Em Lecture Presentation Handout

8/2/2019 Em Lecture Presentation Handout

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Production Economics Introduction

Decisions of Managers

Managers make resource allocation decisions about

production operations

marketing

financing and

personnel


Production decisions determine the types and amounts of inputs suchas

land

labor

raw and processed materials

factories, machinery, equipment,

to be used in the production of a desired quantity of output.DURAN & GVEN (METU) EM 517 Week 6 Industrial Engineering Dept. 1 / 26

Production Economics Introduction


Managers must decide not only

what to produce for the market

but also how to produce it in the most efficient or least cost

mannerTherefore, managers objective is

to minimize cost for a given output or

to maximize output for a given input budget.

Economic Theory of Production

consists of a conceptual framework to assist managers in decidinghow to combine most efficiently the various inputs needed to producethe desired output given the existing technology.

DURAN & GVEN (METU) EM 517 Week 6 Industrial Engineering Dept. 2 / 26


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Production Economics Production Function

Production Function

The theory of production centers around the concept of aproduction function

A production function relates the most that can be produced froma given set of inputs

A Production Function is the maximum quantity from any amountsof inputs

Production functions allow measures of the marginal product ofeach input

Cobb-Douglas Production Function

If L is labor and K is capital, Cobb-Douglas Production Function is

Q= L1K2

where , 1 and 2 are constants.





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Fixed and Variable Inputs

In deciding how to combine the various inputs (L and K) to producethe desired output, inputs are usually classified as being either fixed orvariable

A fixed input is required in the production process but its quantity

employed is constant over a given period of time regardless of thequantity of output produced

A variable input quantity employed in the process changes withthe desired quantity of output

The short run corresponds to the period of time in which one (ormore) of the inputs is fixed

The number of inputs is often larger than just K & L.But economists simplify by suggesting

materials or labor, is variablewhereas plant and equipment is fairly fixed in the short run



The Short Run Production Function

In the short run, because some of the inputs are fixed, only asubset of the total possible input combinations is available to thefirm

To increase output, firm must employ more of the variable input(s)with the given quantity of fixed input(s)

Q= f(X1,X2,X3,X4, . . .)

where say X1 and X2 are variable inputs and the rest are fixed.

Q= f(K,L) is the two input case where the capital, K, is fixedinput

A Production Function with only one variable input, labor ,L, iseasily analyzed.



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Total, Average, Marginal Production Functions

Once the total product function is given the marginal and averageproduct functions can be derived

Average Product is defined as the ratio of total output to theamount of the variable input used in producing the output

Average Product of Labor is defined asAPL =

Q

L

The marginal product is defined as the incremental change in totaloutput Q that can be produced by the use of one more unit ofthe variable input L, while K remains fixed.

The marginal product is defined as

MPL =Q

L=

Q

L

is the output attributable to last unit of labor applied



Average and Marginal Production Functions

Similar to profit functions, the Peak of MPoccurs before the Peakof AP

When MP= AP, we are at the peak of the AP curveDURAN & GVEN (METU) EM 517 Week 6 Industrial Engineering Dept. 8 / 26


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When MP> AP, then AP is risingIf your marginal grade in this class is higher than your grade pointaverage, then your G.P.A is rising

When MP< AP, then AP is fallingIf your batting average is less than that of the New York Yankees,your addition to the team would lower the Yankees team battingaverage

When MP= AP, then AP is at its MAXIf the new hire is just as efficient as the average employee, then theaverage productivity does not change



The Law of Diminishing Marginal Returns

increases in one variable factor of production holding all otherfactors fixed, after some point, marginal product diminishes

Consider the variable factor of Labor. Why we observeDiminishing Marginal Returns?

After a point, each additional worker introduces crowding effects

With enough additional workers, the marginal product of labor maybecome zero or even negative

Some work is just more difficult to accomplish when superfluouspersonnel are present

This is a short run law

DURAN & GVEN (METU) EM 517 Week 6 IndustrialEngineering Dept. 10 / 26


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Relationship between Total, Marginal and Average Profit

Figure illustrates a production function total value added or totalproduct (TP) with a single variable inputIncreasing returns region: TP function is increasing at anincreasing rate

Marginal product (MP) curve measures the slope of the TP curve(MP= Q

L),

MPcurve is increasing up to L1Decreasing returns region: TP function is increasing at adecreasing rate

MP curve is decreasing up to L3Negative returns region: TP function is decreasing

MPcurve continues decreasing, becoming negative beyond L3

An inflection point occurs at L1



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Production Economics Optimal Use of the Variable Output

Optimal Use of the Variable Output

With one of the inputs (K) fixed in the short run, the producer mustdetermine the optimal quantity of the variable input (L) to employin the production process

Should consider output prices and labor costs

Marginal Revenue Product

Marginal revenue product (MRPL) is defined as the amount thatan additional unit of the variable input adds to total revenue

MRPL =TR

L

and MRPL is equal to the marginal product of L (MPL) times themarginal revenue (MRQ) resulting from the increase in outputobtained: MRPL = MPL MRQ


Production Economics Optimal Use of t he Variable Output

Marginal Factor Cost

Marginal factor cost (MFCL) is defined as the amount that anadditional unit of the variable input adds to total cost

MFCL=

TC

L

where TC is the change in cost

Optimal Input Level

we can compute the optimal amount of the variable input to use inthe production process

For the short-run production decision

the optimal level of the variable input occurs where MRPL = MFCL



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Wage

Labor

W=MFC

MRPL

Optimal Labor

MPL

HIRE, if you get more revenue than cost

HIRE if the marginal revenue product > marginal factor cost

At optimum: MRPL = MFCL =W





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Long Run Production Functions

All input factors are variable

Q= f(K,L) is two input example

MPof capital and MPof labor are the derivatives of the production

function

MPL =Q

L

MPK =Q

K

MPof labor declines as more labor is applied.

Also the MPof capital declines as more capital is applied



Production Isoquants

A production function with two variable inputs can be representedgraphically by a set of two-dimensional production isoquants

Production isoquant is either a geometric curve or an algebraicfunction representing all the various combinations of the two

inputs that can be used in producing a given level of output



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The Marginal Rate of Technical Substitution

Isoquant also indicates the rate at which one input may besubstituted for another input in producing the given quantity ofoutput

slope of Isoquant is ratio of Marginal Products, called the MRTS,the marginal rate of technical substitution

MRTS is given by the slope of the curve relating K to L

Marginal rate of technical substitution (MRTS): the amount bywhich one input can be reduced when one more unit of anotherinput is added while holding output constant

Example: it is the rate that capital can be reduced, holding outputconstant, while using one more unit of labor



The Marginal Rate of Technical Substitution

For the production function of two variable inputs: Q= f(X1,X2)

dQ =Q

X1dX1 +

Q

X2dX2 = 0

dX2

dX1=

Q/X1Q/X2

=MP1

MP2= MRTS2,1 > 0

MRTS21 is the rate of substitution of X2 for X1if MRTSLK = 2, it means that 1 unit of capital can replace 2 unitsof labour while output remains the same

this is possible if capital is twice as productive as labour



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Optimal Combination of Inputs

a given level of output can be produced using any of a largenumber of possible combinations of two inputs

Firm needs to determine which combination will minimize the totalcosts for producing the desired output

The objective is to minimize cost for a given output

Isocost Lines

Total cost of each possible input combination is a function of themarket prices of these inputs

Let CL and CK be the per-unit prices of inputs L and K

Total cost (C) of any given input combination is C= CLL+CKK

Isocost lines are the combination of inputs for a given cost, C0,C0 = CLL+CKK





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Minimizing Cost Subject to an Output Constraint

Director of operations desires to release to production a numberof orders for at least Q(2) units of output

Solution should be in the feasible region containing the inputcombinations that lie either on the Q(2) isoquant or on isoquants

that fall aboveThe total cost of producing the required output is minimized byfinding the input combinations within this region that lie on thelowest cost isocost line

CombinationDon the C(2) isocost line satisfies this condition

CombinationsE and F, which also lie on the Q(2) isoquant, yieldhigher total costs because they fall on the C(3) isocost line

Thus, the use of L1 units of input L and K1 units of input K willyield a (constrained) minimum cost solution of C(2) dollars





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Minimizing Cost Subject to an Output Constraint

At the optimal input combination, the slope of the given isoquantmust equal the slope of the C(2) lowest isocost line

The slope of an isoquant is equal to dK/dL

The slope of isocost is equal to dK/dL = CL/CK

dK

dL= MRTS=

MPL

MPK=

CL

CK

MPL

MPK=

CL

CK

MPL

CL=

MPK

CK

This condition is known as equimarginal criterion

Marginal product per dollar input cost of one factor must be equalto the marginal product per dollar input cost of the other factor



In Class Work

Is the following firm efficient?

MPL = 30

MPK = 50

W = 10 (cost of labor)

R= 25 (cost of capital)

If your answer is NO, what should the firm do?

MPL

CL= 3 =

MPK

CK= 2

Firm is inefficient!. A dollar spent on labor produces 3, and a dollarspent on capital produces 2. Shift to more labor until the equimarginalcondition holds.


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Em Lecture Presentation Handout