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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

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Economics of input and product substitution

Economics of Inputand ProductSubstitution

Chapter 7


Topics of discussion
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



Isoquant means “equal quantity”

Output is

identical along

an isoquant

Two inputs

Page 133


Slope of an isoquant
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 isoquant1
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



Plotting the iso cost line
Plotting the Iso-Cost Line

Firm can afford 10 units of

capital at a rental rate of $100

for a budget of $1,000

Capital

10

Labor

100

Page 136


Plotting the iso cost line1
Plotting the Iso-Cost Line

Firm can afford 10 units of

capital at a rental rate of $100

for a budget of $1,000

Capital

10

Firm can afford 100 units of

labor at a wage rate of $10 for

a budget of $1,000

Labor

100

Page 136


Slope of an iso cost line
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 budget or both costs

Change in wage rate

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 budget or both costs

Change in wage rate

Change in rental 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…

Page 136



Least cost decision rule
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 iso-

cost line

Page 139


Least cost decision rule1
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 rule2
Least Cost Decision Rule

This decision rule holds for a larger number of inputs as well…

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 combination of inputs to produce a specific level of output
Least Cost Combination of Inputs to Produce aSpecific 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:

$100×7+$10×60=$1,300

7

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

130

60

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:

$1,300 $100 = 13

13

7

130

60

Page 138



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
Least Cost Combination of Inputs and Outputfor a Specific Budget


What Inputs to Use for a Specific Budget?

M

An iso-cost line for

a specific budget

Capital

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
Economics ofBusiness Expansion


The planning curve
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





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
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
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
Accounting forProduct Prices


Plotting the iso revenue line
Plotting the Iso-Revenue Line

30,000 cases of canned fruit

required at price of $33.33/case

to achieve A TARGET revenue

of $1 million

Canned

fruit

30,000

Canned

vegetables

40,000

Page 150


Plotting the iso revenue line1
Plotting the Iso-Revenue Line

30,000 cases of canned fruit

required at price of $33.33/case

to achieve revenue of $1 million

Canned

fruit

30,000

40,000 cases of canned vegetables

required at price of $25.00/case

to achieve revenue of $1 million

Canned

vegetables

40,000

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 vegetables

Change in price of fruit

Page 150


The iso-revenue line would

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.

Original iso-revenue line

Changes in income or both prices

Change in price of vegetables

Change in price of fruit

Page 150


Original iso-revenue line

Changes in income or both prices

The iso-revenue line would

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

Change in price of vegetables

Change in price of fruit

Page 150


Original iso-revenue line

Changes in income or both prices

The iso-revenue line would

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.

Change in price of vegetables

Change in price of fruit

Page 150


Profit maximizing combination of product prices
Profit Maximizingcombination ofProduct Prices


Combination of products
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 iso-

revenue line

Page 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 Price of vegetables

Canned 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

MRPT

equals

-0.75

Canned fruit Price of vegetables

Canned vegetables Price of fruit

= –

Page 152


Doing the math
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 math1
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
Effects of a Changein 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 iso-revenue curve… line CB. sell twice as many cases of

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 iso-revenue 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
Summary #1 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.

  • 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
Summary #2 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.

  • 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
Chapter 8 focuses on market equilibrium conditions under 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.perfect competition….


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