economics of input and product substitution chapter 7
TRANSCRIPT
Economics of Inputand ProductSubstitution
Chapter 7
Topics of DiscussionConcept of isoquant curveConcept of an iso-cost lineLeast-cost use of inputs Long-run expansion path of input useEconomics of business expansion and
contractionProduction possibilities frontierProfit maximizing combination of
products
2
Physical Relationships
3
Use of Multiple InputsIn Ch. 6 we finished by examining profit
maximizing use of a single input
Lets extend this model to where we have multiple variable inputsLabor, machinery rental, fertilizer
application, pesticide application, energy use, etc.
4
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 InputFixed Inputs
Fixed InputsVariable Inputs
5
Use of Multiple Inputs
Output (i.e. Corn Yield)
250
Nitrogen Fert.
Phos. Fert.
6
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 the same level of output
There is one isoquant for each output level
7
250
Page 107
Isoquant means “equal quantity”Isoquant means “equal quantity”
Two inputs
8
Output isidentical alongan isoquant and different across isoquants
Output isidentical alongan isoquant and different across isoquants
Slope of an IsoquantThe slope of an isoquant is referred to
as the Marginal Rate of Technical Substitution (MRTS) Similar in concept to the MRS we talked
about in consumer theory 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
Pages 106-1079
Slope of an Isoquant
The 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
Pages 106-107
Labor
Capital
Q=Q*
L*
K*
10
A
Slope of an isoquant =Slope of the linetangent at a point
Page 107
MRTSKL here is– 4 ÷ 1 = – 4
MRTSKL here is– 4 ÷ 1 = – 4
11
MRTSKL = ∆K/∆L
Page 107
What is the slope overrange B?
MRTS here is–1 ÷ 1 = –1
MRTS here is–1 ÷ 1 = –1
12
Page 107
What is the slope overrange C?
What is the slope overrange C?
MRTS here is–.5 ÷ 1 = –.5
MRTS here is–.5 ÷ 1 = –.5
13
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
Pages 106-10714
Slope of an IsoquantLets derive the slope of the isoquant
like we did for the indifference curve under consumer theory
∆Q = 0 along an isoquant →
Pages 106-10715
ΔQ ΔQQ f L,K ΔQ ΔL + ΔK
ΔL ΔK
ΔQ ΔQ0 ΔL + ΔK
ΔL ΔKΔQ ΔQ ΔK ΔQ ΔQ
ΔK ΔLΔL ΔKΔK ΔL ΔL
Slope of an Isoquant
Pages 106-10716
LKL
K
MPPΔK ΔQ ΔQMRTS
ΔL ΔKΔL MPP
Labor
Capital
Q=Q*
L*
K*
MRTSKL = –MPPL*/MPPK*
Slope of an Isoquant
Pages 106-10717
Labor
Capital
Q = Q*
L*
K*A
BK**
L**
What is the impact on theMRTS as input combinationchanges from A to B? Why?
Introducing Input Prices
18
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 Similar to the Budget Line in consumer
theory Referred to as the Iso-Cost Line when we
are talking about production
Pages 106-10719
Plotting the Iso-Cost Line
Page 109
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
Combination of Capital and Labor costing $1,000 Referred to as the
$1,000 Iso-Cost Line20
Plotting the Iso-Cost Line
Page 109
How 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 prices of the two inputs)
21
Plotting the Iso-Cost Line
Page 109
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 ÷ PL22
Plotting the Iso-Cost Line
Page 109
Labor
Capital
10
10050 200
$1,000 Iso-Cost Line
Iso-Cost Slope = – PL ÷ PK
PL = $5PL = $10
PL = $20
23
Plotting the Iso-Cost Line
Page 109
Labor
Capital
10
10050 200
$1,000 Iso-Cost Line
Iso-Cost Slope = – PL ÷ PK
20
5
PK = $200
PK = $100
PK = $50
24
Least Cost Combinationof Inputs
25
Least Cost Input Combination
Page 109
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*
26
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
Page 11127
Least Cost Decision RuleWhen the slope of the iso-cost = slope of the
isoquant and the iso-cost is just tangent to the isoquant
–MPPL ÷ MPPK = – (PL ÷ PK)
We can rearrange this equality to the following
Page 111
Isoquant Slope
Isoquant Slope
Iso-cost Line Slope
Iso-cost Line Slope
28
Least Cost Decision Rule
Page 111
=
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 capital
MPP per dollar spent on capital
29
Least Cost Decision Rule
Page 111
The above decision rule holds for all variable inputs• For example, with 5 inputs we would have the
following
3 51 2 4
1 2 3 4 5
MPP MPPMPP MPP MPP
P P P P P
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=
30
Page 111
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)
31
Page 111
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
32
Page 111
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
33
What Happens if the Price of an Input
Changes?
34
Page 112
What Happens if Wage Rate Declines?What Happens if Wage Rate Declines?
Assume initial wage rate and cost of capital result in iso-cost line AB
Assume initial wage rate and cost of capital result in iso-cost line AB
35
Page 112
What Happens if Wage Rate Declines?What Happens if Wage Rate Declines?
Wage rate ↓ means the firm can now afford B* instead of B amount of labor if all costs allocated to labor
Wage rate ↓ means the firm can now afford B* instead of B amount of labor if all costs allocated to labor
36
Page 112
What Happens if Wage Rate Declines?What Happens if Wage Rate Declines?
The new point of tangencyoccurs at H rather than G
The new point of tangencyoccurs at H rather than G
The firm would desire to use more labor and less capital as labor became relatively less expensive
The firm would desire to use more labor and less capital as labor became relatively less expensive
37
What is the minimum cost ofproducing 100 units of output?
Least Cost Combination of Inputs and Outputfor a Specific Budget
38
What Inputs to Use for a Specific Budget?What Inputs to Use for a Specific Budget?
M
N
Labor
Capital
An iso-cost line fora specific budget
An iso-cost line fora specific budget
Page 11339
Page 113
What Inputs to Use for a Specific Budget?What Inputs to Use for a Specific Budget?
A set of isoquants for different output levels
A set of isoquants for different output levels
40
Page 113
What Inputs to Use for a Specific Budget?What Inputs to Use for a Specific Budget?
Firm can afford to produce 75 units of output using C3 units of capital and L3 units of labor
Firm can afford to produce 75 units of output using C3 units of capital and L3 units of labor
41
Page 113
What Inputs to Use for a Specific Budget?What Inputs to Use for a Specific Budget?
The firm’s budget not large enough to produce more than 75 units
The firm’s budget not large enough to produce more than 75 units
42
Page 113
On any point on this isoquant thefirm is not spending available budget here
On any point on this isoquant thefirm is not spending available budget here
What Inputs to Use for a Specific Budget?What Inputs to Use for a Specific Budget?
43
Economics ofBusiness Expansion
44
Long-Run Input Use
During the short run some costs are fixed and other costs are variable
As you increase the planning horizon, more costs become variableEventually over a long-enough time
period all costs are variable
Page 11445
Long-Run Input Use
Page 114
SACA
SACB
SACC
Fixed costs in short run ensure the U-Shaped SAC curves 3 different size firmsA is the smallest, C the
largest
A B CA*A firm wanting to minimize costOperate at size A if production
is in 0A rangeOperate at size B if production
is in AB range
Cost/unit
Output
46
The Planning Curve
The long run average cost (LAC) curvePoints of tangency with a series of short run average
total cost (SAC) curvesTangency not usually at minimum of each SAC curve
Page 114
SACA
SACB
SACC
Output
Tangency Points
LAC
LAC sometimes referred to as Long Run Planning Curve
Cos
t/u
nit
47
Economies of SizeTypical LAC curve
What causes the LAC curve to decline, become relatively flat and then increase?Due to what economists refer to as
economies of size Page 114
Output
Cos
t/u
nit
48
Economies of SizeConstant returns to size
↑(↓) in output is proportional to the ↑(↓) in input use
i.e., double input use → doubling outputDecreasing returns to size
↑ (↓)in output is less than proportional to the ↑(↓) in input use
i.e., double input use → less than double output Increasing returns to size
↑ (↓)in output is more than proportional to the ↑(↓) in input use
i.e., double input use → more than double output Page 11449
Economies of Size
Decreasing returns to size → Firm’s LAC curve are increasing as firm is expanded
Increasing returns to size → Firm’s LAC curve are decreasing as firm is expanded
Page 11550
Economies of SizeReasons for increasing returns of size
Dimensional in nature Double cheese vat size Eventually the gains are reduced
Indivisibility of inputs Equipment available in fixed sizes As firm gets larger can use larger
more efficient equipment Specialization of effort
Labor as well as equipment Volume discounts on large purchases
on productive inputsPage 11651
Economies of SizeDecreasing returns of size
LRC is ↑ → the LRC is tangent to the collection of SAC curves to the right of their minimum
Page 116
SACA
SACB
SACC
Output
Cos
t/u
nit SACD
52
Economies of SizeThe minimum point on the LRC is the
only point that is tangent to the minimum of a particular SAC
Page 116
SAC*
Output
Cos
t/u
nit
LRC
Q*
C*
C* is minimum point on SAC* and on LRC
Only plant size and quantity output where this occurs
53
The Planning Curve
Page 117
SAC1
SAC2
SAC3
Cos
t/u
nit
Output
In the long run, the firm has time to expand or contract the size of their operation Each SAC curve for each size plant has associated
short run marginal cost curve (MC) SACi = SMCi when SACi is at its minimum
SAC4SMC4
SMC3
SMC2
SMC1
54
The Planning Curve
Page 117
SAC1
SAC2
SAC3
Output
SAC4SMC4
SMC3
SMC2
SMC1
Assume the market price for the product is P Assume the firm is of size i The firm maximizes profit by producing where P=MCi
What can you say about the performance of these 4 firms?
P
55
The Planning Curve
Page 117
SAC1
Output
SMC1
Firm 1 would lose money with output price = P Produce where P = SMC1 → Q* At Q*, P < SAC1
P
Q*
56
The Planning Curve
Page 117
SAC2
SAC3
Output
SAC4SMC4
SMC3SMC2
Firms of sizes 2, 3 and 4 would make a positive profit when output price is PP > SAC at profit maximizing levelP-SAC = per unit profit
P
Q2* Q3* Q4*
Per unit profit
57
The Planning Curve
Page 117
SAC2
SAC3
Output
SAC4SMC4
SMC3SMC2
Firm 2’s total profit Per unit profit x Q2*
P
Q2* Q3* Q4*
Firm 2’s Total Profit
58
The Planning Curve
Page 117
SAC2
SAC3
Output
SAC4SMC4
SMC3SMC2
Firm 3’s total profit Per unit profit x Q3*
P
Q2* Q3* Q4*
Firm 3’s Total Profit
59
The Planning Curve
Page 117
SAC2
SAC3
Output
SAC4SMC4
SMC3SMC2
Firm 4’s total profit Per unit profit x Q4*
P
Q2* Q3* Q4*
60
Firm 4’s Total Profit
The Planning Curve
Page 117
SAC1
SAC2
SAC3
Output
SAC4SMC4
SMC3
SMC2
SMC1
Assume the product price falls to PLR
Only Firm 3 will not lose money It only breaks even as PLR=SAC3 (=MC3) For other firms, the price is less than any point on
the other SAC curves Firm 4 would have to reduce its size
P
PLR
61
Page 118
Optimal inputcombinationfor output=10
Optimal inputcombinationfor output=10
How to Expand Firm’s CapacityHow to Expand Firm’s Capacity
62
Page 118
Two options: 1. Point B ?
Two options: 1. Point B ?
How Can the Firm Expand Its Capacity?
63
Page 118
How Can the Firm Expand Its Capacity?
Two options: 1. Point B?2. Point C?
Two options: 1. Point B?2. Point C?
64
Page 118
Optimal inputcombinationfor output=10with budget DE
Optimal inputcombinationfor output=10with budget DE
Optimal input combination for output = 20 with budget represented by FG
Optimal input combination for output = 20 with budget represented by FG
How Can the Firm Expand Its Capacity?
65
Page 118
How Can the Firm Expand Its Capacity?
This combination of inuts costs more to produce 20 units of output since budget HI exceeds budget FG
This combination of inuts costs more to produce 20 units of output since budget HI exceeds budget FG
66
Producing More than One Output
Most agricultural operations produce more than one type of outputFor example a grain farm in Southern
Wisconsin Produces wheat, oats, barley and some
alfalfa hay Raises some cattle on the side
Production of these outputs requires a set of inputsEach output is competing for the use of
limited inputs (e.g. labor, tractor time, etc)67
Producing More than One Output
Lets first address the production decision from a technical perspective Similar to our examination of production
of a single output via the isoquant
68
For a single output we defined an isoquant as the collection input combinations that has the same maximum output represented by that isoquant
Lets now define the collection of output combinations that could be produced with a fixed supply of inputs
Producing More than One Output
69
The collection of outputs technically feasible with a fixed amount of inputs is referred to as the production possibilities set
The boundary of that set is referred to as the production possibilities frontier (PPF)
Producing More than One Output
70
Output combinations within the frontier (boundary) are technically possible but inefficient Can produce more of at least one of the
outputs Again remember that the amount of
inputs available for production is assumed fixed
Producing More than One Output
71
Output combinations on the frontier are technically efficient Can not produce more of at least one
output unless less is produced of at least one of the other outputs
Remember the assumption: The amount of inputs available for production is fixed
Producing More than One Output
72
Page 120
Producing More than One Output
73
Page 120
Points A → J are on the PPF Note axis labels What happens when firm changes
output mix from B to E?
128
10
95
74
Page 120
Level of outputunattainable withwith firm’s existingresources
Level of outputunattainable withwith firm’s existingresources
Inefficient use of firm’s existing resources
Inefficient use of firm’s existing resources
K*
PPF represents maximum attainable products given fixed amount of inputs
75
Slope of the PPF
The slope of the production possibilities curve is referred to as the Marginal Rate of Product Transformation (MRPT)In the above example, the MRPT is given by:
In general we have:
What sign will the MRPT possess?
Page 119
Canned FruitMRPT
Canned Veg.
2
1
YMRPT
Y
Y1
Y2
PPF
76
Page 120
Using slope definitionMRPT = ∆Y2 ÷ ∆Y1
Slope between D and E is –1.30 = – 13 10
Using slope definitionMRPT = ∆Y2 ÷ ∆Y1
Slope between D and E is –1.30 = – 13 10
↑ from30 to 40
↑ from30 to 40
↓ from 108 to 95
↓ from 108 to 95
77
Page 148
95,000- 108,000 -13,000
40,000- 30,000 10,000
÷ - 1.30 =
78
Accounting forProduct Prices
79
Economic Efficiency and Multiple Outputs
Page 122
Up to this point we have only considered technical efficiency, i.e., the PPF
Lets now introduce prices (both output and input) to the modelEnables us to discuss the concept of
economic efficiency in the context of multiple outputs
80
Economic Efficiency and Multiple Outputs
Page 122
Lets start with introducing output prices Assume we have two outputs: canned fruits
(CF) and canned vegetables (CV) PCF and PCV = the prices received for CV
and CV, respectively
What would be the combinations of CF and CV production that would generate $1 million in total revenue (TR)? Collection of these combinations generates
an iso-revenue line
81
Plotting the Iso-Revenue Line
Cases of CF
Cases ofCV
PCF = $33.33/case → 30,000 cases of CF generates revenue of $1 million
PCF = $33.33/case → 30,000 cases of CF generates revenue of $1 million
Page 122
30,000
40,000
Assume PCF=$33.33/case, PCV=$25.00/case
PCV = $25.00/case → 40,000 cases of CV generates revenue of $1 million
PCV = $25.00/case → 40,000 cases of CV generates revenue of $1 million
$1 Mil Iso-Revenue Line$1 Mil Iso-Revenue Line82
Plotting the Iso-Revenue Line
Page 122
Y2
Y1
What is the equation that can be used to identify the R* iso-revenue line?We have 2 products (Y1, Y2) and
associated product prices (PY1,PY2)The R* iso-revenue line is defined via:
R* = PY1Y1 + PY2Y2
→ PY2Y2 = R* – PY1Y1
→ Y2 = (R*÷PY2) – (PY1÷PY2)Y1 General equation for the
R* iso-revenue line
*
Y2
R
P
*
Y1
R
P Y1
Y2
PSlope
P83
Plotting the Iso-Revenue Line
Line AB is original iso-revenue linePCF= $33.33/case, PCV= $25.00/case Combination of outputs that generate the
same amount of revenue
Line AB is original iso-revenue linePCF= $33.33/case, PCV= $25.00/case Combination of outputs that generate the
same amount of revenue
Slope = $25.00 ÷ $33.33 = 0.75
Page 122
CV
CF
PSlope
P
84
Page 122
Plotting the Iso-Revenue LineIso-revenue line would shift out to EF
If the revenue target doubled orOutput prices decrease by 50%
The line would shift in to CD If revenue targets are halved orOutput prices are doubled
Iso-revenue line would shift out to EFIf the revenue target doubled orOutput prices decrease by 50%
The line would shift in to CD If revenue targets are halved orOutput prices are doubled
Note: Slopedoes not change
CV
CF
PSlope
P
85
Page 122
Iso-revenue line would rotate:Out to line BC if PCF ↓ by 50%In to line BD if PCF doubled
Iso-revenue line would rotate:Out to line BC if PCF ↓ by 50%In to line BD if PCF doubled
Plotting the Iso-Revenue Line
Note: Slope is changing
CV
CF
PSlope
P
86
Page 122
Plotting the Iso-Revenue Line
Iso-revenue line would rotate Out to line AD if PCV ↓ by 50% In to line AC if PCV doubled
Iso-revenue line would rotate Out to line AD if PCV ↓ by 50% In to line AC if PCV doubled
Note: Slope is changing
CV
CF
PSlope
P
87
Determining the Profit Maximizing
Combination ofProducts
88
Profit MaximizingCombination of Products
In the cost minimization problem where we produce one productThe input combination that minimizes the cost
of producing a given output level is where The slope of the isocost curve equals the
slope of the isoquant → the isocost curve is just tangent to the
isoquantLets develop a similar decision rule but
this time withMultiple outputsFixed supply of inputs
Page 12489
Page 124
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
)
What is the profit (π) maximizing combination of fruit and veg. to can given current PCF and PCV values?
Remember we have a fixed amount of inputs available Determines location of the PPF → All costs are fixed → Maximizing revenue will
maximize profit
90
Page 124
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
) Lets place on this PPF the $1 Mil. iso-revenue line, AB
Profit MaximizingCombination of Products
A
B
91
Page 124
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
)Profit Maximizing
Combination of Products
The further from the origin the iso-revenue line, the greater the level of revenueR*
1<R*2<R*
3
Why are the iso-revenue lines parallel in this model?
R*2
R*3R*
1
92
Page 124
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
)Profit Maximizing
Combination of Products
R*2
R*3R*
1
To find the maximum revenue attainable given available inputs Lets find the iso-revenue line that is
just tangent to the PPF At the tangency point it is physically
possible to produce that combination of outputs given our fixed input base
93
Page 124
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
)Profit Maximizing
Combination of Products
Shifting line AB out in a parallel fashion holds both prices constant
Shifting line AB out in a parallel fashion holds both prices constant
CV
CF
CF CV
CV CF
PAt M MRPT =
P
Y P=
Y P
Slope of an PPF curve
Slope of an PPF curve
Slope of theIso-cost line
Slope of theIso-cost line
M
94
In summary:The profit maximizing combination of two products is found where the slope of the PPF is equal to the slope of the iso-revenue line and on the highest iso revenue curve possible given the limited inputs
Page 124
Profit MaximizingCombination of Products
95
MRPTequals-0.75
MRPTequals-0.75
125,000 cases of
fruit
125,000 cases of
fruit
Price ratio = -($25.00 ÷ $33.33) = - 0.75Price ratio = -($25.00 ÷ $33.33) = - 0.75
Profit MaximizingCombination of Products
Page 120
18,000 cases of
veg.
18,000 cases of
veg.
96
Doing the Math…Let’s assume PCF is $33.33 and PCV 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
97
Doing the Math…At these same prices, if we instead produce
108,000 cases of fruit and and 30,000 cases of vegetables→ total revenue would fall
Revenue = (108,000 × $33.33) + (30,000 × $25.00) = $3,599,640 + $750,000 = $4,349,640
• $266,610 less than $4,616,250 earned at M
98
Effects of a Changein the Price of One Product
99
Page 125
Profit MaximizingCombination of Products
PCF reduced by 50% Firm must sell twice as many
cases of CF to earn a particular level of revenue
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
)
A
B
This gives us a new iso-revenue curve… line CB
This gives us a new iso-revenue curve… line CB
C
M
100
Page 125
Profit MaximizingCombination of Products
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
)
A
B
C
MTo determine the effects of this
price change on the product mix Shift out the new iso-revenue
curve Until it is just tangent to the PPF
curve
101
Page 125
Profit MaximizingCombination of Products
20
40
60
80
100
120
140
20 40 60 80 100 120 140
Canned Veg. (1,000 Cases)
Can
ned
Fru
it (
1,00
0 C
ases
)
A
B
C
M
N
As a result of a ↓ in PCF
→Firm would shift from M to N
To maximize profit → firm would ↓ production of CF and ↑ production of CV
102
Summary #1Concepts of iso-cost line and isoquantsMarginal rate of technical substitution
(MRTS)Least cost combination of inputs for a specific
output levelEffects of change in input priceLevel of output and combination of inputs for
a specific budgetKey decision rule …seek point where MRTS =
ratio of input prices, or where MPP per dollar spent on inputs are equal
103
Summary #2Concepts of iso-revenue line and the
production possibilities frontierMarginal rate of product transformation
(MRPT)Concept of profit maximizing
combination of productsEffects of change in product priceKey decision rule – maximize profits
where MRPT -ratio of the product prices
104
Chapter 8 focuses on market equilibrium conditions under perfect competition….
105