Production Analysis

PRESENTATION ON

PRODUCTION ANALYSIS

Ashutosh Srivastava 11 A

Ayushi 12 A

Bhoopendra Tiwari 13 A

Chandan Kumar 14 A

Debmalya Das 15 A

Deepika Mishra 16 A

Garima Manchanda 17 A

Gaurav Kr. Varshney 18 A

Gaurav Sarin 19 A

Gurdeep Singh 20 A

By:- THE GO GETTERS

INTRODUCTION

q Every organization uses labor,capital and land or raw materials for the purpose of producing goods and services.

q Whole and sole aim is to maximize total profit.

PRODUCTION AND PRODUCTION FUNCTION

q PRODUCTION:- Refers to the transformation of input resources into outputs of goods and services.

q Inputs are resources used in the production of goods and services.

q Types of inputs: a) FIXED INPUT

b)VARIABLE

PRODUCTION FUNCTION

q Mathematical representation of the relationship:

q Q = f (K, L, La)q Output (Q) is dependent upon the amount of

capital (K), Land (L) and Labour (La) used

PRODUCTION FUNCTION

q States the relationship between inputs and outputsq Inputs – the factors of production classified as:q Land – all natural resources of the earth – not just ‘terra firma’!

q Price paid to acquire land = Rent q Labour – all physical and mental human effort involved in

productionq Price paid to labour = Wages

q Capital – buildings, machinery and equipment not used for its own sake but for the contribution it makes to production

q Price paid for capital = Interest

TYPES OF PRODUCTION FUNCTION

q SHORT RUN: time period during which at least one input is fixed.

q LONG RUN:- time period during which all inputs are variable.

Analysis of Production Function:Short Run

q In the short run at least one factor fixed in supply but all other factors capable of being changed

q Reflects ways in which firms respond to changes in output (demand)

q Can increase or decrease output using more or less of some factors but some likely to be easier to change than others

q Increase in total capacity only possible in the long run

ANALYSIS OF PRODUCTION FUNCTION:SHORT RUN

In times of rising sales (demand) firms can increase labour and capital but only up to a certain level – they will be limited by the amount of space. In this example, land is the fixed factor which cannot be altered in the short run.

ANALYSIS OF PRODUCTION FUNCTION:SHORT RUN

If demand slows down, the firm can reduce its variable factors – in this example it reduces its labour and capital but again, land is the factor which stays fixed.

Analysing the Production Function: Long Run

q The long run is defined as the period of time taken to vary all factors of productionq By doing this, the firm is able to increase its total capacity –

not just short term capacityq Associated with a change in the scale of productionq The period of time varies according to the firm

and the industryq In electricity supply, the time taken to build new capacity

could be many years; for a market stall holder, the ‘long run’ could be as little as a few weeks or months!

Analysis of Production Function:Long Run

In the long run, the firm can change all its factors of production thus increasing its total capacity. In this example it has doubled its capacity

Production FunctionWith Two Inputs

K Q6 10 24 31 36 40 395 12 28 36 40 42 404 12 28 36 40 40 363 10 23 33 36 36 332 7 18 28 30 30 281 3 8 12 14 14 12

1 2 3 4 5 6 L

Q = f(L, K)

Production FunctionWith Two Inputs

Continuous Production Surface

TOTAL PRODUCT (TP)It is derived by holding the quantity of one input constant and changing the quantity of the other input .

MARGINAL PRODUCT (MP)

It is the change in the total product or extra output per unit change in an input used.

For per unit change in labor it is calculated as

MPL = ∆TP ∆L

AVERAGE PRODUCT (AP)

It is the ratio of total product and total unit of the input which is changed to derive the total product.

For per unit change in labor it is calculated as:

APL = TP

L

PRODUCTION OR OUTPUT ELASTICITY (E)

It is the ratio of the percentage change in output and the percentage change in the input which is changed to derive the total product.

For per unit change in labor it is calculated as: For per unit change in labor it is calculated as:

EL = ∆Q∆Q

∆L

LAW OF DIMINISHING RETURN

As we go on using more more units of variable input along with a given amount of fixed input after a point we start getting diminishing returns for the variable input. This is called the law of diminishing return.

Production FunctionWith One Variable Input

Total Product

Marginal Product

Average Product

Production orOutput Elasticity

TP = Q = f(L)

MPL =TP L

APL =TP L

EL =MPL

APL

Production FunctionWith One Variable Input

L Q MPL APL EL

0 0 - - -1 3 3 3 12 8 5 4 1.253 12 4 4 14 14 2 3.5 0.575 14 0 2.8 06 12 -2 2 -1

Total, Marginal, and Average Product of Labor, and Output Elasticity

Production FunctionWith One Variable Input

Production FunctionWith One Variable Input

The declining portion of the marginal product

curve reflects the law of diminishing return.

Optimal Use of theVariable Input

Marginal RevenueProduct of Labor

MRPL = (MPL)(MR)

Marginal ResourceCost of Labor

MRCL =TC L

Optimal Use of Labor MRPL = MRCL

Optimal Use of theVariable Input

L MPL MR = P MRPL MRCL

2.50 4 $10 $40 $203.00 3 10 30 203.50 2 10 20 204.00 1 10 10 204.50 0 10 0 20

Use of Labor is Optimal When L = 3.50

Optimal Use of theVariable Input

Production With TwoVariable Inputs

Isoquants show combinations of two inputs that can produce the same level of output.

Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped.

Production With TwoVariable Inputs

Isoquants

Production With TwoVariable Inputs

Economic Region of Production

Production With TwoVariable Inputs

Marginal Rate of Technical Substitution•It is the absolute value of the slope of isoquants.

•MRTS = -dK/dL

•We multiply dK/dL -1 in order to express the MRTS as a positive number.

•The MRTS is the rate at which the firm would be willing to give up capital in exchange for labor.

Production With TwoVariable InputsMRTS = -(-2.5/1) = 2.5

Optimal Combination of Inputs

Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

C wL rK= +

C wK L

r r= −

C Total Cost=

( )w WageRateof Labor L=

( )r Cost of Capital K=

Optimal Combination of InputsIsocost Lines

AB C = $100, w = r = $10

A’B’ C = $140, w = r = $10

A’’B’’ C = $80, w = r = $10

AB* C = $100, w = $5, r = $10

Optimal Combination of Inputs

MRTS = w/r

Optimal Combination of Inputs

Effect of a Change in Input Prices

EMPIRICAL PRODUCTION FUNCTION

•Cobb-Douglas Production function

Q = A KaLb

where, Q = quantities of output K = capital L = labor

A, a, b = parameters to be estimated empirically

Useful Properties of Cobb-Douglas Production Function

•The marginal product of of capital & the marginal product of labor depend on both the quantity of capital & the quantity of labor used in production.•The exponents of K & L (that is a, b) represent, respectively, the output elasticity of labor & capital and the sum of the exponents measures the returns to scale.

If a+b=1 then Constant Return of Scale

a+b>1 then Increasing Return of Scale

a+b<1 then decreasing Return of Scale

CONT…

• Cobb-Douglas Production Function can be estimated by regression analysis by transforming it into

logQ = logA + alogK + blogL

Returns to Scale

Constant Returns to

Scale

Increasing Returns to

Scale

Decreasing Returns to

Scale

Innovations and Global Competitiveness

• Product Innovation

• Process Innovation

• Product Cycle Model

• Just-In-Time Production System

• Competitive Benchmarking

• Computer-Aided Design (CAD)

• Computer-Aided Manufacturing (CAM)