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Economics of Input and Product SubstitutionPowerPoint Presentation

Economics of Input and Product Substitution

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### Economics of Inputand ProductSubstitution

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

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

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 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

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

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

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

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

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 Combinationof 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 iso-

cost 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 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 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?

As a consequence,

the firm would

desire to use more

labor and less

capital…

Page 140

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

Economics ofBusiness 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

PLR, only size 3 would

not lose money; it would break-even. Size 4 would have to down size its operations!

Page 145

Optimal input

combination

for output=20

with budget FG

Optimal input

combination

for output=10

with budget DE

Page 146

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.

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

between D and E

is –1.30, or:

-1310

Drops from

108 to 95

Increases from

30 to 40

Page 149

unattainable with

with firm’s existing

resources

Inefficient

use of firm’s

existing resources

Page 149

Accounting forProduct Prices

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 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

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

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

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

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 Maximizingcombination ofProduct 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 iso-

revenue line

Page 152

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

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…

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 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 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 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 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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