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Micro EconomicsMicro EconomicsLecture 07Lecture 07
THEORY OF PRODUCTIONTHEORY OF PRODUCTIONLecturer -J.D.T.MadhusankaLecturer -J.D.T.Madhusanka
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Lecture OutlineLecture OutlineTheory of Production –Short-runLaw of Diminishing ReturnsTotal Average and Marginal
ProductStages of Production
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THEORY OF THEORY OF PRODUCTIONPRODUCTION
Production Production refers to the transformation of inputs or
resources into outputs of goods and services
Fixed CostCost incurred with resources, which takes a considerable time to adjust
Variable CostCost incurred with resources, which can quickly be varied to increase or decrease the level of output
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Short-run The time period during, which at
least one input is fixed Long-run The time period during, which all
the inputs are variable
Production Function Production function shows the
relationship between inputs and the maximum attainable output under given technology.
Q = f (L, K, M)
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THE PRODUCTION FUNCTIONTHE PRODUCTION FUNCTION
Out put can be increased by increasing the use of the variable input only
There is a possibility to substitute one input for the other though they are complements
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Properties of a Production Properties of a Production FunctionFunctionThere is a limit to extra production
that can be achieved when more of one input is used while other inputs are held constant.
There is some complementarily among inputs, but it is possible to substitute the use of one input for another without reducing production.
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Production with One Variable input Production with One Variable input – Short-run Production– Short-run Production
Short-run Production Function
Q = f (L ) Total Product of a Variable InputThe amount of output produced where a given amount of that input is used along
some fixed inputs.
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TOTAL PRODUCT CURVETOTAL PRODUCT CURVE
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The Average Product of a Variable Input (AP)
AP is the total product of the variable input divided by the amount of that input used.
APL = TPL / L
Marginal Product of a Variable Input (MP)
MP is the change of the TP of that input corresponding to one unit change in its
use.MPL = ∆ TPL/∆ L
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MARGINAL & AVERAGE PRODUCT MARGINAL & AVERAGE PRODUCT CURVESCURVES
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Relationship Among TP, AP and MPRelationship Among TP, AP and MP
TP
L
L
AP & MP
0
0
MP
AP
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Stages of Production
AP
MP
TP
L
MP & AP
TP
L0
0
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Cont’d… Cont’d… Stages ProductionStages Production
Stage 01MP > AP; AP is Rising
Stage 020< MP < AP
Stage 03MP < 0
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The Law of Diminishing ReturnsThe Law of Diminishing Returns
The law states that MP of the variable input will decline as the proportion of the variable input is increased with the constant level of fixed input
There is a limit that the amount of output
can be produced in a productive facility of a given size
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Optimal Use of a Variable InputOptimal Use of a Variable Input
MPL = PL = Wage (w)
0MPL
L
MPL
w
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Theory of Production – Long-runTheory of Production – Long-run
◦Introduction◦Isoquants ◦Marginal rate of technical substitution◦Isocost◦Producer equilibrium◦Production expansion path
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Production with Two Variable Production with Two Variable InputsInputsLong-run AnalysisLong-run Analysis
In the long-run, all the inputs are variable
Long-run Production Function
Q = F (K,L) = aK + bL
Both capital (K) and labor(L) inputs are variable
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Use of Calculus to Derive MP of Capital and Use of Calculus to Derive MP of Capital and LabourLabour
bL
QMPL
aK
QMPK
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IsoquantIsoquant
An Isoquant shows all different combinations of L & K that can be
used to produce a given level of output
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Properties of IsoquantsProperties of IsoquantsVery powerful tool for non-technical exposition of production theory
Application is similar to indifference curves
Convex t the originDownward slopingDo not intersectFurther from the origin represent greater output levels
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An Isoquant MapAn Isoquant Map
convex to the origin
downward sloping
do not intersect farther from the
origin represents greater output levels
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Marginal Rate of Technical Substitution Marginal Rate of Technical Substitution (MRTS)(MRTS)
MRTS - The slope of an Isoqunat is the rate at which a producer can substitute between two inputs and maintain the same level of output
MRTS = ∆K / ∆ L OR ,
MRTS (K, L) = MPL /MPK
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MRTS and Marginal ProductsMRTS and Marginal Products
The Marginal Rate of Technical Substitution is equal to the Ratio of Marginal Products
MPL . ∆L + MPK . ∆K = 0MPL . ∆L = - MPK . ∆K
∆K = MPL
∆ L MPK
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Law of Diminishing MRTSLaw of Diminishing MRTS
A property of a production function stating that as less of one input is used, increasing amounts of another input must be employed to produce
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Perfect Substitutes and Complementary Perfect Substitutes and Complementary InputsInputs
0 4 8 12
6
4
2
Capital
Capital
Labour0
6
4
2
2 4 6
2k1L
Perfectly Substitutable Inputs- An isoquant is a straight line (so that its absolute slope or MRTS is constant) ), and downward sloping. Complementary Inputs- An isoquant is right angled and efficient production can take place only with a specific ratio of inputs.
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IsocostIsocost
Isocost is a line that represents combinations of inputs that will cost the producer the same amount of money.
wL + rK = C The equation above in
slope/intercept form: K = C – w L r r Slope of the isocost line is –w/r Intercept is C/r
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An Isocost LineAn Isocost Line
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A Shift in an IsocostA Shift in an Isocost
Iso-costs further away from the origin are associated with higher costs.
K
L
C1C0
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A Rotation in an IsocostA Rotation in an Isocost
Changes in input prices change the slope of the isocost line, changing the relevant intercept (Intercept of the labor axis)
L
K
A new isocost line for a decrease in wages (Price of labor)
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Producer Equilibrium – Long-Producer Equilibrium – Long-runrun
(K*,L*) where isocost and isoquant are tangent
The slope of the isoquant is equal to the slope of the isocost line
MPL/MPK = w/r
MPL/w = MPK/r
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Producer EquilibriumProducer Equilibrium
Cost minimization; Given an output constraint entails finding the isocost that is closest to the origin meeting the output constraint
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Production Expansion PathProduction Expansion Path
This joins the tangency points of isoquant curves and the isocost lines
At this equilibrium point, the ratio of marginal product of the two inputs is equal to the price ratio of the two products
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End of the Session