Managerial Economics in a Global Economy

Managerial EconomicsManagerial Economics Prof. M. El-SakkaProf. M. El-Sakka CBA. Kuwait University CBA. Kuwait University

Managerial EconomicsManagerial Economics in a Global Economyin a Global Economy

Chapter 6Chapter 6

Production Theory and EstimationProduction Theory and Estimation


The production function with one variableThe production function with one variable

InputsInputs Labor, Capital, Land …etc.Labor, Capital, Land …etc.

Fixed InputsFixed Inputs

Variable InputsVariable Inputs

Short RunShort Run At least one input is fixedAt least one input is fixed

Long RunLong Run All inputs are variableAll inputs are variable


Total ProductTotal ProductTP = Q = f(L)

Average ProductAverage Product

The total product divided by the amount of the input used. The total product divided by the amount of the input used.

Marginal ProductMarginal ProductThe addition to total output resulting from the addition of the last unit of the The addition to total output resulting from the addition of the last unit of the

input. input.

- Marginal product = negative when TP is decreasing- Marginal product = negative when TP is decreasing

- Marginal product = zero when TP is at its maximum- Marginal product = zero when TP is at its maximum

- Marginal output = Average product when AP reaches maximum- Marginal output = Average product when AP reaches maximum

APL =TP

L

MPL =TP

L


Production or Output Elasticity

EL =MPL

APL

L Q MPL APL EL

0 0 - - -1 3 3 3 12 8 5 4 1.253 12 4 4 14 14 2 3.5 0.575 14 0 2.8 06 12 -2 2 -1

The production functionThe production function is a table, graph, or an equation is a table, graph, or an equation showing the showing the maximum outputmaximum output from inputs. The following table from inputs. The following table is an example (where there is one variable input, the is an example (where there is one variable input, the remaining are constant).remaining are constant).


The Law of Diminishing ReturnsThe Law of Diminishing Returns..

If equal increments of an input are added, and the If equal increments of an input are added, and the quantities of other inputs are held constant, the quantities of other inputs are held constant, the resulting increments of product will decrease beyond resulting increments of product will decrease beyond some point; that is, the marginal product of the input some point; that is, the marginal product of the input will diminish.will diminish.

Note:Note:- The law is an empirical generalization- The law is an empirical generalization

- Technology is assumed to be constant- Technology is assumed to be constant

- There is a change in one input and the others are held - There is a change in one input and the others are held constantconstant


Stages of ProductionStages of Production


The Optimal Level of Utilization of an Input.The Optimal Level of Utilization of an Input.

How much of the variable input should we utilize?. How much of the variable input should we utilize?.

The answer:The answer: we have to compare between we have to compare between the marginal revenue the marginal revenue product MRPproduct MRP of the input and theof the input and the marginal expenditure on the marginal expenditure on the inputinput i.e., the marginal resource cost MRC i.e., the marginal resource cost MRC..

The Marginal Revenue Product:The Marginal Revenue Product: The amount that an The amount that an additional unit of the variable input (Y) adds to the firm’s total additional unit of the variable input (Y) adds to the firm’s total revenue:revenue:

MRPMRPLL = ( = (TR/TR/Q) . (Q) . (Q/Q/L) L)

(marginal revenue × marginal product), Or:(marginal revenue × marginal product), Or:

MRPL = MR . MPLMRPL = MR . MPL


The Marginal Resource CostThe Marginal Resource Cost

The amount that an additional unit of the variable input adds The amount that an additional unit of the variable input adds to the firms total costs.to the firms total costs.

MRCL = MRCL = TC/TC/L; L;

(wage level in a competitive labor market)(wage level in a competitive labor market)

To maximize its profits, the firm should utilize the amount of To maximize its profits, the firm should utilize the amount of input where the marginal revenue product equals the marginal input where the marginal revenue product equals the marginal expenditures.expenditures.

Optimal Use of Labor Optimal Use of Labor MRPL = MRCL MRPL = MRCL


L MPL MR = P MRPL MRCL

2.50 4 $10 $40 $203.00 3 10 30 203.50 2 10 20 204.00 1 10 10 204.50 0 10 0 20

Optimal Use of the Variable InputOptimal Use of the Variable Input

Look at the table. The use of Labor is Optimal When L = 3.50Look at the table. The use of Labor is Optimal When L = 3.50


Optimal Use of the Variable InputOptimal Use of the Variable Input


The Production Function with Two Variable Inputs.The Production Function with Two Variable Inputs.

Q = f ( X1 , X2 );Q = f ( X1 , X2 );

production functionproduction function

CapitalCapital66 1010 2121 3131 3636 4040 39 39 55 1212 2828 3636 4040 4242 404044 1212 2828 3636 4040 4040 363633 1010 2323 2323 3636 3636 333322 77 1818 2828 3030 3030 282811 33 88 1212 1414 1414 1212

11 22 33 44 55 66 LaborLabor


IsoquantsIsoquants

A curve showing all A curve showing all possible (efficient) combinationspossible (efficient) combinations of (two) of (two) inputs that are capable of producing a inputs that are capable of producing a certain quantitycertain quantity of of outputoutput

Production With Two Variable InputsProduction With Two Variable Inputs


Isoquants slope is Isoquants slope is negativenegative, but it may also have positively , but it may also have positively sloped segments. Positive slope implies that increases in both sloped segments. Positive slope implies that increases in both capital and labor are required to maintain a certain output capital and labor are required to maintain a certain output rate. In this case the marginal product of one or the other input rate. In this case the marginal product of one or the other input must be must be negativenegative..

Economic Region of ProductionEconomic Region of Production

Firms will only use combinations of two inputs that are in the Firms will only use combinations of two inputs that are in the economic region of productioneconomic region of production, which is defined by the portion , which is defined by the portion of each isoquant that is negatively slopedof each isoquant that is negatively sloped.


•Hence output will increase if less quantities of the input were used.

•profit maximizing firms will produce on the negatively slopped curves only.


• Marginal Rate of Technical Substitution MRTSMarginal Rate of Technical Substitution MRTS

The rate at which an input can be substituted for another input if The rate at which an input can be substituted for another input if output remains constantoutput remains constant

Q = f ( X1 , X2 )Q = f ( X1 , X2 )

MRTS = - dX2 / dX1; MRTS = - dX2 / dX1; the slope of the isoquantthe slope of the isoquant

Since MRTS = - dX2 / dX1, it follows that (given capital and Since MRTS = - dX2 / dX1, it follows that (given capital and labor are the two inputs)labor are the two inputs)

MRTS = -MRTS = -K/K/L = MPL/MPKL = MPL/MPK


MRTS = -(-2.5/1) = 2.5MRTS = -(-2.5/1) = 2.5


Perfect SubstitutesPerfect Substitutes Perfect ComplementsPerfect Complements


Optimal Combination of InputsOptimal Combination of Inputs

Input combinations that can be obtained from a total outlay M is:Input combinations that can be obtained from a total outlay M is:

M =PL . L + PK . K;M =PL . L + PK . K;

The various combinations of capital and labor can be represented by The various combinations of capital and labor can be represented by a straight line. This line is called the isocost curve. Its slope is:a straight line. This line is called the isocost curve. Its slope is: -PL / PK.-PL / PK.

Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

C = total costC = total cost W = wage rate W = wage rate r = cost of capitalr = cost of capital

C wL rK


Isocost LinesIsocost Lines

ABAB C = $100, C = $100, w = r = $10w = r = $10 A’B’A’B’ C = $140, C = $140, w = r = $10w = r = $10 A’’B’’A’’B’’ C = $80, C = $80, w = r = $10w = r = $10 AB*AB* C = $100, C = $100, w = $5, r = $10w = $5, r = $10


To determine the optimal combination of inputs, we To determine the optimal combination of inputs, we superimpose the isocost on the isoquant map.superimpose the isocost on the isoquant map.


The firm should pick the point on the isocost that is on The firm should pick the point on the isocost that is on (tangent) the highest isoquant. i.e,(tangent) the highest isoquant. i.e,

MPL / MPK = PL / PKMPL / MPK = PL / PK

OrOr

MPL / PL = MPK / PKMPL / PL = MPK / PK ( maximization condition ) ( maximization condition )

If we use more than two inputs the optimal combination of If we use more than two inputs the optimal combination of inputs is:inputs is:

MPa / Pa = MPb / Pb = . . . = MPn / PnMPa / Pa = MPb / Pb = . . . = MPn / Pn


Effect of a Change in Input PricesEffect of a Change in Input Prices


Returns to ScaleReturns to Scale

How output responds in the long run to changes in the scale of How output responds in the long run to changes in the scale of the firm. Suppose that the firm increases inputs by the same the firm. Suppose that the firm increases inputs by the same proportion; what will happen to output.proportion; what will happen to output.

a - output may increase by a a - output may increase by a larger proportionlarger proportion of each input. This of each input. This is the case of is the case of increasing returns to scaleincreasing returns to scale..

b - output may increase by a b - output may increase by a smaller proportionsmaller proportion than each of the than each of the inputs. This is the case of inputs. This is the case of decreasing returns to scaledecreasing returns to scale. .

c - output may increase by the same proportion of each of the c - output may increase by the same proportion of each of the inputs. This is the case of inputs. This is the case of constant returns to scaleconstant returns to scale. .


Production Function Q = f (L, K)Production Function Q = f (L, K)

Q = f (hL, hK)Q = f (hL, hK)

If If = h, then f has constant returns to scale. = h, then f has constant returns to scale. If If > h, then f has increasing returns to scale. > h, then f has increasing returns to scale. If If < h, the f has decreasing returns to scale < h, the f has decreasing returns to scale.

Constant Returns Increasing Decreasing Returns

to Scale Returns to Scale to Scale


Causes of increasing returns to scale.Causes of increasing returns to scale.- geometric relations (technical characteristics of tools)- geometric relations (technical characteristics of tools)

- specialization- specialization

- probabilistic considerations, the greater the number of - probabilistic considerations, the greater the number of customers, customer behavior tends to be more stable, the customers, customer behavior tends to be more stable, the firm’s inventory may not need to increase in proportion to its firm’s inventory may not need to increase in proportion to its salessales

Causes of decreasing returns to scaleCauses of decreasing returns to scale- the difficulty of coordinating a large scale enterprise. large - the difficulty of coordinating a large scale enterprise. large

teams seem to be less effective than small teamsteams seem to be less effective than small teams


The output elasticity The output elasticity εε

To measure whether there are increasing or To measure whether there are increasing or decreasing returns or constant returns to scale, the decreasing returns or constant returns to scale, the output elasticity can be computed.output elasticity can be computed.

The output elasticity is the percentage change in The output elasticity is the percentage change in output resulting from one percentage change in all output resulting from one percentage change in all inputs. inputs.

If If εε > 1 > 1 increasing returns to scale increasing returns to scale If If εε < 1 < 1 decreasing returns to scale decreasing returns to scale If If εε = 1 = 1 constant returns to scale constant returns to scale


Cobb-Douglas Production FunctionCobb-Douglas Production Function

Q = AKQ = AKaaLLbb

Estimated using Natural LogarithmsEstimated using Natural Logarithms

ln Q = ln A + a ln K + b ln Lln Q = ln A + a ln K + b ln L

If a+b = 1If a+b = 1 constant returnsconstant returns If a+b > 1If a+b > 1 increasing returnsincreasing returns If a+b < 1If a+b < 1 decreasing returnsdecreasing returns


Innovations and Global CompetitivenessInnovations and Global Competitiveness

Product InnovationProduct Innovation Process InnovationProcess Innovation Product Cycle ModelProduct Cycle Model Just-In-Time Production SystemJust-In-Time Production System Competitive BenchmarkingCompetitive Benchmarking Computer-Aided Design (CAD)Computer-Aided Design (CAD) Computer-Aided Manufacturing (CAM)Computer-Aided Manufacturing (CAM)


e.g.e.g.

Q = 0.8LQ = 0.8L0.30.3 K K0.80.8

multiply both inputs by 1.01multiply both inputs by 1.01

Q = 0.8(1.01L)Q = 0.8(1.01L).3.3 ( 1.01K) ( 1.01K).8.8

= 0.8(1.01)= 0.8(1.01)1.11.1LL.3.3KK.8.8

= (1.01)= (1.01)1.11.1 (.8L (.8L.3.3 K K.8.8))

= (1.01)= (1.01)1.11.1 Q Q

= 1.011 Q= 1.011 Q

if the quantity of both inputs increases by 1% output will increase if the quantity of both inputs increases by 1% output will increase by 1.1%.by 1.1%.

Managerial Economics in a Global Economy

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