output production for a single firm, for an industry, or for a nation. Just to illustrate, a production function of a wheat farm might have the form:

W=F(L,A,M,F,T,R)

That is, production of wheat in tons (W) depends on the use of labor measured in days (L), land in acres (A), machinery in dollars (M), fertilizer in tons (F), mean summer temperature in degrees (T), and rainfall in inches (R).

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Production Functions

Letting q represent the output of a particular good during a period, K represent capital use, L represent labor input, and M represent raw materials, the following equation represents a production function.

),,( MLKfq

Properties of Production Functions It is generally assumed that a production function, F(L,C),

satisfies the following properties: F(L,0) = 0, F(0,C) = 0 (both factor inputs are required for output) dF/dL > 0, dF/dC > 0 (an increase in either input increases output)

At a given set of inputs (L,C), the production function may show decreasing, constant, or increasing “returns to scale”:

If F(kL, kC) < kF(L,C), there are decreasing returns to scale If F(kL, kC) = kF(L,C), there are constant returns to scale If F(kL, kC) > kF(L,C), there are increasing returns to scale

Constant returns to scale imply that the total income from output production equals the total costs from inputs:

pF(L,C) = wL + rC

(p the price per unit output, w and r costs of labor and capital).

The Cobb-Douglas Production Function

The simplest production function is the Cobb-Douglas model. It has the following form:

Q=aLbCc

where Q stands for output, L for labor, and C for capital. The parameters a, b, and c (the latter two being the exponents) are estimated from empirical data.

If b + c = 1, the Cobb-Douglas model shows constant returns to scale. If b + c > 1, it shows increasing returns to scale, and if b + c < 1, diminishing returns to scale.

Productivity Measurement

Economic Productivity Productivity growth is the rate of change in

output per unit of input. Labor productivity is the change in output per

worker hour. Causes of Productivity Growth

Efficiency gains reflect better input use. Capital deepening is growth in the amount of

capital workers have available for use.