(UNIT 3) PRODUCTION & COST ANALYSIS

PRODUCTION FUNCTIONIt refers to the technological or engineering relationship between the inputs of a commodity & the output produced by themThe 4 factors of production are1.Land2.Labour3.Capital4.Organisation or management

Production function (schedule)Units of capital(K)

Labour (L)(No.of workers)Output quantity (Q)15202153033542250500

Production function (Equation)Q = f (L, K, Ld, M, T, etc.)WhereQ -- Output of commodity XL -- Labour employed in the production of XK Capital employed in the production of XLd Land employed in the production of XM Managerial function employed in the production of XT Technology employed in the production of X

Two time frames of production function 1.Short run :--Here at least one of the inputs remain constant, while other inputs vary --Different output & capital for a constant input pattern of production function is referred as return to a factor & 2.Long Run--A pattern of input combinations wherein both the inputs increase or decrease relates to long run changes in production function--If input change in the same proportion, then the pattern of production function is referred as return to scale

3 types of production function1.production function with one variable input 2.production function with 2 variable input3.Production function with all variable input

1.production function with one variable input factor/short run analysis of production function**It is explained with Law of variable Proportions/Law of Diminishing Marginal Returns/Law of Diminishing Marginal ProductivityLaw of Variable Proportions:It states that as more & more of one factor input is employed & if all other input quantities are held constant, a point will eventually be reached where additional quantities of varying input will yield diminishing marginal contributions to total productTerms used in law of variable proportions:1.Total Product (TP or Q)2.Marginal Product (MP)3.Average Product (AP)If variable Labour is L, thenMarginal Product of Labour MPL= Q/ LAverage Product of Labour APL=Q/L

Example:Capital is Fixed

Var input(L)TPMP(Q/ L)AP(Q/L)15-(5/1)5215(15-5)/(2-1)=10(15/2)7.5335(35-15)/(3-2)=20(35/3)11.7445(45-35)/(4-3)=10(45/4)11.25550(50-45)/(5-4)=5(50/5)10645(45-50)/(6-5)=-5(45/6)7.5

Output (Q)Var input Labour (L)x1x2x3TPLAPLMPLXYMP>10

3 stages of production function from the graph1.STAGE 1: starts from 0 units of variable input (L) to AP of at maximum (till X2)2.STAGE 2:It follows stage I & then proceeds to a point where MPL of (L) is 0(point X3).Here TPL is maximum3.STAGE 3:It continues from Previous pointInterpretation:-At stage I/stage III: No rational firm will operate.-At stage I : The firm is grossly under utilizing its fixed capacity. So in this MPL increases-At stage III: The firm grossly over utilizes its fixed capacity

2.production function with two variable input factor/short run (only 2 var)or Long run (more than 2 var) analysis of production function

Example: 2 var input : Labour (L),capital (K)

Labour(L)Output Quantity (Q)15204221530503354270442508055065836466180Units of capital(K)250500750

From the above table ,If a firm want to produce 42 units of output, then the possible combinations are (4,250) (3,500) (1,750)Plotting these points on graph & line joining these combinations of labour & capital is called as isoquant/iso-product curve/Equal product curve/Production indifference curve

IsoquantIt is defined as the locus of all those combinations of 2 inputs that produce the same amount of outputUnit of Capital (K)Units of labour (L)0yxQ = 42Q=50

Characteristics of isoquant map1.They are falling (reducing)2.The higher the isoquant is, the higher is the output3.No 2 isoquant intersect with each other4.They are convex towards the origin

Types of Isoquant:1.Linear Isoquant2.Input-Output Isoquant / Right angled Isoquant / Leontief Isoquant3.Kinked Isoquant /Convex Isoquant /Activity analysis isoquant / Linear Programming Isoquant4.Smooth Convex Isoquant

1.Linear IsoquantNatural GasDiesel OilxyQ1Q2Q3Electric PowerIt is assumed that perfect substitutability between Factors of production is possible.Example: Gas or oil to generate power

2.Input-Output Isoquant / Right angled Isoquant / Leontief Isoquant

We assume strict Complementary /Zero substitutability between the inputsWhen there is only one method of production of any commodityExample: Wheels cannot be replaced by carts & vice versayxcartswheelsQ1=1 vehicleQ2=2 vehicleQ3=3 vehicle

3.Kinked Isoquant /Convex Isoquant /Activity analysis isoquant / Linear Programming IsoquantIt is assumed limited substitutability of capital & LabourOnly few process is used for production.substitutability of input factors is possible only at kinksK3K2K1L1L2L3XYQ1Q2Units of labourUnits of leathershoe

Example: labour(L1) & leather(K1) or labour(L2) & leather(K2) (by reducing wastages) or more labour(L3) & more leather(k3) (more carefully reducing wastages)

4.Smooth Convex IsoquantIt is assumes continuous substitutability of capital & labour only over a certain range beyond which input cannot be substitutedUnits of Capital(K)Units of labour(L)QxY

Least cost combination of inputsTo get least cost of production, optimal combination of inputs(resources) will be consideredExample: Price of Labour (PL) : Rs 10 / unitPrice of capital (PK) : Rs 5 / unitProduction table

Q=2unitsQ=4 unitsQ=6 unitsLkLKLK11721731521031241139411510

If one needs to get 6 units of output , then the possible combinations are (3,17) (4,11) (5,10)Calculation of least cost combination of outputMethod 1:Finding each output cost & choosing the minimal oneMethod 2:Finding by Geometrically

Method 1:Finding each output costFor 6 unitsHere 95 is minimal & (4,11) is chosen the best

LKCost of production315(3x10)+(15x5)=105411(4x10)+(11x5)=95510(5x10)+(10x5)=100

Method 2:Finding by Geometrically M = (L x PL)+ (K x PK) Where M sum of money availableL units of labourPL Price of labour for each unit of labourK units of capital needed to produce a given quantity of outputPK Price of capital for each unit of capital

If the entrepreneur has Rs.95 then he can go for (4,11)Also he can buy 9.5 units of labour (L) with no capita (K) i.e., (L*10) + 0 = 95, Therefore L = 9.5And he can buy 19 units of capital (K) with no labour (L) i.e., 0 + (K*5) = 95, Therefore K = 19Under various combination of L & K represented graphically called Isocost line for M=95

IsocostDefinition: An isocost (isocost line) is the locus of all those combinations of input factors (factors of production) that can be bought with a given sum of money here Rs.95) Units of Capital (K)xM=95yUnits of labour (L)M=90M=85

Determination of least cost input combinationsHere isocost map is superimpose on isoquant mapIt is possible because the axes in both maps represent the same input variableUnits of Capital (K)xyUnits of labour (L)ABCScale line

3.Production function with all variable inputfactors/long run production function/return to scaleTwo ways:1. Both L & K change in same proportion i.e., K/L ratio of production remains same for any output2. L & K change in different proportion i.e., K/L ratio of production varies with change in output

Therefore increase in output when all inputs vary in same proportion is known as return to scale

3 alternative situation arise in return to scale1.Increasing return to scale2.Constant return to scale3.Decreasing return to scale

3 alternative situation arise in return to scale1.Increasing return to scale:If output increases more than proportionate to increase in all inputsCauses:In large scale production work is divided to small parts & each individual can attain specialization by handling only one part of the workSome industries are not able to undertake production at small scale Example: aircraft & shipping industrySome industries increased single operation which gives some dimensional advantagesExample: industries where storage is important such as chemical 2.Constant return to scale:if output increases by same percentage as all inputs3.Decreasing return to scale:If increase in output is less than proportionate to increase in all inputsCauses:Coordination & control becomes increasingly difficultInformation in organisation is lost when transmitted down from top level managers & vice versa when transmitted to top from down

Statistical production function(charles & paul H.Douglas) Q = A Lb K1-b (or) Q = 1.01 L0.75 K0.25

WhereQ - total outputA - constantL - units of labourK - units of capital b - parameters

Properties of Charles & Paul H.Douglas production function1.Both L & K should be positive for Q to exist2. Sum of the parameters (b , 1-b) = 1 which is constant return to scale Latest version is : Q = A L K when + = 1; return to scale is constant when + > 1; return to scale is increasing when + < 1; return to scale is decreasing

3.Parameter represents input factors - shares in output Example: =wage share & =rental share total share total income4.It is used to find short run relationship of inputs & output Marginal physical product of labour (MPPL)= (Q/L) Marginal physical product of labour (MPPL)= (Q/K)5.It has elasticity of substitution as unity , which is used in formulation of an income policy

Managerial uses of Production FunctionUsed to Compute least cost Input combination for given outputUsed to Compute maximum input output combination for a given costIt is useful in deciding on the value of employing a variable input factorIt aids in long run decision making (increasing return to scale implies increasing production)decreasing return to scale implies decreasing productionProducer is indifferent about increasing / decreasing return to scale provided the demand is of no constraint

COSTIt is the money spent (directly/indirectly) on producing & selling a product to the customersIt refers to the outlay of funds for productive producing a good or serviceIt states from raw materials (procuring, transporting, preparing) through production costs (labour, power, machinery) till selling (maintenance, advertisement, salary, incentive) the product to customer.

COST TYPES/COST CONCEPT

1.Actual Cost & opportunity cost2.Incremental cost & sunk cost3.Explicit cost & Implicit cost4.Past cost & Future cost5.Accounting & economic6.Private & social7.Direct & Indirect Cost8.Controllable & Non Controllable costs9.Replacement & Original Costs10.Shut down & abandonment cost11.Urgent & Postponable Cost12.Business cost & full cost13.Fixed & Variable Cost14.Short run & Long run cost15.Incremental & Marginal cost16.Average cost, Marginal costs & total cost

1.(a) Actual Cost /acquisition costs/outlay cost/absolute cost & (b) opportunity cost/alternate cost

(a) Costs which a firm incurs for producing /acquiring a product /service Ex: raw material cost, labour cost(b) * It is measured in terms of revenue / benefit, which could have been generated / earned by employing that good or service in some other alternative use. * Difference between actual & opportunity cost is called as economic profit / economic rent

2.(a) Incremental cost/Differential cost & (b) sunk costIt is the additional cost due to a change in the level / nature of business activityEx: adding new product line , changing distribution channel(b) Costs that are not altered by a change in quantity produced & cannot be recoveredEx: depreciation of Equipments

3. (a)Explicit /out of pocket/ paid out cost & (b)Implicit /book/ imputed cost(a) Those expenses which are actually paid by the firm It is recorded in profit & loss accountEx: rent, wage paid(b) These are theoretical costs that they go unrecognized by the accounting systemEx: for owner the cost spend is ignored

4.(a) Past cost & (b) Future cost

They are actual costs incurred in the past & are generally contained in financial accountsEx:It helps for future(b) Costs that are expected to occur in some future period It is concerned for the managerial decision makers

5.(a) Accounting cost & (b) economic cost(a) It points how much expenditure has already been incurred on a particular process/ on productionIt is used for tax planning purposes(b) It is in nature of incremental costs both imputed & explicit costs as well as the opportunity costsIt is used in managerial decision making

6.(a) Private cost & (b) social costThose costs which are actually incurred/ provided for the business activity by an individual / business firmTotal costs to society on account of production of a good Ex: Polluting land/water

7.(a) Direct /traceable/assignable cost& (b) Indirect /non traceable/common/non assignable CostWhich have direct relationship with a unit of operation like a product , a process or a department of a firmCosts whose course cannot be easily & definitely traced to the plant , a product , a process or departmentEx: land cost, building cost cannot be directly attributed to cost of per unit of product

8.Controllable & Non Controllable costsCosts which are capable of being controlled/regulated by the managersCosts which are not capable of controllingCosts which are involved in obsolescence & depreciation

9.Replacement & Original CostsCosts that the firm incurs if it wants to replace/acquire the same assets nowCosts paid for assets such as land , building, cost of plant, equipment & materials at price paid originally for them

10.Shut down & abandonment cost

Cost which the firm incurs if it temporarily stops its operation Example: fixed costs, sheltering cost of equipment(b) Costs of retiring altogether a fixed asset from useExample: war time use machines

11.Urgent & Postponable Cost

The cost the firm must incur so that the operations of the firm continueExample: Cost of material , labour, fuel(b) Cost where postponement does not affect the operational efficiency of firmExample: maintenance cost

12.Business cost & full cost

Costs which are known in profit & loss account for legal & tax purposesIt is the sum of Opportunity costs & normal profits

13.Fixed & Variable Cost

Costs of firm which is part of total cost & which does not vary with output

(b) The cost which vary with the outputTFCoutputoutputTVCFCVC

14.Short run & Long run costA period in which supply of at least one of inputs cannot be changed by firmExample: building, machinery(b) A period in which inputs can be varied as desired

15.Incremental & Marginal cost

It is important when dealing with decision where discrete alternatives are comparedIt is change in any number of units of output or even a change in quality of output(b) It is the amount added to TC by a unit increase in output

16.Average cost, Marginal costs & total costAverage cost = total cost units producedMarginal cost=extra cost of producing one additional unit

Total cost = fixed cost + variable cost

DETERMINANTS OF COSTLevel of OutputPrices of input factorsProduction lot sizeSize of plantOutput stabilityLaws of returnsLevel of capacity utilizationPeriod under considerationTechnologyLearning effectBreadth of product rangeGeographical location

COST-OUTPUT RELATIONSHIPThe 2 aspects are1.Cost output relationship in short run (firms cannot alter its fixed equipment)2.Cost output relationship in Long run (firms has sufficient time to alter its fixed equipments)

1.Cost output relationship in short runIt is studied in terms ofAverage Fixed Cost & outputAverage Variable Cost & OutputAverage Total Cost & Output

(a) Average Fixed Cost (AFC) & output

Increase in output results in decrease in FC/unitTotal Fixed cost(TFC) is same for any outputAverage Fixed cost(AFC) = TFC units of o/p producedExample, (a) when TFC is Rs.1000, O/P units is 10Then AFC =1000/10 = 100 units(b) when TFC is Rs.1000, O/P units is 20Then AFC =1000/20 = 50 unitsTherefore AFC falls as O/P increases

(b) Average Variable Cost (AVC) & Output

It will first decrease & then rise as more & more units are producedBecause when increase in variable factors will leads to efficiency of inputs which first increases & then decreasesOnce optimum capacity of production is reached, any future increase in output beyond optimum capacity will surely increase the AVCExample: To produce increase in output after reaching optimum level , more & more workers have to be appointed which leads to overcrowding & results in high wage rates.

(c) Average Total Cost (ATC) & Output

It decreases with increase in output to certain level & then starts to increase upTurning point in cost from downward trend to upward trend in ATC comes little later than in case of AVCATC = AFC + AVCLeast cost output level is where ATC is minimum & not AVC

figOutput CostsShort-Run output cost curves

fig

Relationship between ATC, AVC & MC3 costs fall atfirst & then remains constant & rise as output increasesRate of change in MC is less than AVC & hence minimum MC is at output lower than output at which AVC is minimumATC falls for a longer range of output than AVC & hence the minimum AVCAVC = MC, when AVC is the least ATC =MC , when ATC is the least

Cost Output relationship in long runThere wont be any fixed cost in long runIt also referred as cost of producing different levels of output by changing size of plant / scale of production.

Costoutput0ATC1ATC2ATC3CDEXYAB

A minimum point of ATC2 is at C, produces output of OAIf output increases to OB & when firm continues in old scale, then the least cost point in ATC2 is EIf the output increases to OB with increase in scale, then the new least cost point is D in ATC3 curveHere BD will be less than BELong run Average cost (LAC) curve is drawn using no. of Short run Average Cost (SAC) curves

LRAC (Envelope curve)CostsOutputODeriving a long-run average cost curve:SAC1SAC2SAC3SAC4SAC5A1(E=D)

Nature of Long Run Cost Curves1.LAC curve is tangential to SAC curve & also called as envelope curve2.LAC curve is U shape, it is because lower average costs at first till optimum scale of production & then it rise3.LAC curve never cut by any SAC curve4.LAC curve will touch the optimum scale curve at optimum scale curves least cost point(A1)5.At A1, Economies = Diseconomies

Usefulness of LAC curveIt helps the organization to determine size of plant to be adopted for producing the given outputWhen firm operate in increasing return to scale, it is economical to under use a slightly larger plant operating at less than its minimum cost output level than to over use a smaller plant

Economies & Diseconomies of scaleThe existence of this is responsible for U shaped LAC curveIt is concerned with behavior as plant size changesWhen LAC declines as output increases which says the cost structure is characterized by economies of scaleWhen LAC increases as output increases which says the cost structure is characterized by Diseconomies of scaleWhen LAC is constant it is neither economies nor diseconomies of scale

A typical long-run average cost curveOutputOCostsEconomiesof scaleConstantcostsDiseconomiesof scale

2 types of economies & DiseconomiesExternal Economieswhich are available to all firms in an industryEx: Constructing railway line will decrease transport cost for all firmsb) Internal EconomiesWhich are available to a particular firm & gives it an advantage over other firms engaged in production of same products in industry Various factors involved are(1)Labour economies & Diseconomies(2)Technical Process economies & Diseconomies(3)Managerial economies & Diseconomies(4)Marketing economies & Diseconomies(5)Financial economies & Diseconomies(6)Diversification in output economies & Diseconomies(7)Diversification of market economies & Diseconomies(8)Risk spreading economies & Diseconomies

ESTIMATION OF COST OUTPUT RELATIONSHIPIt can be estimated through the following 3 approaches(1)Accounting MethodHere the TC is classified to fixed, variable & semi-variable costsAverage VC, range of o/p within which the semi variable is fixed & amount of FC are determined on the basis of inspection & experienceAfter these steps TC, average & marginal costs for each output level is obtained through simple arithmetic(2)Engineering MethodIt is derived by estimating the physical units of various input factors i.e., plant size, man hours, etcOnce it is determined, they are multiplied by the respective current/expected factor prices & added together to yield cost estimates for that output level

(3)Econometric MethodExpressions of common forms areLinear: TC = a1 + b1xQuadratic: TC = a2 + b2x + c2x2Cubic: TC = a3 + b3x + c3x2 + d3x3where, x - O/P a1,b1,c1,d1 --- constantTo determines not only partial cost function cost output relationship on assumption that other determinants of cost (factor prices technology) are constant but also to determine the comprehensive cost function , which allows variations in all the factors influencing cost.

*