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7/27/2019 Lecture - 10 - Isoquant Approach
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Cost of Production: The
Isoquant-Isocost approach/least cost
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WHAT IS ISOQUANT?
ISO- EQUAL/ SAME
QUANT- QUANTITY
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The different combinations oflabor and capital used toproduce a certain quantity of
products are illustrated throughIsoquants.
`ISOQUANTS`
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Isoquant curve a curve that representscombinations of factors of production that results in
equal amounts of output.
A point on the isoquant curve is technically
efficient.
An ISOQUANT CURVE shows differentcombinations of labor and and capital to producecertain output.
The isoquant curve is bowed inward because of the
law of diminishing marginal productivity.
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Labor Machines Pairs of shoes
A 1 4 15
B 2 2 15
C 4 1 15
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1 2 3 4 5
5
4
3
2
1
0
workers
m
a
c
h
i
n
e
s 4 10 13 15 16
10 15 18 20 21
13 18 22 24 25
15 21 24 26 27
`ISPOOSED SHU` PRODUCTION
(Shoes per day)
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Isoquant map a set of isoquant curves that showtechnically efficient combinations of inputs that canproduce different levels of output.
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An Isoquant Map
a
b
c
10 sweaters
15 sweaters
Capital(machin
esperday)
Labor (workers per day)
21 sweaters
51
4
2
0
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PROPERTIES OF ISOQUANTS
some of the main properties of isoquants.
Isoquants further from the origin represent greater
output levels
Isoquants slope down to the right
Isoquants do not intersect
Isoquants are usually convex to the origin/that is,bowed towards the origin.
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An Isoquant that Lies Above and to the Right ofAnother Represents a Higher Output Level:
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An Isoquant Slopes Downward fromLeft to Right:
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Isoquants Cannot Cut Each Other:
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Isoquants are Convex to the Origin:
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The marginal rate of technicalsubstitution
Isoquants are typically convex to the origin reflectingthe fact that the two factors are substitutable foreach other at varying rates.
It measures the reduction in one input per unitincrease in the other input that is just sufficient tomaintain a constant level of production. For example,the marginal rate of substitution of labor for capital
gives the amount of capital that can be replaced byone unit of labor while keeping output unchanged.
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The marginal rate of technicalsubstitution
Or Marginal rate of substitution for production therate at which one factor must be added to compensate forthe loss of another factor, to keep output constant
It is the slope of the isoquant curve
The absolute value of the slope at a point on the isoquantcurve equals the ratio of the marginal productivity of labor
to the marginal productivity of machines.
onsubstitutiofrateMarginal
MP
MPSlope
machine
labor
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The marginal rate of technicalsubstitution
To move from point A to point B in the diagram, the amount
of capital is reduced from Ka to Kb while the amount of laboris increased only from La to Lb. To move from point C topoint D, the amount of capital is reduced from Kc to Kd whilethe amount of labo ris increased from Lc to Ld.
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The opposite is true when going in the otherdirection (from D to C to B to A). In this case we arelooking at the marginal rate of technical substitution
capital for labour (which is the reciprocal of themarginal rate of technical substitution labour forcapital).
It can also be shown that the marginal rate of
substitution labour for capital, is equal to themarginal physical product of labour divided by themarginal physical product of capital.
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The Marginal Rate of TechnicalSubstitution
13 sweaters
a
b
Capital(machinesperday)
Labor (workers per day)51
1
0
3
MRTS =-1/3
MRTS =- 3
2.5
5
2.5
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Factor
Combinations
Units
ofLabor
Units of
Capital
Units of Output of
Commodity X
MRTS of Labor
for Capital
A 1 15 150 -B 2 11 150 4:1C 3 8 150 3:1D 4 6 150 2:1
E 5 5 150 1:1
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Isocost LinesIsocost line a line that representsalternative combinations of factors ofproduction that have the same costs.
An Isocost line shows all the
combinations of capital(machines)and labor(workers) that can be
bought for a given total cost
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Isocost Line
b
d
Capital(machinesperday)
Labor (workers per day)40
4Total Cost = $100
c
e
a
PL= $25
PK= $25
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The Isocost Equation
The Isocost line can be described by an equation:
TC = PLL + PKK
To calculate the isocost equation, divide the firms
Total Cost by the price of capital and then subtract(PL/PK)L from both sides of the resulting equation.The isocost equation is:
K = TC/PK (PL/PK) L
This equation tells us how the firm can vary itscapital input as it varies its labor input, holding totalcost constant.
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Isocost Map
1
2
3
4
5
1 2 3 4 5
TC=$75 TC=$100 TC=$125
M
a
c
h
I
n
e
s
workers
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Input Prices and the Isocost Line
Capital(machinesperday)
Labor (workers per day)
40
4
Labor $50
Capital $25
2
2
B Ac
Labor $25
Capital $25
Labor $25
Capital $50
TC = $100
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The Least-Cost Technique ofProduction
a
b
Capital(machines
perday)
Labor (workers per day)
51
2
0
4
5
c
15 sweaters
Least-Costtechnique
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Exercise
Q.1.Define Iso-cost line with the help of adiagram.
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Exercise
Draw the Iso-cost curve for theTC=$150,
L = $25 & K = $50L = $50 & K = $25
L = $25 & K = $25
L = $50 & K = $50
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