Economics of Input
and Product
Substitution
Chapter 7
Topics of Discussion
Concepts of isoquants and iso-cost line
Least-cost use of inputs
Long-run expansion of input use
Economics of business expansion and
contraction
Production possibilities frontier
Profit maximizing combination of
products
Physical Relationships
Isoquant means “equal quantity”
Output is
identical along
an isoquant
Two inputs
Page 133
Slope of an Isoquant
The slope of an isoquant is referred to as the
Marginal Rate of Technical Substitution, or
MRTS. The value of the MRTS in our example
is given by:
MRTS = Capital ÷ labor
Page 133
Slope of an Isoquant
The slope of an isoquant is referred to as the
Marginal Rate of Technical Substitution, or
MRTS. The value of the MRTS in our example
is given by:
MRTS = Capital ÷ labor
If output remains unchanged along an isoquant,
the loss in output from decreasing labor must be
identical to the gain in output from adding capital.
Page 133
MRTS
here is
-4÷1= -4
Page 133
What is the slope over
range B?
Page 133
What is the slope over
range B?
MRTS
here is
-1÷1= -1
Page 133
What is the slope over
range C?
Page 133
What is the slope over
range C?
MRTS
here is
-.5÷1= -.5
Page 133
Introducing Input Prices
Plotting the Iso-Cost Line
Capital
Firm can afford 10 units of
capital at a rental rate of $100
for a budget of $1,000
10
100
Labor
Page 136
Plotting the Iso-Cost Line
Capital
Firm can afford 10 units of
capital at a rental rate of $100
for a budget of $1,000
10
Firm can afford 100 units of
labor at a wage rate of $10 for
a budget of $1,000
100
Labor
Page 136
Slope of an Iso-cost Line
The slope of an iso-cost in our example is given by:
Slope = - (wage rate ÷ rental rate)
or the negative of the ratio of the price of the two
Inputs. See footnote 5 on page 179 for the derivation
of this slope based upon the budget constraint (hint:
solve equation below for the use of capital).
($10 × use of labor)+($100 × use of capital)=$1,000
Page 135
Original iso-cost line
Change in budget or both costs
Line AB represents
the original iso-cost
line for capital and
labor…
Change in wage rate
Change in rental rate
Page 136
Original iso-cost line
Change in budget or both costs
The iso-cost line would shift out
to line EF if the firm’s available
budget doubled (or costs fell in
half) or back to line CD if the
available budget halved (or costs
doubled.
Change in wage rate
Change in rental rate
Page 136
Original iso-cost line
Change in wage rate
Change in budget or both costs
Change in rental rate
If wage rates fell in half,
the line would shift out to
AF. The iso-cost line would
shift in to line AD if wage
rates doubled…
Page 136
Original iso-cost line
Change in wage rate
The iso-cost line would
shift out to line BE if rental
rate fell in half while the
line would shift in to line
BC if the rental rate for
capital doubled…
Change in budget or both costs
Change in rental rate
Page 136
Least Cost Combination
of Inputs
Least Cost Decision Rule
The least cost combination of two inputs (labor and
capital in our example) occurs where the slope of the
iso-cost list is tangent to the isoquant:
MPPLABOR ÷ MPPCAPITAL = -(wage rate ÷ rental rate)
Slope of an
isoquant
Slope of isocost line Page 139
Least Cost Decision Rule
The least cost combination of labor and capital in
out example also occurs where:
MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate
MPP per dollar
spent on labor
=
MPP per dollar
spent on capital
Page 139
Least Cost Decision Rule
This
decision
rule holds
a larger
The
least
cost combination
of labor for
and capital
in
out
example also
occurs where:
number
of inputs
as well…
MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate
MPP per dollar
spent on labor
=
MPP per dollar
spent on capital
Page 139
Least Cost Combination
of Inputs to Produce a
Specific Level of Output
Least Cost Input Choice for 100 Units
Iso-cost line for $1,000.
Its slope reflects price of
labor and capital.
Page 138
Least Cost Input Choice for 100 Units
We can determine
this graphically by
observing where
these two curves
are tangent….
Page 138
Least Cost Input Choice for 100 Units
We can shift the original
iso-cost line from AB out
in a parallel fashion to
A*B* (which leaves prices
unchanged) which just
touches the isoquant at G
Page 138
Least Cost Input Choice for 100 Units
At the point of tangency, we know that:
slope of isoquant = slope of iso-cost line, or…
MPPLABOR ÷ MPPCAPITAL = - (wage rate ÷ rental rate)
Page 138
Least Cost Input Choice for 100 Units
At the point of tangency, therefore, the MPP per
dollar spent on labor is equal to the MPP per
dollar spent on capital!!! See equation (8.5) on
page 181, which is analogous to equation (4.2)
back on page 76 for consumers.
Page 138
Least Cost Input Choice for 100 Units
This therefore represents
the cheapest combination of
capital and labor to produce
100 units of output…
Page 138
Least Cost Input Choice for 100 Units
If I told you the value of C1
and L1 and asked you for
the value of A* and B*,
how would you find them?
Page 138
Least Cost Input Choice for 100 Units
If I told you that point G
represents 7 units of capital
and 60 units of labor, and
that the wage rate is $10
and the rental rate is $100,
then at point G we must be
spending $1,300, or:
7
$100×7+$10×60=$1,300
60
Page 138
Least Cost Input Choice for 100 Units
If point G represents a total
cost of $1,300, we know that
every point on this iso-cost
line also represents $1,300.
If the wage rate is $10, then
point B* must represent 130
units of labor, or:
$1,300$10 = 130
7
60
130
Page 138
Least Cost Input Choice for 100 Units
And the rental rate is $100,
then point A* must
represents 13 units of
capital, or:
13
$1,300 $100 = 13
7
60
130
Page 138
What Happens if the
Price of an Input
Changes?
What Happens if Wage Rate Declines?
Assume the initial
wage rate and cost
of capital results in
the iso-cost line AB
Page 140
What Happens if Wage Rate Declines?
Wage rate decline
means that the firm
can now afford B*
instead of B…
Page 140
What Happens if Wage Rate Declines?
The new point of tangency
occurs at H rather than G.
Page 140
What Happens if Wage Rate Declines?
As a consequence,
the firm would
desire to use more
labor and less
capital…
Page 140
Least Cost Combination
of Inputs and Output
for a Specific Budget
What Inputs to Use for a Specific Budget?
M
An iso-cost line for
a specific budget
N
Labor
Page 141
What Inputs to Use for a Specific Budget?
A set of isoquants
for different levels
of output…
Page 141
What Inputs to Use for a Specific Budget?
Firm can afford to
produce only 75 units
of output using C3 units
of capital and L3 units
of labor
Page 141
What Inputs to Use for a Specific Budget?
The firm’s budget
is not large enough
to operate at 100
or 125 units…
Page 141
What Inputs to Use for a Specific Budget?
Firm is not spending
available budget here…
Page 141
Economics of
Business Expansion
The Planning Curve
The long run average cost (LAC) curve reflects points
of tangency with a series of short run average total cost
(SAC) curves. The point on the LAC where the following
holds is the long run equilibrium position (QLR) of the
firm:
SAC = LAC = PLR
where MC represents marginal cost and PLR represents
the long run price, respectively.
Page 145
What can we say about the four
firms in this graph?
Page 145
Size 1 would lose
money at price P
Page 145
Firm size 2, 3 and 4
would earn a profit
at price P….
Q3
Page 145
Firm #2’s profit would
be the area shown
below…
Q3
Page 145
Firm #3’s profit would
be the area shown
below…
Q3
Page 145
Firm #4’s profit would
be the area shown
below…
Q3
Page 145
If price were to fall to
PLR, only size 3 would
not lose money; it
would break-even. Size
4 would have to down
size its operations!
Page 145
How to Expand Firm’s Capacity
Optimal input
combination
for output=10
Page 146
How to Expand Firm’s Capacity
Two options:
1. Point B ?
Page 146
How to Expand Firm’s Capacity
Two options:
1. Point B?
2. Point C?
Page 146
Expanding Firm’s Capacity
Optimal input
combination
for output=20
with budget FG
Optimal input
combination
for output=10
with budget DE
Page 146
Expanding Firm’s Capacity
This combination
costs more to
produce 20 units
of output since
budget HI exceeds
budget FG
Page 146
Production Possibilities
The goal is to find that combination of
products that maximizes revenue for
the maximum technical efficiency
on the production
possibilities frontier.
Shows the substitution
between two products
given the most efficient
use of firm’s resources
Page 149
Slope of the PPF
The slope of the production possibilities curve
is referred to as the Marginal Rate of
Product Transformation, or MRPT. The value
of the MRPT in our example is given by:
MRPT =  canned fruit ÷ canned vegetables
Page 148
Slope over range
between D and E
is –1.30, or:
-1310
Drops from
108 to 95
Increases from
30 to 40
Page 149
95,000
- 108,000
-13,000
÷
40,000
- 30,000
10,000
=
- 1.30
Page 148
Inefficient
use of firm’s
resources
Page 149
Level of output
unattainable with
with firm’s existing
resources
Inefficient
use of firm’s
existing
resources
Page 149
Accounting for
Product Prices
Plotting the Iso-Revenue Line
Canned
fruit
30,000 cases of canned fruit
required at price of $33.33/case
to achieve A TARGET revenue
of $1 million
30,000
40,000
Canned
vegetables
Page 150
Plotting the Iso-Revenue Line
Canned
fruit
30,000 cases of canned fruit
required at price of $33.33/case
to achieve revenue of $1 million
30,000
40,000 cases of canned vegetables
required at price of $25.00/case
to achieve revenue of $1 million
40,000
Canned
vegetables
Page 150
Original iso-revenue line
Changes in income or both prices
Line AB is the original
iso-revenue line, indicating
the number of cases needed
to reach a specific sales
target.
Change in price of fruit
Change in price of vegetables
Page 150
The iso-revenue line would
Original iso-revenue line
shift out to line EF if the
revenue target doubled (or
prices fell in half) while the
line would shift in to line
CD if revenue targets fell in
half or prices doubled.
Change in price of fruit
Changes in income or both prices
Change in price of vegetables
Page 150
Original iso-revenue line
Change in price of fruit
Changes in income or both prices
The iso-revenue line would
Change in price of vegetables
shift out to line BC is the
price of fruit fell in half
but shift in to line BD if
the price of fruit doubled
Page 150
Original iso-revenue line
The iso-revenue
line would
Change in price of fruit
shift out to line AD if the
price of vegetables fell in half
but shift in to line AC is the
price of fruit doubled.
Changes in income or both prices
Change in price of vegetables
Page 150
Profit Maximizing
combination of
Product Prices
Combination of Products
The profit maximizing combination of two products
is found where the slope of the production possibilities
frontier (PPF) is equal to the slope of the iso-revenue
Curve, or where:
Canned fruit
Price of vegetables
= –
Canned vegetables
Price of fruit
Slope of an
PPF curve
Slope of isorevenue linePage 152
Assume Line AB represents
revenue for $1 million.
Page 153
We want to find the
profit maximizing
combination to “can”
given the current
prices of canned fruit
and vegetables.
Page 153
Canned fruit
Canned vegetables
= –
Price of vegetables
Price of fruit
Shifting line AB out in
a parallel fashion
holds both prices
constant at their
current level
Page 153
125,000
cases of
fruit
18,000
cases of
vegetables
MRPT
equals
-0.75
Page 152
Price ratio = -($25.00 ÷ $33.33) = - 0.75
125,000
cases of
fruit
18,000
cases of
vegetables
MRPT
equals
-0.75
Page 152
Price ratio = -($25.00 ÷ $33.33) = - 0.75
125,000
cases of
fruit
18,000
cases of
vegetables
Canned fruit
Canned vegetables
= –
MRPT
equals
-0.75
Price of vegetables
Price of fruit
Page 152
Doing the Math…
Let’s assume the price of a case of canned fruit is
$33.33 while the price of a case of canned
vegetables is $25.00. If point M represents 125,000
cases of fruit and 18,000 cases of vegetables, then
total revenue at point M is:
Revenue = 125,000 × $33.33 + 18,000 × $25.00
= $4,166,250 + $450,000 = $4,616,250
Doing the Math…
At these same prices, if we instead produce
108,000 cases of fruit and and 30,000 cases of
vegetables, then total revenue would fall to:
Revenue = 108,000 × $33.33 + 30,000 × $25.00
= $3,599,640 + $750,000 = $4,349,640
which is $266,610 less than the $4,616,250 earned
at point M.
Effects of a Change
in the Price of
One Product
If the price of canned fruit
fell in half, the firm must
sell twice as many cases of
canned fruit to earn $1
million if it focused solely
on fruit production.
Page 153
This gives us a new isorevenue curve… line CB.
Page 153
To see the effects of this
price change, we can shift
the new iso-revenue curve
out to the point of
tangency with the PPF
curve….
Page 153
Shifting the new isorevenue curve in a
parallel fashion out to a
point of tangency with
the PPF curve, we get a
new combination of
products required to
maximize profit.
Page 153
The firm would shift from
point M on the PPF to
point N as a result of the
decline in the price of fruit.
That is, to maximize profit,
the firm would cut back its
production of canned fruit
and produce more canned
vegetables.
Page 153
Summary #1
 Concepts of iso-cost line and isoquants
 Marginal rate of technical substitution
(MRTS)
 Least cost combination of inputs for a
specific output level
 Effects of change in input price
 Level of output and combination of
inputs for a specific budget
 Key decision rule …seek point where
MRTS = ratio of input prices, or
where MPP per dollar spent on inputs
are equal
Summary #2
 Concepts of iso-revenue line and the
production possibilities frontier
 Marginal rate of product
transformation (MRPT)
 Concept of profit maximizing
combination of products
 Effects of change in product price
 Key decision rule – maximize profits
where MRPT equals the ratio of the
product prices
Chapter 8 focuses on market
equilibrium conditions under
perfect competition….