economic analysis for managers (eco 501) fall:2 012 semester
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Economic Analysis for Managers (ECO 501) Fall:2 012 Semester. Khurrum S. Mughal. Theme of the Lecture. Production Theory Introduction The Production Function Production with One Variable Input Production with Two Variable Input Returns to Scale. Production. - PowerPoint PPT PresentationTRANSCRIPT
Economic Analysis for Managers (ECO 501)
Fall:2012 Semester
Khurrum S. Mughal
1
Production Theory Introduction
◦ The Production Function
Production with One Variable Input
Production with Two Variable Input
Returns to Scale2
Theme of the Lecture
Production refers to the transformation of inputs or resources into outputs of goods and services
Production
INPUTS
CAPITAL
EntrepreneurWorkersLand &
Structures
LABOR
Machineryplant &equipment
Natural Resources
Production
Short Run- At least one input is fixed
Long Run - All inputs are variable◦ The length of long run depends on industry.
Factors of Production
Level of production can be altered changing the proportion of variable inputs
Output = Fixed inputs + Variable inputs
• Scale of production can be altered by changing the supply of all the inputs (only in the long run)
Output = Total inputs(variable inputs)
Level and Scale of Production
General equation for Production Function:
Q = f (K,L), where
L = Labour
K = Capital
Maximum rate of output per unit of time obtainable
from given rate of Capital and Labour
An engineering concept: Relates out puts and inputs
7
Production Function
6 10 24 31 36 40 395 12 28 36 40 42 404 12 28 36 40 40 363 10 23 33 36 36 332 7 18 28 30 30 281 3 8 12 14 14 12
1 2 3 4 5 6
Q = f(L, K)
Ca
pit
al (
K)
Labor (L)
Production Function with Two Inputs
Substitutability between factors of production
Returns to Scale vs Returns to Factor
Devoid of economics
Production Theory Introduction
◦ The Production Function
Production with One Variable Input
Production with Two Variable Input
Returns to Scale9
Theme of the Lecture
Q = f (K,L), where K is fixed
10
Production With One Variable Input
Total Product TP = Q = f(L)
Marginal Product MPL =TP L
Average Product APL =TP L
Production orOutput Elasticity
Q/Q L/L
Q/ L Q/L
== =ELMPL
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
Total, Marginal, and Average Product of Labor, and Output Elasticity
Production With One Variable Input
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
Total, Marginal, and Average Product of Labor, and Output Elasticity
Production With One Variable Input
-3
-2
-1
0
1
2
3
4
5
0 1 2 3 4 5 6 7
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6 7
6
A
B
C
D E
F
B’ C’
A’D’
E’F’
I
TotalProduct
Marginal& AverageProduct
Labor
Labor
TP
MP
AP
G
Law of Diminishing Returns and Stages of Production
Stage II of Labor Stage III of LaborStage I of Labor
1:◦ Marginal product reaches a maximum at L1 (Point of
Inflection G). The total product function changes from increasing at a increasing rate to increasing at a decreasing rate.
2:◦ MP intersects AP at its maximum at L2.
3:◦ MP becomes negative at labor rate L3 and TP reaches
its maximum.
14
Relationship Among Production Functions
Marginal RevenueProduct of Labor
MRPL = (MPL)(MR)
Optimal Use of Labor MRPL = w
Optimal use of the Variable Input
L MPL MR = P
2.50 4 $103.00 3 103.50 2 104.00 1 104.50 0 10
Assumption : Firm hires additional units of labor at constant wage rate = $20
Optimal use of the Variable Input
L MPL MR = P MRPL w
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
Use of Labor is Optimal When L = 3.50
Assumption : Firm hires additional units of labor at constant wage rate
Optimal use of the Variable Input
2.5 3.0 3.5 4.0 4.5
40
30
20
10
0
w = $20
dL = MRPL
Units of Labor Used
$
Optimal use of the Variable Input
Production function of global electronics: Q=2k0.5L0.5
Compute Optimal use of labor when◦ K is fixed at 9, ◦ Price is Rs. 6 per unit ◦ and wage rate is Rs. 2 per unit
19
Optimal use of the Variable Input
Production Theory Introduction
◦ The Production Function
Production with One Variable Input
Production with Two Variable Input
Returns to Scale20
Theme of the Lecture
Isoquants show combinations of two inputs that can produce the same level of output.
K
Q
6 10 24 31 36 40 395 12 28 36 40 42 404 12 28 36 40 40 363 10 23 33 36 36 332 7 18 28 30 30 281 3 8 12 14 14 12
1 2 3 4 5 6 L
Production with Two Variable Input
K
Marginal Rate of Technical Substitution
A movement down an Isoquant the ◦ gain in out put from using more labor equals loss
in output from using less capital
MRTS: Slope of the Isoquant
23
_ (MPL) = MRTS (MPK)
Marginal Rate of Technical Substitution
Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.
C wL rK
C wK L
r r
C Total Cost
( )w WageRateof Labor L
( )r Cost of Capital K
ISOCOST
10
8
6
4
2
2 4 6 8 10
Capital
Labor
1K
1L
AB C = $100, w = r = $10A
B
slope = -w/r = -1
vertical intercept = 10
Isocost Line
4 8 10 12 14 16 20
14
10 8
4
A
A’
B B’ B*
0 Labor
CapitalIsocost Lines
AB C = $100, w = r = $10
A’B’ C = $140, w = r = $10
AB* C = $100, w = $5, r = $10
Isocost Line
MRTS = w/r
Isocost Lines
AB C = $100, w = r = $10
A’B’ C = $140, w = r = $10
A’’B’’ C = $80, w = r = $10
Optimal Combination of Inputs
MPL = MPK
w r
MPL = wMPK r
Optimal Employment of Two Inputs
Optimal combination is where slope of Iso Cost and that of Isoquant are equal:
To maximize Profits, each input must be hired at the efficient input rate
◦ MRPL = w = (MPL)(MR)◦ MRPK = r = (MPK)(MR)
Profit Maximizing follows that the firm must be operating efficiently
MPL = MPK
w r
MPL = wMPK r
Profit Maximization
Expansion Path
Production Theory Introduction
◦ The Production Function
Production with One Variable Input
Production with Two Variable Input
Returns to Scale31
Theme of the Lecture
Production Function Q = f(L, K)
Q = f(hL, hK)
If = h, constant returns to scale.
If > h, increasing returns to scale.
If < h, decreasing returns to scale.
Economies of Scale - Returns to Scale
Constant Returns to
Scale
Increasing Returns to
Scale
Decreasing Returns to
Scale
Returns to Scale
Cobb-Douglas Production Function
Q = AKaLb
If a + b = 1, constant returns to scale.
If a + b > 1, increasing returns to scale.
If a + b <1, decreasing returns to scale.
Returns to Scale in An Empirical Production Function
Sources of Increasing Returns to Scale
Technologies that are effective at larger scale of production generally have higher unit costs at lower level of production
Labor Specialization◦ Labor may specialize in their specific tasks and
perform it efficiently
Inventory economies◦ Larger firms have lesser need for machine
inventory backup
Sources of Decreasing Returns to Scale
Managerial Issues due to large size of the firm
Increased Transportation costs
Larger labor costs due to requirement of increased wages to attract labor from farther areas
Economies of Scope
Using facility for producing additional products◦ E.g. Daewoo Bus Service for passenger and cargo
movement
Using unique skills or comparative advantage◦ Proctor & Gamble using its existing sales staff and
production capabilities for marketing various products as substitutes and complements
Measuring Productivity
Total Factor Productivity