Economics of Input Input Combination
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Transcript of Economics of Input Input Combination
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Economics of Inputinput combinations
Prepared By: Milan Padariya
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Topics of DiscussionConcept of isoquant curveConcept of an iso-cost lineLeast-cost use of inputs
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Physical Relationships
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Use of Multiple Inputs
This lecture will refer to situations where we have multiple variable inputsLabor, machinery rental, fertilizer application,
pesticide application, etc.
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Use of Multiple InputsOur general single input production function
looked like the following: Output = f(labor | capital, land, energy, etc)
Lets extend this to a two input production function Output = f(labor, capital | land, energy, etc)
Variable Input Fixed Inputs
Fixed InputsVariable Inputs
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Use of Multiple InputsOutput (i.e. Corn Yield)
250
Nitrogen Fert.
Phos. Fert.
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Use of Multiple InputsIf we take a slice at a level of
output we obtain what is referred as an isoquantSimilar to the indifference
curve we covered when we reviewed consumer theory
Shows collection of multiple inputs that generates a particular output level
There is one isoquant for each output level
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Output isidentical alongan isoquant and different across isoquants
Isoquant means “equal quantity”Isoquant means “equal quantity”
Two inputs
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Slope of an IsoquantThe slope of an isoquant is referred to as
the Marginal Rate of Technical Substitution (MRTS) The value of the MRTS in our example is given
by: MRTS = Capital ÷ Labor Provides a quantitative measure of the
changes in input use as one moves along a particular isoquant
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Slope of an IsoquantThe slope of an isoquant is the
Marginal Rate of Technical Substitution (MRTS) Output remains unchanged along an
isoquant The ↓ in output from decreasing labor
must be identical to the ↑ in output from adding capital as you move along an isoquant
Labor
CapitalQ=Q*
L*
K*
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MRTS here is– 4 ÷ 1 = – 4
MRTS here is– 4 ÷ 1 = – 4
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What is the slope overrange B?
MRTS here is–1 ÷ 1 = –1
MRTS here is–1 ÷ 1 = –1
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What is the slope overrange C?What is the slope overrange C?
MRTS here is–.5 ÷ 1 = –.5
MRTS here is–.5 ÷ 1 = –.5
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Slope of an IsoquantSince the MRTS is the slope of the
isoquant, the MRTS typically changes as you move along a particular isoquantMRTS becomes less negative as shown
above as you move down an isoquant
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Introducing Input Prices
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Plotting the Iso-Cost LineLets assume we have the following
Wage Rate is $10/hour Capital Rental Rate is $100/hour
What are the combinations of Labor and Capital that can be purchased for $1000 Lets introduce the Iso-Cost Line
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Plotting the Iso-Cost Line
Labor
Capital
10
100
Firm can afford 100 hour of labor at a wage rate of $10/hour for a budget of $1,000
Firm can afford 100 hour of labor at a wage rate of $10/hour for a budget of $1,000
Firm can afford 10 hours ofcapital at a rental rate of $100/hr with a budget of $1,000
Firm can afford 10 hours ofcapital at a rental rate of $100/hr with a budget of $1,000
Combination of Capital and Labor costing $1,000 Referred to as the $1,000 Iso-Cost
Line
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Plotting the Iso-Cost LineHow can we define the equation of this iso-
cost line? Given a $1000 total cost we have:
$1000 = PK x Capital + PL x Labor → Capital =
(1000÷PK) – (PL÷ PK) x Labor→The slope of an iso-cost in our example is
given by:Slope = –PL ÷ PK
(i.e., the negative of the ratio of the price of the two inputs)
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Plotting the Iso-Cost Line
Labor
Capital
20
200
10
5
10050
Doubling of Cost
Note: Parallel cost linesgiven constant prices
Original Cost Line
2,000÷PK
500 ÷ PK
Halving of Cost
500 ÷ PL 2000 ÷ PL
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Plotting the Iso-Cost Line
Labor
Capital
10
10050 200
$1,000 Iso-Cost Line
Iso-Cost Slope = – PK ÷ PL
PL = $5PL = $10
PL = $20
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Plotting the Iso-Cost Line
Labor
Capital
10
10050 200
$1,000 Iso-Cost Line
Iso-Cost Slope = – PK ÷ PL
20
5
PK = $200
PK = $100
PK = $50
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Least Cost Combinationof Inputs
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Least Cost Input Combination
Labor
CapitalTVC are predefined Iso-Cost Lines
TVC*
TVC**
TVC***
TVC*** > TVC** > TVC*
A
B
C
Pt. C: Combination of inputs that cannot produce Q*
Pt. A: Combination of inputs that have the highest of the two costs of producing Q*
Pt. B: Least cost combination of inputs to produce Q*
Q*
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Least Cost Decision RuleThe least cost combination of two inputs
(i.e., labor and capital) to produce a certain output level Occurs where the iso-cost line is tangent to
the isoquant Lowest possible cost for producing that level
of output represented by that isoquant This tangency point implies the slope of the
isoquant = the slope of that iso-cost curve at that combination of inputs
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Least Cost Decision RuleWhen the slope of the iso-cost = slope of the
isoquant and the iso-cost is just tangent to the isoquant
–MPPK ÷ MPPL = – (PK ÷ PL)
We can rearrange this equality to the following
Isoquant Slope
Isoquant Slope
Iso-cost Line SlopeIso-cost
Line Slope
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Least Cost Decision Rule
=
L K
L k
MPP MPP
P P
MPP per dollar spent on labor
MPP per dollar spent on labor
MPP per dollar spent on capitalMPP per dollar spent on capital
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Least Cost Decision Rule
3 51 2 4
1 2 3 4 5
MPP MPPMPP MPP MPP
P P P P P
The above decision rule holds for all variable inputs• For example, with 5 inputs we would have the
following
MPP1 per $ spent on Input 1
MPP1 per $ spent on Input 1 = MPP2 per $ spent
on Input 2
MPP2 per $ spent on Input 2 = …… =MPP5 per $ spent
on Input 5
MPP5 per $ spent on Input 5=
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Least Cost Input Choice for 100 Units of OutputLeast Cost Input Choice for 100 Units of Output
7
60
Point G represents 7 hrs of capital and 60 hrs of labor
Wage rate is $10/hr and rental rate is $100/hr
→ at G cost is $1,300 = (100×7) + (10×60)
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7
60
G represents a total cost of $1,300 every input combination on the iso-cost line costs $1,300
With $10 wage rate → B* represent 130 units of labor: $1,300$10 = 130
G represents a total cost of $1,300 every input combination on the iso-cost line costs $1,300
With $10 wage rate → B* represent 130 units of labor: $1,300$10 = 130
130
Least Cost Input Choice for 100 Units of OutputLeast Cost Input Choice for 100 Units of Output
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130
Capital rental rate is $100/hr → A* represents 13 hrs of capital,
$1,300 $100 = 13
Capital rental rate is $100/hr → A* represents 13 hrs of capital,
$1,300 $100 = 1313
Least Cost Input Choice for 100 Units of OutputLeast Cost Input Choice for 100 Units of Output