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Production Economics Introduction
Decisions of Managers
Managers make resource allocation decisions about
production operations
marketing
financing and
personnel
Decisions of Managers
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
Decisions of Managers
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.
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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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Production Economics Production Function
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Production Economics Production Function
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
DURAN & GVEN (METU) EM 517 Week 6 Industrial Engineering Dept. 5 / 26
Production Economics Production Function
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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Production Economics Production Function
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
DURAN & GVEN (METU) EM 517 Week 6 Industrial Engineering Dept. 7 / 26
Production Economics Production Function
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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Production Economics Production Function
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
DURAN & GVEN (METU) EM 517 Week 6 Industrial Engineering Dept. 9 / 26
Production Economics Production Function
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
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Production Economics Production Function
DURAN & GVEN (METU) EM 517 Week 6 IndustrialEngineering Dept. 11 / 26
Production Economics Production Function
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
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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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Production Economics Optimal Use of the Variable Output
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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Production Economics Optimal Use of t he Variable Output
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Production Economics Optimal Use of the Variable Output
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
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Production Economics Optimal Use of t he Variable Output
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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Production Economics Optimal Use of the Variable Output
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
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Production Economics Optimal Use of t he Variable Output
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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Production Economics Optimal Use of the Variable Output
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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Production Economics Optimal Use of t he Variable Output
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Production Economics Optimal Use of the Variable Output
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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Production Economics Optimal Use of t he Variable Output
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Production Economics Optimal Use of the Variable Output
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
DURAN & GVEN (METU) EM 517 Week 6 IndustrialEngineering Dept. 25 / 26
Production Economics Optimal Use of t he Variable Output
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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