View stunning SlideShares in full-screen with the new iOS app!Introducing SlideShare for AndroidExplore all your favorite topics in the SlideShare appGet the SlideShare app to Save for Later — even offline
View stunning SlideShares in full-screen with the new Android app!View stunning SlideShares in full-screen with the new iOS app!
4.
Use of Multiple Inputs
This lecture will refer to situations where
we have multiple variable inputs
Labor, machinery rental, fertilizer application,
pesticide application, etc.
4
5.
Use of Multiple Inputs
Our general single input production function
looked like the following:
Output = f(labor | capital, land, energy, etc)
Variable Input
Fixed Inputs
Lets extend this to a two input production
function
Output = f(labor, capital | land, energy, etc)
Variable Inputs
5
Fixed Inputs
6.
Use of Multiple Inputs
Output (i.e. Corn Yield)
Phos. Fert.
250
Nitrogen Fert.
6
7.
Use of Multiple Inputs
If we take a slice at a level of
250
output we obtain what is
referred as an isoquant
Similar 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
8.
Isoquant means “equal quantity”
Output is
identical along
an isoquant and
different across
isoquants
Two inputs
9.
Slope of an Isoquant
The 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
10.
Slope of an Isoquant
The slope of an isoquant is the
Capital
Q=Q*
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
K*
L*
Labor
12.
What is the slope over
range B?
MRTS here is
–1 1 = –1
13.
What is the slope over
range C?
MRTS here is
–.5 1 = –.5
14.
Slope of an Isoquant
Since the MRTS is the slope of the
isoquant, the MRTS typically changes
as you move along a particular
isoquant
MRTS becomes less negative as shown
above as you move down an isoquant
16.
Plotting the Iso-Cost Line
Lets 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
17.
Plotting the Iso-Cost Line
Capital
Firm can afford 10 hours of
capital at a rental rate of $100/hr with a
budget of $1,000
10
Firm can afford 100 hour of labor at a wage
rate of $10/hour for a budget of $1,000
Combination of Capital and Labor
costing $1,000
Referred to as the $1,000 Iso-Cost
Line
100
Labor
18.
Plotting the Iso-Cost Line
How can we define the equation of this isocost 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)
19.
Plotting the Iso-Cost Line
Capital
2,000 PK
20
Doubling of Cost
Original Cost Line
Note: Parallel cost lines
given constant prices
10
500
PK
5
Halving of Cost
Labor
50
500
PL
200
100
2000
PL
20.
Plotting the Iso-Cost Line
Capital
$1,000 Iso-Cost Line
Iso-Cost Slope = – PK
10
PL = $10
PL = $20
50
100
PL
PL = $5
200
Labor
21.
Plotting the Iso-Cost Line
Capital
20
$1,000 Iso-Cost Line
Iso-Cost Slope = – PK
PK = $50
PL
10
PK = $100
5
PK = $200
50
100
200
Labor
23.
Least Cost Input Combination
TVC are predefined Iso-Cost Lines
Capital
TVC*** > TVC** > TVC*
Q*
TVC***
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*
A
TVC**
B
TVC*
C
Labor
24.
Least Cost Decision Rule
The 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
25.
Least Cost Decision Rule
When the slope of the iso-cost = slope of the
isoquant and the iso-cost is just tangent to the
isoquant
–MPPK
MPPL
=
Isoquant
Slope
– (PK
PL)
Iso-cost
Line Slope
We can rearrange this equality to the
following
26.
Least Cost Decision Rule
MPPL
PL
MPP per dollar
spent on labor
MPPK
Pk
=
MPP per dollar
spent on capital
27.
Least Cost Decision Rule
The above decision rule holds for all variable
inputs
• For example, with 5 inputs we would have the
following
MPP1
P1
MPP1 per $ spent
on Input 1
MPP2
P2
=
MPP3
P3
MPP2 per $ spent
on Input 2
MPP4
P4
=…
…
=
MPP5
P5
MPP5 per $ spent
on=
Input 5
28.
Least Cost Input Choice for 100 Units of Output
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)
7
60
29.
Least Cost Input Choice for 100 Units of Output
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
7
60
130
30.
Least Cost Input Choice for 100 Units of Output
Capital rental rate is $100/hr
13
→ A* represents 13 hrs of
capital, $1,300 $100 = 13
130
Views
Actions
Embeds 0
Report content