Micro EconomicsMicro EconomicsLecture 07Lecture 07

THEORY OF PRODUCTIONTHEORY OF PRODUCTIONLecturer -J.D.T.MadhusankaLecturer -J.D.T.Madhusanka

Lecture OutlineLecture OutlineTheory of Production –Short-runLaw of Diminishing ReturnsTotal Average and Marginal

ProductStages of Production

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

 

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)

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

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.

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.

TOTAL PRODUCT CURVETOTAL PRODUCT CURVE

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

MARGINAL & AVERAGE PRODUCT MARGINAL & AVERAGE PRODUCT CURVESCURVES

 

Relationship Among TP, AP and MPRelationship Among TP, AP and MP

TP

L

L

AP & MP

0

0

MP

AP

Stages of Production

AP

MP

TP

L

MP & AP

TP

L0

0

Cont’d… Cont’d… Stages ProductionStages Production

Stage 01MP > AP; AP is Rising

Stage 020< MP < AP

Stage 03MP < 0

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

Optimal Use of a Variable InputOptimal Use of a Variable Input

MPL = PL = Wage (w)

0MPL

L

MPL

w

Theory of Production – Long-runTheory of Production – Long-run

◦Introduction◦Isoquants ◦Marginal rate of technical substitution◦Isocost◦Producer equilibrium◦Production expansion path

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

 

Use of Calculus to Derive MP of Capital and Use of Calculus to Derive MP of Capital and LabourLabour

bL

QMPL

aK

QMPK

IsoquantIsoquant

An Isoquant shows all different combinations of L & K that can be

used to produce a given level of output

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

An Isoquant MapAn Isoquant Map

convex to the origin

downward sloping

do not intersect farther from the

origin represents greater output levels

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

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

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

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.

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 

An Isocost LineAn Isocost Line

A Shift in an IsocostA Shift in an Isocost

Iso-costs further away from the origin are associated with higher costs.

K

L

C1C0

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)

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

Producer EquilibriumProducer Equilibrium

Cost minimization; Given an output constraint entails finding the isocost that is closest to the origin meeting the output constraint

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

End of the Session