Production and Cost of Production

Aims & ObjectivesAfter studying this lesson, you will be able to understand:● Theory of Production

● The production function● Short run vs Long run● Total, Average and Marginal Product● Law of Diminishing Returns to a factor● Stages of Production● Returns to Scale● Concepts of isoquant & isocost line● Idea of producer’s equilibrium

● Theory of Cost● Economic vs Accounting Cost● Short run costs and cost curves● Long run costs and cost curves● Economies & diseconomies of scale● Economies of Scope● Learning Curves

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Theory of Production

Production Functions Is a technical relation that connects factor inputs and output. It specifies the maximum output that can be produced with a given

quantity of inputs. It is defined for a given state of engineering and technical knowledge

It may be represented as Q = Q (K, L) Where, the production process employs only two inputs Labour (L) and

Capital (K) and Q is the quantity of output

● A general form of production function can be expressed as Q = Q (I1, I2, I3……….In)

Where Q is the quantity of output and inputs are represented as I1,I2……..In

● Cobb- Douglas is a type of production function and is given as Q = AKLβ Where A denotes state of technology, K & L are the inputs/factors and & β are called the transformation parameters

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Short run Vs Long run

●Short run in production refers to a time period when some inputs used in production are fixed and some are variable

●Long run in production refers to a time period when all inputs used in production are variable

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TP, AP, MP

●Three very important concepts related to production analysis are:

●Total product (TP)●Average product (AP)●Marginal product (MP)

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Total Product

●Total product is total output.

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Average Product● It is the total product divided by the number of

variable input employed. That is, it is the production per unit of input. It may be represented as,

● APx = Q/x

Where Q denotes total product and x denotes quantity of input x

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Marginal Product●Marginal Product is the change in output caused by

increasing input use.● It is represented as: MPX=∂Q/∂X

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

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AP curve rises at first, reaches a maximum and falls thereafter.MP also rises at first, reaches a maximum and falls thereafter.When AP is rising MP > APWhen AP is maximum MP = APWhen AP is falling MP < AP

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Law of diminishing returns to variable factor/law of variable proportion

●As more and more of a variable input is added in production while holding all other inputs fixed, the additional output obtained is gradually lesser and lesser

●Alternatively stated, the Marginal Product of each unit of input will decline as the amount of that input increases, holding all other inputs constant.

●Diminishing Returns to a Factor explains the shape of the TP curve and also explains the most efficient stage of production

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Stage I – origin to X2Stage II – X2 to X3Stage III- beyond X3

Stages of production13

Stage I – origin to X2Stage II – X1 to X3 – the most efficient stage of productionStage III- beyond X3

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Returns to Scale●Returns to scale show the output effect of increasing all

inputs.●Three types of returns to scale

Increasing returns to scale ⇒ ∂Q/Q ÷ ∂Xi/Xi > 1 Constant returns to scale ⇒ ∂Q/Q ÷ ∂Xi/Xi = 1 Decreasing returns to scale ⇒ ∂Q/Q ÷ ∂Xi/Xi < 1

Where ∂Q/Q denotes proportional change in output ∂Xi/Xi denotes proportional change in input

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Returns to Scale and Returns to a Factor

●Returns to scale measure output effect of increasing all inputs.- Long run phenomenon

●Returns to a factor measure output effect of increasing one input. – Short run phenomenon

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Input Combination Choice

●Two tools are used● Production Isoquants and● Isocost lines

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Isoquants●Drawn in an input space it shows the different

combination of inputs that can produce the same level of output.

●Characteristics of an isoquant Downward sloping – implies input substitutability. Concave to the origin No two isoquants intersect each other - imply imperfect

substitutability Higher isoquants represent higher levels of output

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Perfect substitutes Perfect complements

Usual Shape

Different Shapes of an Isoquant

Marginal Rate of Technical Substitution

● This shows the rate at which one factor may be substituted for another. Its is given as

MRTSXY = - ΔY/ΔX = -MPX/MPY.

● MRTSXY gives the slope of an isoquant

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Isocost line

●This shows the various combinations of the inputs that can be had for the same cost outlay.

● It is represented as C = Px.x + Py. y

Where C denotes the total cost outlay x & y are the quantity of the two inputs used Px & Py are the given respective prices of the two inputsy

x

C = Px.x + Py. y

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●Producer reaches his equilibrium when he maximizes his profit by ● Producing the maximum possible output for a given cost or

..….a

▫ Minimizing cost for a given level of output ……b

Producer’s equilibrium

E

Case: a Case: b

E

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Producer’s equilibriumEquilibrium in both these cases occurs when an

isocost line gets tangent to an isoquant In case a, the given isocost line became tangent to

the highest possible isoqant at E In case b, the lowest possible isocost line became

tangent to the given isoquantThe condition for producer’s equilibrium is thus, the

same in both case:

Slope of isoquant = slope of isocost

MRTSxy = Px/Py

Or MPx/MPy = Px/Py

●Additionally, the isoquant must be concave to the origin

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Theory of Cost

Economic Costs

●The payment that must be made to obtain and retain the services of a resource● Explicit Costs

√ Monetary payments

● Implicit Costs● Value of next best use● Self-owned resources● Includes normal profit

LO1 7-25

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Accounting Profit and Normal Profit

• Accounting profit = Revenue – Explicit Costs

• Economic profit = Accounting Profit – Implicit Costs

• Economic profit (to summarize)=Total Revenue – Economic Costs=Total Revenue – Explicit Costs – Implicit Costs

LO1 7-26

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Cost Function ●In economic theory, costs are taken as a function of

output. C = C (Q)●Output is produced by combining the use of fixed

factors & variable factors.●In short run, some factors are fixed and others are

variable. Accordingly, there is a fixed cost and a variable cost in the short run while in the long run all costs are variable cost

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Short run total costs● Short run total cost (STC) is the sum total of Total fixed

cost (TFC) and Total variable cost (TVC)

● Shapes of Short run cost curves

STC = TFC + TVC

TFC

TVC

TC

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Explanations for shapes of total cost curves

● TFC curve is horizontal – this is because total fixed cost remains fixed at all levels of output including zero level of output

● TVC curve is upward rising- this is because total variable cost varies directly with the level of output and is zero when output is zero. In particular, it rises at a diminishing rate initially and then at an increasing rate. This is explained by the shape of the Total Product Curve, which in turn in explained by the Law of Diminishing Marginal Returns to a Factor. The Law states that as the input of the variable factor increases with fixed factor remaining constant total product rises initially at a increasing rate but then at a diminishing rate, eventually reaching a maximum and falling thereafter

● TC curve is upward rising – Total cost which is sum of TFC and TVC looks like the TVC curve and hence its shape too is explained by the law of Diminishing Returns to a Factor. But unlike the TVC curve, TC curve starts from the level of TFC curve. This is because at zero output there is no TVC and TC equals TFC. The difference between TC curve and TVC curve is given by the TFC

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Average cost curves• It is the cost per unit of output. It is given as

• Shapes of Short run cost curves:

ATC or AC = TC/Q where TC denotes total cost & Q

denotes total output = (TFC + TVC)/Q = TFC/Q + TVC/Q = AFC + AVC

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Explanation for shapes of Average cost curves● Shape of AFC curve: AFC = TFC /q TFC remains constant throughout, so as output increases TFC/q falls throughout.

● Shape of AVC curve: Let labour be the only variable factor hired in quantity ‘L’ and paid a given wage of Rs w per unit. Thus, TVC = wL AVC =TVC/q = wL/q Or, AVC = w/{1/(q/L)} Or AVC 1/(q/L) i.e. AVC is inversely related to q/L which is

the Average Product of labour. Thus, as AP of labour curve is dome-shaped, AVC curve is U-shaped ie. When AP rises at first, AVC falls, when AP falls thereafter, AVC starts rising

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Explanation for shapes of Average cost curves

●Shape of AC curve: The AC curve is a vertical summation of AFC and

AVC curves. Initially when both AFC and AVC are falling AC also falls, then when AVC starts rising, AC under the influence of the falling AFC falls briefly. But thereafter the rising AVC pushes the AC curve up. Thus, the minimum point of AC curve comes after the minimum point of AVC curve

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Marginal Cost●It is defined as the addition to total cost due to one

unit addition in the total output

Marginal Cost, MC = d(TC)/dq = TCq+1 - TCq where d denotes change, q denotes output and C denotes cost

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Marginal Cost is independent of fixed cost● MC = TCq+1 – TCq

= (TFCq+1 + TVC q ) – (TFCq + TVCq)

= TFCq+1 + TVC q – TFCq – TVCq

= TVC q – TVCq (since TFCq+1 = TFCq & cancels)

● Thus, MC = d(TC)/q or MC = d(TVC)/q

● This implies whenever an additional unit of output is produced the entire addition to cost is addition to variable costs.

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Shape of Marginal cost curve● Let labour be the only variable factor hired in quantity ‘L’ and paid a given wage of Rs w per unit. Thus, TVC = wL

● Therefore, MC = d(TVC)/q = d(wL)d/q = w dL/dq Or, MC = w/{1/(dq/dL)} Or, MC 1/(dq/dL) i.e. MC is inversely related to dq/dL which is the

Marginal Product of labour. Thus, as MP of labour curve is dome-shaped, MC curve is U-shaped ie. When MP rises at first, MC falls, when MP falls thereafter, MC starts rising

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Per-Unit, or Average, Costs

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Co

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1 2 3 4 5 6 7 8 9 100 Q

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AFC

ATCAVC

AVC

AFC

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Marginal Cost

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1 2 3 4 5 6 7 8 9 100 Q

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AFC

MC

ATCAVC

AVC

AFC

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MC and Marginal Product

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MPAP

MCAVC

Quantity of Output

Quantity of Labor

Production Curves

Cost Curves

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Long-Run Production Costs

●The firm can change all input amounts, including plant size.

●All costs are variable in the long run.●Long run ATC

● Different short run ATCs

LO4 7-39

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Firm Size and Costs

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ATC-1

ATC-2

ATC-3 ATC-4

ATC-5

Output

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The Long-Run Cost Curve

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Long-runATC

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ATC-1

ATC-2

ATC-3 ATC-4

ATC-5

Output

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Economies & Diseconomies of Scale

Internal Economies & Diseconomies●When a firm expands in size by increasing the scale of its

output, certain cost advantages (due to factors like division of labor, indivisibility of factors etc) accrue to the firm. This is referred to as internal economies

●When a firm grows larger and larger, there could be several cost disadvantages facing the firm. This is referred as internal diseconomies. Eg: diseconomies due to managerial issues like trade union related to large scale production

External Economies & Diseconomies●External economies occur when there are physical and

cost advantages that result from the general development of the industry

●External diseconomies arise when the industry expands in size indefinitely and the control of the industry becomes a problem

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Economies and Diseconomies of Scale●Economies of scale• Labor specialization• Managerial specialization• Efficient capital• Other factors

●Constant returns to scale

●Diseconomies of scale• Control and coordination problems• Communication problems• Worker Alienation• Shirking

LO4 7-43

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MES and Industry Structure●Minimum Efficient Scale (MES):• Lowest level of output where long- run average costs are

minimized• Can determine the structure of the industry

LO4 7-44

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MES and Industry Structure

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Output

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Long-runATC

EconomiesOf Scale

Constant ReturnsTo Scale

DiseconomiesOf Scale

q1 q2

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MES and Industry Structure

LO4

Output

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EconomiesOf Scale

DiseconomiesOf Scale

Long-runATC

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MES and Industry Structure

LO4

Output

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Long-runATC

EconomiesOf Scale

DiseconomiesOf Scale

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Don’t Cry Over Sunk Costs

• Sunk costs • Costs have already been incurred and thus are

irrecoverable• Rule: Do not engage in any activity where MB<MC• Rule: Ignore sunk costs• They are irrecoverable

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Economies of Scope●Economies of Scope Concept

● Scope economies are cost advantages that stem from producing multiple outputs.

● Big scope economies explain the popularity of multi-product firms.

● Without scope economies, firms specialize.

●Exploiting Scope Economies● Scope economics often shape competitive strategy for new

products.

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Learning curve

●As firms gain experience in production of a commodity or service, their average cost of production usually declines. i.e. for a given level of output per time period, the increasing cumulative total output over many time periods often provides the manufacturing experience that enables firms to lower their average cost of production

●The learning curve shows the decline in the average input cost of production with rising cumulative total outputs over time

●Example: It may take 1000 hours to assemble the 100th aircraft, but only 700 hours to assemble the 200th aircraft as mangers and workers become more efficient as they gain production experience

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Learning curve contd..

●The adjacent figure shows that average cost declines as the unit of production increases. In particular it is convex from the origin as average cost declines at a decreasing rate. This implies that a firm usually achieves the largest decline in average costs when production process is relatively new & less decline as the firm matures

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Thank You