THEORY OF PRODUCTION
Production theory deals with physical relationship i.e. technical & Technological relations between input & between Output & inputs.
PRODUCTION –> Means a process by which a commodity or commodities are transformed into a different usable commodity.
Services like transport, legal, medical consultancy, storage for future use, wholesaling, retailing are also productive activities.
INPUT & OUTPUT
INPUT–> Inputs are of two types
1. Fixed–> whose supply is inelastic in short run. All its users can’t employ more of it in short run. E.g. plant, machinery, building.
2. Variable factors–> Whose supply in short run is elastic e.g. labour & raw material
Goods & services that comes out of production process.
SHORT RUN & LONG RUN
SHORT RUN–> Supply of certain inputs is fixed production can be increased by increase in use of variable inputs.
LONG RUN–> Supply of all inputs is elastic but not enough to permit a change in technology.
Production function is a tool of analysis used to explain the relationship between input & output. It describes the technological relationship between input & output.
It tells that production depends on certain ships. It can be in the form of specific inputs.
* Graphed line
* An algebra aqua
* Mathematical model
Classification of input by economist
* Raw material
E.g. a = f (K, L)
K = Capital
L = Labor
(i) Perfect divisibility of both inputs & outputs.
(ii) Limited substitution of one factor for the other.
(iii) Constrict technology
(iv) Inelastic supply of fixed factors in the short-term.
Laws of Production
Laws of variable proportions laws of returns to scale (long-run)
Law of Returns to variable proportions of fixed factors
Law of Diminishing Returns (or variable proportion) Relationship between varying factor proportions & output when more & more units of a variable input are applied to a given quantity of fixed inputs the total output may initially increase at an increasing rate & then at a constant rate but it will eventually increase at diminishing rates. I.e. the marginal increase in the total output eventually decreases when additional units of variable factors are applied to a given quantity.
Here we take K (capital) as constant & Labor (L) as variable
Q = f (L)
MPL= TPN – TPN-1(first derivative of the Production Function)
In stage I
The first increases MPL also increase TPL continues to increase but at diminishing rate.
In stage II
I.e. after 5th worker. TPL is max at the employment of 10th worker beyond this level of output TPL decreases in stage III.
Factors Behind the Laws of Returns
Stage I – Law of increasing returns is an operation.
Stage II – Law of diminishing returns is in application.
Indivisibility of fixed factor (capital)
– (Results in under utilization of capital of labor are less than its optimum number). If less than 6 workers is underutilizing of K.
– (Increase in labor productivity is that employment of additional workers leads to advantages of division of labor until optimum capital labor combination is reached because of specialization of labor)
Once optimum capital labor rate is reached employment of additional workers will amount to substitution of capital with labor. But there is a limit to which one input can be substituted for another i.e. elasticity of substitution between input is not in fete. Also difficult to assign specialized task & return of firm must operate
– Technology remains unchanged
– Input prices.
– Variable factors are homogenous
Application of the Law of Diminishing Returns.
> Empirical Law is not applied universally
> Technology remains fixed effect of an additional input when technology changes can’t be explained.
> Is all input are increase in all input
> How much to produce
> What no. Of workers to apply to a given fixed input.
Marginal Revenue Productivity & Labor Employment
Equip-marginal Principal – Marginal revenue productivity of labor equals the marginal wags rate.
The marginal revenue productivity is the value of product resulting from the marginal unit of variable input (labor).
MRP = MPP x P
(Marginal revenue Product) (Marginal Physical Productivity) x (Price)
When MRP = wage rate tells the no. of labor to be employed.
Profit is max when MR = MC
P1 P AW=MW
MRP & MW
At point P, the no. of worker = ON should be employed.
Total output = ON x APC (Average Labor Productivity)
Long Term Laws of Production
In the long-run supply of both. The input is supposed to be elastic & firms can hire. Larger quantities of both labor & capital.
Laws of returns to scale are explained through production function & curves.
Iso-quant curve (Greek word)
Equal quantity also known as “Equal product curve” or “Production indifference curve”.
An asquint curve is focus of points representing various combinations of two inputs – capital & labor yielding the same output.
Indifference curve Iso-quant
2 consumer good 2 reducer goods
Measures utility measures output.
Ok4 + OL1 = 100
K4 A Ok3 + OL2 = 100
L1 L2 L3 L4
Substitution of one factor for other leaves the unaffected. I.e. substitution of labor for capital such that all quantity of commodity
i.e. IQ = 100
Properties of Iso-quant
– Negative slope in the economic region (region in which substitution between inputs is technology possible). It indicates substitution is possible i.e. if one is ? the other has to be ? to keep output.
– Convex to origin – implies not only the substitution between the inputs but also that marginal rate of technical substitution (MRTS) is the economic region.
MRTS = ?K = Slope of iso-quant.
The rate of which marginal unite of labor can substitute margin. Unit of capital
MRTS ? : No factor is perfect substitute for another.
?K1 > ?K2 > ?K3
?L1 ?L2 ?L3
If ?K1 = ?K2 = ?K3 but ?L1 = ?L2 = ?L3
– Can’t intersect or be tangent to each other – intersection means that a given quantity of a commodity can be produced with a smaller as well as a larger input-combination, which is not possible until Marginal productive greater than Zero.
– Upper iso-quant Represent higher level of output
Laws of Returns to scale
(i) Increasing Returns to Scales – Proportionate change in both the inputs K & L leads to more than. Proportionate change in output. I.e. if K & L are successively double the corresponding output is more than doubled.
1K Q 40
1L 2L 3L
> Technical & managerial indivisibility
– Higher degree of specialization composite
* Technology for higher forms division
* Own transport & strong facility of Labor.
– Dimensional relation – 15 x 10 = 150
30 x 20 = 600
(ii) Constant Returns to scale- when the change in output is proportional to the change in inputs K & L are doubled is also doubled.
1K + 1L = 10 ] DOUBLE
2K + 2L = 20 50% increase in K & L to
3K + 3L = 30 50% increase in Q
1K Q 30
1L 2L 3L
Reason – limits of the economics of scale.
When economies of scale reach their limits & diseconomies are yet to begin.
– Where factors of production are perfectly divisible
– Technology is such that capital Labor ratio is fixed.
– Production fine is homogenous of degree
Decreasing Returns to Scale
Proportionate change in input (K & L) leads to a less proportional change in output.
1K + 1L = 10
2K + 2L = 18 50% increase (K & L) or increase 33.3%
3K + 3L = 24
1K Q 24
1L 2L 3L
> Diseconomies of scale
> Diminishing returns to management i.e. managerial diseconomies
> Limitedness or exhaustibility of natural resources as by increasing six of coalmine it is not necessary that coal deposits also increases.
Qx = P (K, L)
When all the inputs are increased in the same proportion & the proportion can be factored out then prod fune is called homogenous prod function of degree or linear prod function.
KQx = f (kK, kL)
= k (K, L)
Prod fune of degree I implies const. Return to scale
HQn = f (kK, kL)
If h = K Const. Returns to scale.
If h > K increasing Returns to scale.
If h < K decreasing Returns to scale.
If Qn = 5K + 10L
Qn1 = 5 (1) + K (2)
25 = 5 + 20
(K = 2, L=4)
If Qn2 = 5 (1 x 2) + 10 (2×2)
58 = 10 + 40
Qn2 = 50 = 2 h=2
K = h const return, h>K increasing, h<K decreasing
Degree of production function & returned to scale
K = k’ exponent is in case of prod. Fune of degree 1.
But prod. Funct. can be have exponent quarter or less than 1.
Let exponent k is R where R = 1
F (RK, RL) = Rr (K, L) = Rr (Q)
If R>1 & r<1 decreasing returns
If R>1 & r>1 increasing returns
If R>1 & r=1 constant returns
Q =K0.25 L 0.50
HQ = (Rk)0.25 (Rl)0.50
HQ = R0.25+0.50 [K 0.25 L 0.50]
HQ = K0.75 (K0.25, L0.50)
H =K0.75 R = 0.75 < 1 ?decreasing Returns
Q = K 0.75 L 1.25 ? 0.50
HQ= (RK)0.75 (RL)1.25 (RX)0.50
HQ = R 0.75+1.25+0.50 (K 0.75 L 1.25 ? 0.50)
= R 2.5 (K 0.75 L1.25 ? 0.50)
H = K 2.5 R = 2.5 > 1 increasing returns
If h = K R=1 Constant Return
Economies of Scale
– Economies in production (i) Technology advantage (ii) advantages of division of labor & specialization.
– Economies in marketing (sales force better utilization)
* Large scale purchase raw materials
* Distribution through whole sealers
* Low cost sales persons
* Advertising low cost
– Managerial economies
* Specialization in management
* Mechanization of managerial fune.
* Decentralization of decisions making
* Advanced technology of communication.
– Economies in transport & storage
* Own means of transport prevents delay
* Create their own god owns less storage cost.
– Large-scale of purchase of raw material.
– Acquisition of finance at less contest rate.
– Lower advt. Rates charged for large-scale advertising.
– Concessional rates by transport companies.
– Lower wage-rates if mono Portia employees
Optimal input combination
OK3 + OL1 = 100 OK2 + OL2 = 100 OK1 + OL3 = 1
Technically any point can be chosen but not economically.
Only one combination gives the min-cost that point or combination is chosen
Let total cost
C = KPk + LPl
C-LPL = LPL
K = C – PL.L
L = C – PK.K
The line from alternative combination of K & L can be purchased out of total cost C is know as Iso-cost Is cost Isoclines or budget line or budget constraint line.
Ok1= C – PL . L (Where L=0)
K2 PK PK
K1 OL1 = C – PK . K (Where K=0)
L1 L2 L3
-?K = slope of Iso cost represents
Marginal rate of exchange (MRE)
Least cost factor criteria
– First order condition
– Second order condition
-?K = MPL
?K = MRE
MPL = Marginal Physical Productivities of L & K.
Least-cost input combination
Input combination at which factor exchange ratios of their marginal productivities.
MPL = PL or MPL = MPK
MPK PK PL PK
MPL = slope of Iso-quant
Least-cost combination exists at a point where Iso-quants are to the Iso-cost.
-?K = MPL
First order at A & Q also is on upper Iso-quant
Large firm will choose point P.
Least cost criterion in value terms.
PL = MRPL or MRPL = MRPK
PK MRPK PL PK
Effect of change in Input Price.
It all input prices change in the same proportion the relative prices of inputs remain unaffected.
Change in input combination result from the substitution effect of change in relative price of input.
Cost minimizing firms substitution relative cheaper input for costlier one. This is known as substitution effect.
As a result of change in P reduces K by K1 K2 && increases L1 L2. This is known as input price effect.
Substitution effect = Price effect – budget effect
Price effect = L1 L2
Budget effect = L1 L2
Substitution effect = L1 L2 – L1 L2 = L2 L3
If price of an input ? level of output ? & vice-versa.
Firm employs more of cheaper input & less of costlier one.
L1 L2 L L3 L’ W
Cost & Output Relation
Short-run cost – output relations
Total Cost (TC) – Actual Cost that must be incurred to produce a given quantity of output.
TC = TFC + TVC
(Total Fixed Cost) + (Total Variable Cost)
For a given Q
Average Cost AC = TC = TFC + TVC
Average Fixed Cost AFC = TFC
AVC = TVC
AC = AFC + AVC
Marginal cost (MC) = change in total cost divided by the change in total output.
MC = ?TC or dTC
?TC = ?TFC + ?TVC
In the short-run ?TFC = O. ?TC = ?TFC
If ?Q = 1 MC = ?TVC
Cost function & cost output Relations
Let the cost Function
TC = a + bQ – CQ2 + dQ3
A = fixed cost
B, c, d, = variable cost parameters.
TFC remain fined for the whole range of output & hence takes the form of horizontal line TFC. The TVC curve shows that the total variable cost first increases at decreasing rate & then at an increasing rate. The slope of curve gives the rate of increase. The pattern of TVC is because law of increasing & dominating returns to the variable inputs.
Average Fixed Cost
AVC = TFC
AFC curve is a rectangle hyper.
Average variable cost (AVC)
AVC = TVC
Critical value of AVC
The critical value of Q (in respect of AVC) is that value of Q at which AVC is min. AVC is min when its (decreasing rate of change equals Zero.
Q = dAVC = O.
Q = -0.9 + 0.10Q = 0
Average Cost (AC)
The average cost is defined as AC = TC
AC = 10 + 6Q – 0.9Q2 = 0.05Q3
= 10 + 6 – 0.9Q + 0.05Q2
AC curve is U-shaped
Critical value of Q in respect of AC is one at which AC is minimize.
dAC = 10 – 0.9 + 0.10 = 0
Q3 – 9Q2 – 100 = 0
Critical value of output in respect of AC is 10 i.e. AC reaches its min. at Q = 10
Short Run Cost Curves
Marginal cost (MC)
MC = dTC
dTC = 6 – 1.8Q + 0.15Q2
MC = TCM – TCn-1
Critical value of Q in respect of MC is 6 or 7.
Curve & the laws of diminishing returns,
If more & more units of a variable input are applied to the given amount of a fined input the marginal cost initially decrease but eventually increases.
Both AFC & AVC are declining because of internal economies.
AC = AFC = AVC AC is also declining
If operation of output AFC continues to fell AVC starts increasing because of fast increase in the TVC.
Rate of fall in AC decreases. The AC reaches its min. when output increases to 10 units. Beyond this level AC Starts increasing which show that the law of diminishing returns comes in operation.
Downward trued in the MC shows increasing marginal productivity of the variable input due mainly to internal economy resulting form increase in productive.
Upward trend in MC shows increase in TVC & decreasing marginal productive of the variable inputs.
Important Cost Relationships
– As long as AFC & AVC fall, AC also falls
– When AFC falls but AVC increases change in AC depends on the rate of change in AFC.
If decrees in AFC > increase in AVC, AC?
If decrees in AFC = ? in AVC AC =
If decrees in AFC < ? in AVC AC?
– When MC is ? rate of fall in MC is > then that AC. MC is attributed to a single marginal unite while in case of AC. The decreasing MC is distributed over all the enter output.
– MC ? AC at a lower rate when MC ? it increase at a relatively lower rate which is sufficient only for reduce the rate of decrease to of AC & not sufficient to push the AC ?. AC continues to ? even if MC ?.
– MC intersects AC at its min point at this point AC is const AC = MC
PV Ratio = S-V x 100
BEP (SALE VALUE) = Fixed expenses
Contribution per unit
Margin of Safety = Profit x Sales
Margin of safety = Profit
Margin of safety = Sa-Sb x 100
(Represents the diff between the sales at break-even point & the total actual sales)
Sa = Actual Sales Sb = Sales of BEP
Optimum output in short-run
Optimum level of output is one, which can be produced at a minimum average cost, given the technology.
The minimum level of AC is determined by the point of inter section between AC & MC curves.
At this level output AC = MC. Production below or beyond this level will be in optional. It production is less than 10 it will leave some scope for reducing AC by producing more, because MC < AC. If production is > then AC can be reduces by reducing output.
Optimum level of output is not occasional the max-profit output.
Long Run Cost – Output Relations
In long run supply of all the inputs become elastic.
Long run cost output relations therefore implies the relationship between the changing scale of the firm & the total output.
Long run curves are composed of a service of short run cost curves.
Long Run Total Cost Curve (LTC)
LTC can be draw through min points of STG, STG2 & STG3.
STC2 STC3 LTC
O1 O2 O3
Long-Run Average Cost Curve (LAC)
There is one AC associated with each “STC”.
Firm has a service of SAC curves, each having a bottom point showing the min. SAC. For instance C, Q is the min AC when the firm has only one plant.
AC ? to C2 Q2 when second point is added & then ? to C3Q3 after inclusion of third plant.
LAC curve is also known as “Envelope curve” or “Planning Curve”. It serves as a guide to plan the expansion of production.
Total Cost SAC2
O1 O2 O3
With subsequent increase in the output LTC first? at a decreasing rate. Then at increasing rate. As
a result LAC initially decreases until optimum ultimately of second plant & then it begins to ?.
When the scale of firm expands unit cost of production initially ?. But ultimately ?
The decrease in unit cost is attributers so the internal & external economies & ? to internal & external diseconomies.
Long-run marginal Cost Curve.
If we draw from point A, B & C to the x-axis, the corresponding output levels will be QQ, QQ2, & QQ3. The AQ1 intersect the SMC BQ2, LMC is MQ. If output ? to OQ2, LMC ? BQ2. Similarly CQ3 measures the LMC at output OQ3.
LMC must be equal to SMC for the output at which the corresponding SAC is tangent to the LAC. At the point of tangent LAC = SAC. For all other levels of output SAC>LAC. For all level of output corresponding to LAC = SAC LMC = SMC.
For all other level of output LMC is either > or < then SMC.
LMC intersects LAC. When LAC is at its minimum i.e. point B.
There is one & only one short run plant sign whose min SAC coincides with the min LAC.
SAC2 = SMC2 = LAC = LMC at point B.
Optimum plant size & long-run cost corves.
Long-run cost curves helps in deciding the optimum size of the firm.
Optimum size is on which ensure the most efficient utilization of resources.
For a state of technology there is a using size of the firm & of output associated with the least lost concept.
Optimum size consists of 2 plants, which produce OQ2 units of a product at min LAC of BQ2.
The downtrend in LAC indicates that until output reaches the level of OQ, the firm is of non-optimal site.
Technology should be such which gives min. LAC where SMC = LAC = LMC
Cost A B
Q1 Q2 Q3
Break Even Analysis
Break-even analysis or (profit contribution analysis) is an important analytical technique used to study the relationship between the total cost, total revenue, & total profits & losses over the whole range of stipulated output.
It is the point where cost & revenue break even i.e. the profitable & non-profitable range of production or TR = TC.
BEP as linear cost & revenue functions
Let TFC = 100 & TVC = Rs.10/unit
Than short run cost function.
TC = 100 + 10Q
& Let price of firm’s product = Rs.15
TR = 15Q.
Cost / B
?Q = 1
TC is vertical summation of TFC & TVC. TR intersects the TC at point B where Q = 20 at this point TC breaks even with TR.
TR = TC
15Q = 100 + 10Q
Q = 20
Limitations – In real life cost & revenue fune are not linear; there can’t be single point as BEP. In reality functions may be non-linear. So that (To May increase at an increasing rate while the (TR) increases at decreasing rate.
There can be 2 BEPS, which determine the upper & lower limits of profitable output.
Non-liner Cost & Revenue functions
Q1 Q3 Q2
At B1 & B2 TR = TC – upper & lower break-even points.
Between B1 & B2 TR>TC – profits & also more than Q & less than Q2 will earn profits.
COST / FC
Contribution analysis is the analysis of incremental revenue & incremental cost of a business decisions or business activity.
Contribution is the difference between total revenue & variable cost
TR – TVC = Contribution
Below the output OQ, the total contribute is less than finale cost which amounts to loss.
Beyond OQ contribution exceeds fixed cost difference is a contribution towards project.
Contribution over the time personal indicates the commandment that the mgt. Has made for fixed expenditure & do show when it will be recovered & profit will begin to emerge.
Profit volume ratio
Helps in making product PV ratio that produce taken also PV ratio per unit time is taken as the basis of choice.
PV ratio = S-V x 1000
S = Selling Price V = Variable Cost
BEP (Sales value) = Fixed Expenses
Profit volume analysis charts.
Revenue Cash BEP
VC (Cash Outlay)
Profit Volume Analysis
Use of BEP
– Sales volume to earn a given amount of return on capital.
– Profit can be forecasted
– Effect of change in vol. of sale, sales price, cost of product can be appraised.
– Choice of products or process can be made.
– Impact of increase or decreases in fixed & variable cost.
– Effect of high FC & LVC on the total cost
– Inter-firm comparisons of profitability.
– Cash BEP helps in planning of cash requirements.
– Emphasis for achieving economy.
– Angle of incident & margin safety also helps.
– Can be applied to only single product system.
– It can’t usefully apply if cost & price data can’t be ascertains before hand & where historical data are not relevant for estimate future cost & price.
MARKET STRUCTORE AND PRICING THEORY
Market – system in which buyers & seller bargain for price.
The number of seller of product in a market determines the nature & degree of competition in the market. The nature degree of competition makes the structure of the market.
Different types of market structures
– Perfect or pure competition – large number of sellers selling a homogenous product.
– Monopoly – A single seller of product without a close substitute.
– Monopoly Competition – A fairly large number of sellers selling different products.
– Oligopoly – A small number of big seller selling the same product (e.g. petroleum) or differentiated products.
– Bilateral Monopoly – A small number of buyers competing against a small number of sellers.
Pricing under perfect competitor
> Large number of seller & buyers – No single seller cannot affect the market prices by changing his supply nor can a single buyer by changing his demand.
> Monogenetic of Products – Buyers do not distinguish between then nor do they prefer the product of one firm to that of another, no firm gains competitive advantage.
> Perfect mobility of factors of production – in or out an industry & from one firm to another.
> Frie entry & free exit of forms – no restriction legal.
> Perfect knowledge – perfect buyers & sellers are fully aware of nature of produce its availability sale ability & price.
> Absence of collusion or artificial restraint – collusion like sellers car lets or guilds buyers.
E.g. of perfect competition share market, security bound & agriculture market.
Price Determination – Price is determined by the market forces – market demand & market supply.
Market Demand – Sum of the quantity demanded by each individual from at different prices.
Market Supply – It is the sum of quantity supplied by the individual firms in the industry.
Seller in a perfectly competitive market is “price taker” not a ‘Price Maker”.
For a Profit maximizing the main problems is to adjust its output to the market price. So that profit is maximum.
Mode of price determination (Price & its variation) depends on the time taken by supply position to adjust itself to the changing demand condition.
Pricing in Market Period (very short run)
In a market period the total output of a product is fixed.
Stock is fixed; the supply curve is perfectly in elastic.
Price is determined solely by the demand conditions supply is an inactive agent.
Equilibrium point is the point of intersection between demand & supply curves.
If demand increases than rent rises from; this place is paring miters for all the buyers. E.g. daily fish markets stock markets daily mill market, coffin market etc. during natural calamity essential mediums during epidemics.
Pricing in the short run
Short run in which firms can neither do not change their size, nor quit, now can new firms enter the industry.
Supply can be increased cord creased by increasing cor-decreasing the variable inputs.
Supply curve is elastic
Q’ Q M
E’ AVC AR’=MR’
Given the price PQ [=OP1] an individual form can produce & sell any quantity at this price.
The firms must adjust their output to the price PQ as per their cost curves in order to maximize their profit.
Profit is max when MR = MC as price is fixed AR = PQ
At point E MR = MC. Total Max. Profit is shown by area P1 TNE.
Profit = (AR -AC) Q
AR = EM, AC = NM & Q = OM
Profit = (EM – NM) OM = P1TNE
EM – NM = EN Profit = EN
EN is the max. Super normal profit at given & cost curves.
Firms may make losses in the short run.
It market price decreases to P1Q1 due to downward shift in the demand curve to D’D’ then equilibrium point will be E’ where AR’ – MR’ – MC but AR’ < AC.
– Firm increase loss
But since in short run it may not be desirable to close down the production.
– The firm minimizes its losses by adjusting its output where it covers its MC. The firm service in the short run so long it covers it MC.
No firm is large enough to influence the price friend fixes lower prices it incur loss & if higher prices than sale is less.
– Firm must-adjust their output to new market price.
Pricing in the long run.
In the long him the firm can adjust their size or quite the market & new firms care enter.
If AR > AC firm make economic or super normal profit; supply curve shifts rich toward because new firms get attracted toward the industry causing decrease in price.
AR < AL than marginal firms quit the industry causing a leftward shift in supply curve causing an increase in price.
This process continues until price is so determined that AR = AC & firms earn only normal profit.
S SMC LMC
SMC SAC LAC
Pricing under pure Monopoly
Pure monopoly – signifies an absolute power to produce & sell a product, which has no close substitute. I.e. cross elasticity is either zero or negative.
Monopoly industry is a single firm industry. Firm &industry are identical in a monopoly market. Equilibrium of the firm is the monopoly of the industry.
The monopoly product has district physical properties recognized by its buyers & distinctness lasts over many years.
Causes & kinds of Monopoly
(i) Legal restriction & barriers to entry of new firms
(ii) Sole control over the supply of scare & key raw material.
(iii) Efficiency & economics of scale. (Natural monopoly emerge out of technological conditions of efficiency)
Public utility sector (Postal, telephone service) franchise monopoly.
Pricing & output secession
In a monopoly market cost coeditors i.e. AC & MC curves in a competitive & monopoly market are generally identical revenue conditions different.
AR & MR curves are different under monopoly because, unlike a competitive firm & demand curve is downward sloping.
The slope of MR curve is twice that of AR.
A profit-maximizing firm chooses a price output combination at which MR – SMC.
Given the demand curve AR = D, the output OQ can be sold per time unit at only one price i.e. PQ (=OP1)
Out price & profit are simultaneously determined in the monopoly firm. Hence the firm is in state of equilibrium.
Profit (AR – SAC) = (PQ – MQ) = PM
? = OQ x PM = P1PMP2
TR = P.Q. P = 500 – 5Q TC = 50 x 20Q x Q2
MR = lTR MC = lTC
? = TR – TC
– If AR > AC, there is economic profit for the firm.
– If AR = AC, the firm earns only normal profit.
– If AR < AC, though only a theoretical possibility the firm makes losses.
Pricing & output decision in the long – run.
A monopolist gets an opportunity to expand the size of its firm with a view to enhance its long-run profits.
Expansion of plant size depends on
– Size of the market – expected economic profits – rich of inviting legal restrictors.
J P1 SMC2
K P2 LMC
Q1 Q2 MR Output
The total monopoly profit has been LP2SC. The monopolist produces a larger output & changes a lower price & makes a larger monopoly profit in the long run.
Short run equilibrium price P1Q1 equilibrium price P2Q2.
If there are barriers to entry the monopoly firm may not reach the optimal scale of production (OQ2) in the run, nor it may make full utilization of its easting capacity.
Price discrimination under Monopoly.
When consumers are discriminated on the basis of these factors in regard to price charged from them it is called price discrimination” e.g. doctors, lawyers, movie, cinema show, railways, & airways, electricity rates for commercial & lower.
Necessary conditions for price discrimination
– Different markets must be separable.
– Elasticity of demand must be different in different market.
– There must be imperfect competition in the market.
Degree of price discrimination
First degree – When a seller is in a position to know the price each customer is willing to pay, he sets the price accordingly & tries to extract the whole consumer surplus.
He sets the price at its highest level – level at which all those who are willing to by the commodity buy at least one unit each.
After extruding the surplus of this section of conducer he gradually lowers down the price. So that surplus of the second unit is extracted & the procedure continues until a surplus available at a price where MC = MR.
In large sized market second degree price discrimination or block pricing method is used.
Q1 Q2 Q3 Output
The marketer siphon off only the major part of the consumer’s surplus.
He divided his potential buyers in blocks rich middle & poor.
Highest to rich & SOON
(a) No. of consumer is large
(b) Price rationing can be done.
(c) Single rate is applicable for a large no. of buyers.
(d) Demand curve for the entire consumer is identical.
Third degree – Different prices in different markets having different elastic ties.
In each market.
MC & MR in each market is equaled & price in each market is fixed accordingly.
Price-quantity combination that can maximize his profit in each market is chosen.
Market A Market B Total Market
It is profitable in two or more markets separated from each other by geographical distance, transport barriers or cost of transportation, legal restriction on the inter – regional or inter state transportation of commodities.
Measure of Monopoly Power.
– No. of firms criterion
– Concentration Ratio
Pricing Under Monopolistic competition
Monopolistic competition is defined as market setting in which a large no. of sellers sell differentiated product.
– Large number of sellers.
– Free entry & free exit.
– Perfect factors mobility.
– Complete dissemination of market information.
– Differentiated products.
In monopolist products are differentiated by brand name, trademark, design, color & shape, packaging credit terms.
Despite products differentiation each product is a perfect substitute for the revel products.
Decisions are not absolutely independent of each other in perfect competition.
Short run price & output determination
P1 P S AC
The economic profit PM (per unit) exists in the short run because of no possibility of new firms extiring the industry.
Rate of profit would not be same for all the firms under monopoly competition because of different in the elasticity of demand. It price is ? than more than normal profit. Some firms will have lower profit because of higher long run price & output.
The existence of economic profit attracts new firms, which intensifies the competition on one hand but reduces individual firms share in the total supply.
At the stage where AR = /AC. At equilibrium point the existing firms step their expansion & new firms ease to enter the industry.
At OQ Quantity & PQ Price all firms earn normal profit as PQ = /AC
When all the firms reach their equilibrium point there will be no tendency of new firms entering or old firms of new firms entering or old firms quality the industry.
Price Determination under oligopoly
Oligopoly is a reduced form of monopolist competition. It is competition a man few big seller, each selling either differentiate or homogenous products.
Few – the number is so small that market share of each firm is so large that it can influence the market price.
Automobile industry is an outstanding e.g. differentiated oligopolies.
Homogenous Heterogeneous (or pure)
(Homogenous Product) (Differentiated Products
e.g. cooking gas, cement, baby food, e.g. automobile, Cigarettes,
vegetable oils, cable wire, dry batteries etc. Refrigerators & TV etc.
Interdependence & inter determinateness of price
Due to fewness of their number oligopolies are in keen competition with each other. The competition between them takes the form of action reaction & counteraction in the absence of collusion between competing firms. In this kind of a market firm’s business decision become independent.
The competition between oligopolies generally takes 3 forms.
– Free competition in which oligopolies wage price war against each other fight tooth & mail which ultimately takes the form of non-price competition. (Kind demand curve analysis)
– When competition is among unequal the larger firms plays the row of price-maker & smaller ones become the price-taker.
– Collusion between firms under cartel system of price agreement.
(Different models form book)
Price leadership is an informal position of a firm in roast oligopolsta industries,
Economics of scale or form’s ability so forecast market conditions accurately or a combination of these factors. Typical case played by the dominant form the largest form in the industry the dominant from the largest form in the industry, the dominant form takes lead in making price changes $ the smaller ones follow.
In the barometric price leadership one of the firms not necessarily the dominant one takes lead in announcing change in price, particularly when such a change is due fat is not effected due to uncertainty in the market. Such price leadership exist only ? number of forms is small
? entry to the industry is restudies
? Products are, by large homogenous.
? demand for industry is inelastic $ has very low elasticity
? forms have almost someday cost curves.
Collusion model: the cartel
A cartel is an association of business forms formed by an explicit agreement between then.
Under cartel agreements “the forms jointly establish a cartel organizations to make price $ output decisions to establish production quotas for each form, $ to supervise the market act vices of the form in the industry.
Cartel are formed with a view to
(1) Eliminating uncertainly sorrow riding the Market .
(2) Restraining competition $ thirdly ensuring monopoly gains to the cartel group.
Cost- pals pricing or Mark -up pricing
AVC (m) =gross profit margin (GPM)
P=AVC+ AVC (m)
= AVC (1+m)
MC =MR (profit max)
MR = P (1 -1/e)
Pricing new product
Cost plus pricing or Mark-up pricing
“Average Cost Pricing” or “Full Cost Pricing”
Under this method is adding “fair” percentages of profit margin to the average variable cost (AVC).
P = AVC + AVC (m)
M is the up percentage AVC (m) = gross profit margin (GPM).
M is the mark-up percentage.
AVC (m) = gross profit margin (GPM).
Mark-up percentage (m) is fixed so as to cover average margin (NPM). Thus
AVC (m) = AFC + NPM
The firm estimates the average variable cost by ascertaining the volumes of its output for a given period of time. The optimum level of output or capacity output is used as standard output in computer the AC.
TVC = Direct cost (cost of labor & raw materials) + other variable cost
AVC = TVC (Standard output)
Mark-up firms always take into account what the market will bear & the competition in market.
Mark-up Pricing & Margin list Rules
“Rule of thumb” method.
CAPITAL BUDGETING AND INVESTMENT DECISIONS
Capital budgeting is essentially a process of conceding, generating, evaluating & selecting the most profitable projects for investing the funds available to the firm.
Pre-requests of capital budgeting
Capital Expenditure: – only long-term capital expenditure i.e. those in adjustable in the short-run are taken into. Those involving a commitment for at least one year are considered. Items in capital budgeting.
> Expenditure on new capital equipments.
> Long-term assets
> Expansion or diversification
> Addition to existing stock of capital
> Replacement of depreciated capital.
> Advt. which bear fruit over time.
> Research development & innovation.
Deciding Planning Period
Uncertainty forecasting Judgment & hence a careful planning.
> Effective planning execution & control.
> Possible dovetailing of old plan with new ones.
> Assement of economics of scale & determination of plant size.
> Financial planning & timely acquisition of necessary finances.
Choice of decision rules
The criterion & decision rules are chosen on the basis of objective of the form such as profit assets building, a regular costs flow etc.
1st step – Define the objective of investment.
2nd step – Evaluating the project important evaluating – criteria are
> Discounted cash flow (present flow criterion)
> Net present worth
> Internal rate of return.
> Pay back period.
3rd step – approach for the final selecting of projects.
Limited funds & firm has to select from large amount of funds & invest in many
Few no. of mutually exclusive & alternative project at a time rank all the projects under
Projects. Consideration projects whose cost = its return is
Collection of Necessary Data
Cost of Capital Projects.
(1) Expected Rate of Return.
(2) Availability of Alternative Projects.
(3) Period of Fruition, Maturity & Overall Long activity
(4) Market Rate of Interest
(5) Degree of Uncertainty
Demand For Capital
Investment Criteria & Decisions
(a) Pay-back period (Payout)
Defined, as the time required recovering the total investment outlay from the gross earnings.
Pay-back Period = Total investment outlay
Across return per period
Project cost = 40,000
Yields an annual income of RS.8, 000 than pay back period = 90,000 = 5
Year Total Fixed Outlay Annual cash flow Cumulative (TC)
1 10,000 4,000 4,000
2 3,500 7,500
3 2,500 10,000
4 1,500 11,500
5 1,000 12,500
Pay back period is 3 year
Project with lowest pay back is preferred.
NPV A rupee received today is worth more than a rupee rejected tomorrow.
NPE = PV – C
= N Rn I – C
S (Hr) n
J = 1
C = Total Cost of Investment
TPC = ? Cn
J=1 (1+r) n
= ? Rn-Cn
J=1 (1+r) n
NPV>0 is selected
One with higher NPV is preferred.
IRR (Break Even Rate)
? Rn – ? Cn = 0
J=1(1+r) n J=1 (i+r) n
R= IRR IRR > marketing rate
Then its worth to invest & borrow
Kinked demand curve
(1) Rival firms follow the price ranges both cut & hike
(2) The rival firms don’t follow the price changes.
(3) Rival firms don’t react to price-helps but they do follow the price-cuts.
To begin with, let us suppose that market demand curve for a product is given by dd, curve & that the initial price is fired at PQ.
Now let one firm change its price if rival firms react in manner (i) I.e. they react with ? for ? & ? for ? the price changing firm will move along the demand curve dd. & it rival firms do not follow the price changes, then the price changing firm will move along the demand curve DD’.
Dd’ based on (i) is lost elastic than DD’ based on reaction (ii) Now let us suppose the firms behave like (iii) which is more realistic; now let firm ? its price rival firms will not follow; demand for its product decreases considerably indicating a greater elasticity. The firm is therefore forced down form Demand curve dp to DP. Thus the relevant segment of demand curve for it is DP.
Now suppose alternatively the firm’s ? its price. The rival firms ? their price otherwise they would lose their customers. This prevents the firm to gain felt advantage of price cut along the demand curve below paint P rotates down. Thus the relevant segment of demand curve for the oligopolies is Pd’. The two relevant segment of the demand curve relevant demand curve DPd’ which has “kind at point Po’.
Now let us draw MR curves. MR curve drawn on the basic take the shake a discontinuous curves DJKh.
Dj Correspond DP.
Kl Correspond Pd’.
Now let draw MC curves original is MC’ intersecting MR at K since at output OQ MR = MC, the firm makes max. Profit now even if MC shift to MC2 or any level between J & K, the firms profit is not affected.
Output & price both are stable.
PRICE LEADER SHIP
P3 P3 MC
P’ A B P’
Dm MR AR
MC1 MC2 MC
Q1 Q2 Q
Production: – Defined as the conversion of inputs – men, machines, materials, money, methods & management (6Ms) into output through a transpiration process.
Production involves the greatest bulk of the companies employees bulk of the companies employees & is responsible for a large portion of firm’s assets
> It has a major impact on the quality of the goods & cost of production.
> It is the central fun of an org. or we can safe production as the heart of any org.
Production Mgt. Function
(a) Planning Product Planning
Designing of the conversion process
(b) Organization Determines the activities required to achieve the operations. Sub-systems
goals & assign authority & responsibility for currying them out.
(c) Controlling Includes all activities that ensure that actual performance is in accordance with planned performance.
Objectives of production mgt.
Main objectives of any firm is to Increase profitability by
> Higher efficiency
> Higher Productivity
> Improving quality
> Give customers more confidence
> Optimal use of resources
> Use of manpower, machines or machining wastage of materials.
> Ensuring quality of goods at manual cost through use of SQC.
> Constituting toward all round productivity through decision-making QT/OQ techniques.
Scope of Production Mgt.
(1) Activities relating to designing or formulation of the production system.
(2) Activities relating to analyzing & controlling of production operate after the prod. System has been activates.
Activities To Produce System Designing
Design of Tool
& Drawing Selection & Operation of
Designing Development Size of firm
Selection of the Materials Handling
Overall plan Handling System
Activities relating to analysis & control of production
Production Control Control of quality
through process control
Control on inventory Control on
Such as raw materials work in process
Finished goods etc.
Decision Making in Prod. Mgt.
Determines how firm’s resources can most effectively be utilized.
Strategic (decision have tactical (can be implemented in one
Implication of long duration year or less)
Over one year
Human resource Mgt.
Location & facility engineering
Process designing & equipment selection
Quality assurance control
Productivity & wastivity
The efficiency with which the inputs are converted into output i.e. effectiveness of outputs & inputs is called productivity of the system.
Conceptually productivity is defined as an attitude of mind & prevention of all kinds of waste.
Mathematically Productivity = Output
= Goods or services produce
S all factors of production
When both input & output are in the same unit productivity reduces to moor number.
It can be expressed as % of output to input or OMS – output per man stable or production/month
GNP (Gross national product) as per capital income or output per hectare.
For incentive schemes
Productivity = SMH
= Standard Man has earned
Actual Man has worked
Wastivity – Inverse of Productivity Productivity
The measurement of wastage or tool for measuring the efficiency of inputs is called wastivity.
Idling of resources
goods & Services
Higher conversion Goods Produced not
As per specifications
Factors for improving productivity
Productivity = Output
Can be increased by ? output keeping input const.
Or reducing for same output.
Or increasing output proportionately higher than increases affected in inputs.
Factors contributing to increase of productivity can be summarized as:
> Better utilization of resources like men, machines & materials.
> Listing efficient & effective methods of working.
> Good & systematic plan laid outs.
> Proper maintenance policy.
> Appropriate technology
> Better HRM methods.
> Modern HRM methods mgt. By MBO rather than by crises etc.
In a manufacturing unite the etc. time allowed for the production of a unit as 5 hrs. If in a particular month 126 units are produced by employing a persons & an allowable delays are found to be 44 members.
ESH = Earned standard hrs.
STD Time/unit = 5 hrs.
Production = 126 units
ESH = 5 x 126 = 630 hrs.
AMH = available man hrs.
Manpower employed = 4P
Monthly working hrs. = 4 x 25 x 8
= 800 hrs.
Allowed delays = 44 hrs.
AMH = (88-44)
= 756 hrs.
Productivity = ESH x 100
= 630 x 100
Wastivity = 100 – 83.33%
Product selection & product development
Autonomous work teams in which Lean Production systems; workers are
Research marketing etc. are given more organized in work teams & parts & tools
Freedom & responsibility for the enter are positioned to where they are needed.
& development effort; Save huge amount assembly line use more co-ordination
of time & money. With customers.
Product design directly affects product quality production costs & customer satisfaction; product design is crucial to success.
During the designing of products following pts. Are taken into consideration.
1. The detailed ch. Of each product are established.
2. The ch. Of a product directly affect how a product can be produced.
3. How the product is produced determines the design of production system.
Ch. Of product
How product can be produced
Design of prod. System.
Product innovation sources
Developing new products
Getting new products to market
Improving the designed crusting products
Designing product for case of prod.
Designing products for quality
Sources of product innovation
Customers Engineering Managers Marketing Production
The formal research department, which work toward the design & development of new products & services & prod process.
About 5% of all new-product ideas survive to production & only about one in ten of these are successful. It is best to cancel unpromising new-products services development projects early so that human effort development money can be directed toward more promising projects but it is not possible.
Getting new products to market aster
To succeed in global competition companies must design, develop & introduce products faster.
Companies can do it by use of autonomous design & development teams.
MNCs like IBM etc. are given decision-making responsibility & more freedom to design & introduce new products.
Time ? & cost ?; times do not deal with red tape or bureaucrat or another method is with the use of CAD/CAM.
Engineers can store design in database & change as per the requirements.
The concepts of simultaneous engineering have significantly compressed the design production & introduction cycle of new products is called concurrent engineering.
Improving the design of crusting products
The focus of this effort is to improve performance quality & cost with the objective of maintaining or market share of mattering products e.g. refining of products in order to sure money.
Designing for case of production
Design products for case of production is a key way for man factures to be competitive with foreign manufacturers.
Specification detailed Standardization design activity Simplifications
Description of a material that reduces variety among an elimination of
Part of product including group of products or parts. Complex features so
Measures such as viscosity standardization leads to reductions that the intended
Surface finish PH Value etc. in no of models results in higher funct. Is performed
Quality or more customers with reduction cost.
Designing for quality: – quality into the product designer is the first step in producing products of superior quality.
Quality is determined by the customer’s perception of the excellence of the ch. Of produce & services.
Designing Developing New Services
Degree of standardization degree of customers contact mix of physical &
Of a service in delivering the service intangible service.
Process planning & design
Process planning is intense for new products & services but planning can also occur as capacity needs change business or market conditions change or technology sufferer machines become available.
The type of production process to be selected must necessary follow directly from the operation strategies.
Once process planning has been completed the fundamental structure & character of the operations function is set.
The process planning & design system
Major factors affecting process design decisions
(1) Nature of Product/service demand
Productions process must have adequate capacity to produce the volume product services customer wants.
(2) Degree of vertical integration
Integration with supplier customers less in new org.
Now a days outsourcing is the strategy.
Degree of automation
Can reduce cost & time of labor increases product quality & flexibility.
Traditionally it was only way to produce products of high quality was to produce products in small quantities by expert craftsmen but mass production is also mass production is quality.
Types of process designs
Product- focused – describe a form of production processing orgn. in which prod. Departments are organized according to the type of product/service being produced.
Also known as production line or continuous production.
It tend to follow direct linear trashing precuts / services lend proceed through production without stopping.
Continuous path of raw materials components sub assembles follow in the product focused production.
Applied to two general form
Product focused require
Higher initial investment levels because of
(1) Use of more expensive, fixed position materials handling equipment such as overhead conveyors.
(2) The use of equipment that is specialized lot a particular product such a automatic welding machines product flexibility is now.
Advantages lower labor skill require
Reduced worker training
Case of planning & controlling prod.
Process-focused describe a form of prod. In which prod. Operations are grouped according to type of process also referred as intermittent production on a start & stop basic or also known as job shops; products move form dept. to dept. in batches that are usually determined by customer’s orders.
Zig-hag type routes with
Job spend the large majority of line in waiting used to hospitals, automobile repair etc.
Adv. Less initial investment
Mobile material handling equipment
Disadv. More supervision
More skilled & trained employee
Complex prod. Planning &control
Group technology / cellular manufacturing
GT code to each product
(1) It is easier to determine how to route parts through production
(2) Number of part designs can be reduced.
(3) Parts with
Debur Debur2 Debur3 Debur4 Drill 1 Drill 2 Drill 3
Saw 1 Saw 2 Saw 3 Saw 4
Grinder1 Grinder2 Grinder3 Grinder4
Lathi1 Lathi2 Lathi3 Mill 1 Mill 2 Mill 3 Mill 4
Deciding Among Processing Alternatives Batch Size.
Many Number of Product Design
Capital Requirement For Process Design
Cost Function Of Processing Alternatives Job Shop
Number Of Units
Break Even Analysis
Don’t have time
Value of money
Financial Analysis: Process & Control Chart
Process F.C. V.C.
A $ 110,000 $ 2
B 80,000 4
J 75,000 5
At 10,000 units per year
Production planning & control
Production planning – It is concerned with the planning of various input (Men, Machines, Materials etc.) for a given period of time so that the customers could get right quality of products at right place, period & in time.
Long strategic Medium Aggregate Short routines
Production control – measures the actual performance of the production units & taking remedies action called for to see that the production is actually in not less than the target or standard set in advance.
Main functions of p roduction planning & control.
(1) Order preparation
(2) Materials planning
(6) Progressing (Control) i.e. collection of data from various manufacturing shops recoding the progress of work & comparing against the plan.
(7) Expediting – Chasing intensively the bottle need areas causing delays interruptions in carrying out smooth prod. & taking appropriate action from time to time.
Production planning problems in job shop production & continuous (mass products) systems.
Problems depend upon the following factors:
(a) Product variety & production quantity.
For job shop prod – Low quantity product complex consisting of many components each of which must be processed through multiple operation requires detailed scheduling & co-order ting of large member of different components.
Mass prod – More or single product in large quantity production impel for large components facility is organized as a product size.
For job shop – planning is emphasized
For mass prod – controlling is emphasized.
Planning is done at the broadest level. The details of the individual product requirement the detailed scheduling of various resources & other faculties is normally left to the individual at lower level to carry.
Various steps involved.
(1) Forecasting of resources (normally up to a years time)
(2) State of system at the end of last period.
(3) For the upcoming period the size of workforce & prod rate.
(4) The above decision could leads to herring are firing of personnel thereby expanding or combating the effective capacity of the productive system.
(5) Technique of aggregate planning are
> Graphical method
> Linear decision rule (LDR)
(1) Make use of the available facilities & resources to ensure their optimum use.
(2) Increases the range of attritions for capacity by fixing the size of work force & production rate.
(3) Inventories for work – in progress & finished goods are made during ban demand so as to use the same to melt the peak demand.
(4) More time is devoted to produce more from the same machinery capacity though properly employing the sequencing & scheduling technique.
Variables studied under the aggregate planning are: –
> Prod rate
> Labor employment
Sub-controlling (if permissible)
Strategies involved in aggregate planning
(1) Without changing Prod level – during loan demand sale can be ? by special discount schemes cutting prices etc.
(2) During periods of ? method of back logging of orders can be of adopted like it demand on the willingness of the customers.
(3) Change in prod level – when demand ? the output can be changed by herring workers temper airily production can be increased by keeping workers on overtimes or through special incentive sachems or through special incentive schemes by altering capacity by increase of few equipments machinery by changing the planned plan shut downs.
– Demand ? changing output by logging of demotating employees or reducing capacity by switching of part machinery.
By appropriate inventory level
Inventory of furnished good ? during period of low demand & it can be used to meet high demand seasonal demand.
Through acquiring part of goods from other manufactured producers rather than making in house.
Common to service industries orgn. Companies, which can’t short products, are services.
April 200 20 Oct 200 20
May 81 27 Nov 176 22
June 210 27 Dec 84 28
July 560 28 Jan 108 27
Aug 805 23 Feb 190 19
Sept. 100 25 March 450 25
Show daily requirement, cumulative demand & average demand.
Month Forecast No. of Demand Cumulative Cumulative
Demand days Per day Per day units
200 20 200/20=10
Average demand = Total Demand
Total prod. Days
Varying work force level to meet demand.
Month Demand Working Days
April 1000 25
May 2340 26
Jun 846 24
July 1674 27
Aug 1408 22
Sept. 1512 18
Company employee’s 20 persons at an average salary of Rs.222/- months. Each unit of prod. Requires 4 standard hers. Herring cost = Rs.1500 month.
Month Men Reqd.
100 x 4 = 20
25 x 8
2340 x 4 = 45
26 x 8
20 x 2000 = 49000
45 x 2000 = 90000 + 25 x 1500
Keeping work force fixed
Number of men employed = 30.
Inventory carrying cost = Rs.6/unit/month
Shortage Cost = Rs.100/unit/month
Men Reqd. Regular salary Investors
April 30 60000 = 30 x 2000 1500-1000 = 500
May 30 60000 500 + 1560-2340 = -280
June 30 60000 -280 + 1440 – 86 = 296
July 30 60000 296 + 1620 + 1674 = 242
Aug 30 60000
Sept. 30 60000
1500 = 25 x 8 x 30
Material planning is a technique of determining the requirements of raw materials components, spares etc. required for the manufactured of the product.
If the delivery data of the finished products is known in advance the ordering time & quantity of other work in progress can be planned accurately with the help mathematical calculate while doing MRP keep in consideration
> Components sub in assemblies & assemblies are know so that they all can participate for the planning of required materials.
> Inventory in hand.
E.g A, LT = 2
B (2) LT = 1 C (4) LT = 3 D (3) LT = 2
E (3) LT = 3 F (3) LT = 3 G (5) LT = 3 H (6) LT = 1
D racket indicate no. of units required LT = Lead-time.
If 100 units of ‘A’ are required to be slipped in 8 weeks.
(1) Purpose the bill of materials
(2) Find the required of various item at different level.
(3) Draw the planned under release
Bill of material
Part code Number Required Level
B 2 1
E 3 2
F 3 2
C 4 1
D 3 1
G 5 2
H 6 2
A, LT =2
B(2) LT = 1 C(3) LP = 2 D(L)LT=2
E(3) F(2) G(2) H(3)
LT=3 LT=1 LT=2 LT=3
K(1) I(2) M(3) LT=1 LT=2
LT=1 LT=2 LT=3
100 Units on 12th day.
CPM & PERT
A must be completed before b.
b & c can occur concur entry. But after a is finished.
d & b must be finished before c & d
Dash shows dummy a before either b or c &
both must be completed before d.
a b d
a & b must be completed before activity c & b
a b must be completed before d.
a =20 b =10 c = 8 e== 7 f = 6
d = 11 Dummy h = 13 I =5
CPM with highest EF
EF= earliest finish.
LF of f & I = 63
LFh = Lfi – Di
Lfe = LFh – Dh Latest elopsed finished
S = LF – EF
Lfi = EF1
Activity optimistic Most likely pessimer
to tm tp
Mean duration to + 4tm + t p
tp – to
Variance of path i.e CPM = V a + V b + V c addition of Var.
U Path = V
Probability of computing.
= given – actual