Agri 2312 chapter 7 economics of input and product substitution

Introduction to Agricultural Economics, 5th edPenson, Capps, Rosson, and Woodward

© 2010 Pearson Higher Education,Upper Saddle River, NJ 07458. • All Rights

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Economics of Inputand ProductSubstitution

Chapter 7



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Topics of DiscussionConcepts of isoquants and iso-cost lineLeast-cost use of inputs Long-run expansion of input useEconomics of business expansion and

contractionProduction possibilities frontierProfit maximizing combination of

products



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Physical Relationships



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Page 107

Output isidentical alongan isoquant

Output isidentical alongan isoquant

Isoquant means “equal quantity”Isoquant means “equal quantity”

Two inputsTwo inputs



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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

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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 beidentical to the gain in output from adding capital.

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Page 107

MRTShere is-4÷1= -4




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What is the slope overrange B?




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What is the slope overrange C?




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MRTShere is-.5÷1= -.5

MRTShere is-.5÷1= -.5



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Introducing Input Prices



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Plotting the Iso-Cost Line

Capital

Labor

Firm can afford 10 units ofcapital at a rental rate of $100for a budget of $1,000


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10

100



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Plotting the Iso-Cost Line

Capital

Labor

Firm can afford 100 units oflabor at a wage rate of $10 fora budget of $1,000

Firm can afford 100 units oflabor at a wage rate of $10 fora budget of $1,000

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10

100





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Slope of an Iso-cost LineThe 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 twoInputs. 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

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Original iso-cost line Change in budget or both costs

Change in wage rate Change in rental rate

Page 109

Line AB representsthe original iso-costline for capital andlabor…

Line AB representsthe original iso-costline for capital andlabor…



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Page 109

The iso-cost line would shift outto line EF if the firm’s availablebudget doubled (or costs fell inhalf) or back to line CD if theavailable budget halved (or costsdoubled.

The iso-cost line would shift outto line EF if the firm’s availablebudget doubled (or costs fell inhalf) or back to line CD if theavailable budget halved (or costsdoubled.



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Page 109

If wage rates doubled the linewould shift out to AF whilethe iso-cost line would shiftin to line AD if wage ratesdoubled…

If wage rates doubled the linewould shift out to AF whilethe iso-cost line would shiftin to line AD if wage ratesdoubled…



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Page 109

The iso-cost line wouldshift out to line BE if rentalrate fell in half while theline would shift in to lineBC if the rental rate forcapital doubled…

The iso-cost line wouldshift out to line BE if rentalrate fell in half while theline would shift in to lineBC if the rental rate forcapital doubled…



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Least Cost Combinationof Inputs



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Least Cost Decision RuleThe 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)

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Slope of an isoquant

Slope of an isoquant

Slope of iso- cost line

Slope of iso- cost line



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Least Cost Decision RuleThe least cost combination of labor and capital in out example also occurs where:

MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate

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MPP per dollar spent on labor


MPP per dollar spent on capitalMPP per dollar spent on capital=



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Least Cost Decision RuleThe least cost combination of labor and capital in out example also occurs where:

MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate

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MPP per dollar spent on capitalMPP per dollar spent on capital=

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



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Least Cost Combination of Inputs to Produce a

Specific Level of Output



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Page 111

Iso-cost line for $1,000.Its slope reflects price oflabor and capital.

Iso-cost line for $1,000.Its slope reflects price oflabor and capital.

Least Cost Input Choice for 100 UnitsLeast Cost Input Choice for 100 Units



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We can determinethis graphically byobserving wherethese two curves are tangent….

We can determinethis graphically byobserving wherethese two curves are tangent….



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We can shift the original iso-cost line from AB out in a parallel fashion to A*B* (which leaves pricesunchanged) which just touches the isoquant at G

We can shift the original iso-cost line from AB out in a parallel fashion to A*B* (which leaves pricesunchanged) which just touches the isoquant at G




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Page 111


At the point of tangency, we know that:slope of isoquant = slope of iso-cost line, or…MPPLABOR ÷ MPPCAPITAL = - (wage rate ÷ rental rate)

At the point of tangency, we know that:slope of isoquant = slope of iso-cost line, or…MPPLABOR ÷ MPPCAPITAL = - (wage rate ÷ rental rate)



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Page 111


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.

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.



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This therefore represents the cheapest combination of capital and labor to produce 100 units of output…

This therefore represents the cheapest combination of capital and labor to produce 100 units of output…

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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?

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?

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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

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

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7

60



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130

7

60

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

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



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130

13

7

60

And the rental rate is $100, then point A* must represents 13 units of capital, or:

$1,300 $100 = 13

And the rental rate is $100, then point A* must represents 13 units of capital, or:

$1,300 $100 = 13



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What Happens if the Price of an Input

Changes?



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Page 112

Assume the initialwage rate and costof capital results inthe iso-cost line AB

Assume the initialwage rate and costof capital results inthe iso-cost line AB

What Happens if Wage Rate Declines?What Happens if Wage Rate Declines?



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Page 112

Wage rate declinemeans that the firmcan now afford B* instead of B…

Wage rate declinemeans that the firmcan now afford B* instead of B…




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Page 112


The new point of tangencyoccurs at H rather than G.

The new point of tangencyoccurs at H rather than G.



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Page 112


As a consequence,the firm woulddesire to use morelabor and less capital…

As a consequence,the firm woulddesire to use morelabor and less capital…



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Least Cost Combination of Inputs and Outputfor a Specific Budget



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What Inputs to Use for a Specific Budget?What Inputs to Use for a Specific Budget?

M

N

Labor

Cap

ital

An iso-cost line fora specific budget

An iso-cost line fora specific budget

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A set of isoquantsfor different levelsof output…

A set of isoquantsfor different levelsof output…



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Page 113

Firm can afford toproduce only 75 units of output using C3 unitsof capital and L3 unitsof labor

Firm can afford toproduce only 75 units of output using C3 unitsof capital and L3 unitsof labor




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Page 113

The firm’s budgetis not large enoughto operate at 100 or 125 units…

The firm’s budgetis not large enoughto operate at 100 or 125 units…




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Page 113

Firm is not spendingavailable budget here…

Firm is not spendingavailable budget here…




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Economics ofBusiness Expansion



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The Planning Curve

The long run average cost (LAC) curve reflects pointsof 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.

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Page 117

What can we say about the fourfirms in this graph?

What can we say about the fourfirms in this graph?



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Page 117

Size 1 would losemoney at price P

Size 1 would losemoney at price P



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Q3

Firm size 2, 3 and 4would earn a profitat price P….

Firm size 2, 3 and 4would earn a profitat price P….



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Q3

Firm #2’s profit would be the area shown below…




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Q3





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Q3





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If price were to fall to PLR, only size 3 wouldnot lose money; it would break-even. Size 4 would have to down size its operations!

If price were to fall to PLR, only size 3 wouldnot lose money; it would break-even. Size 4 would have to down size its operations!



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Page 118

Optimal inputcombinationfor output=10

Optimal inputcombinationfor output=10

How to Expand Firm’s CapacityHow to Expand Firm’s Capacity



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Two options: 1. Point B ?

Two options: 1. Point B ?



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Two options: 1. Point B?2. Point C?

Two options: 1. Point B?2. Point C?



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Optimal inputcombinationfor output=10with budget DE

Optimal inputcombinationfor output=10with budget DE

Optimal inputcombination for output=20with budget FG

Optimal inputcombination for output=20with budget FG

Expanding Firm’s CapacityExpanding Firm’s Capacity



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Page 118

This combinationcosts more toproduce 20 units of output sincebudget HI exceedsbudget FG

This combinationcosts more toproduce 20 units of output sincebudget HI exceedsbudget FG

Expanding Firm’s CapacityExpanding Firm’s Capacity



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Production Possibilities

The goal is to find that combination of products that maximizes revenue for the maximum technical efficiency on the production possibilities frontier.



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Shows the substitution between two products given the most efficientuse of firm’s resources

Shows the substitution between two products given the most efficientuse of firm’s resources



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Slope of the PPF

The slope of the production possibilities curveis 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

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Page 120

Drops from 108 to 95

Drops from 108 to 95

Increases from30 to 40

Increases from30 to 40

Slope over rangebetween D and Eis –1.30, or:-1310

Slope over rangebetween D and Eis –1.30, or:-1310



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Page 148

95,000- 108,000 -13,000

40,000- 30,000 10,000

÷ - 1.30 =



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Inefficientuse of firm’sresources

Inefficientuse of firm’sresources



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Level of outputunattainable withwith firm’s existingresources

Level of outputunattainable withwith firm’s existingresources

Inefficientuse of firm’sexisting resources

Inefficientuse of firm’sexisting resources



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Accounting forProduct Prices



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Plotting the Iso-Revenue Line

Cannedfruit

Cannedvegetables

30,000 cases of canned fruitrequired at price of $33.33/caseto achieve A TARGET revenue of $1 million

30,000 cases of canned fruitrequired at price of $33.33/caseto achieve A TARGET revenue of $1 million

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30,000

40,000



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Plotting the Iso-Revenue Line

Cannedfruit

Cannedvegetables

40,000 cases of canned vegetablesrequired at price of $25.00/caseto achieve revenue of $1 million

40,000 cases of canned vegetablesrequired at price of $25.00/caseto achieve revenue of $1 million

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30,000

40,000

30,000 cases of canned fruitrequired at price of $33.33/caseto achieve revenue of $1 million

30,000 cases of canned fruitrequired at price of $33.33/caseto achieve revenue of $1 million



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Original iso-revenue line Changes in income or both prices

Change in price of fruit Change in price of vegetables

Line AB is the originaliso-revenue line, indicatingthe number of cases neededto reach a specific salestarget.

Line AB is the originaliso-revenue line, indicatingthe number of cases neededto reach a specific salestarget.



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Change in price of fruit Change in price of vegetables

The iso-revenue line wouldshift out to line EF if therevenue target doubled (orprices fell in half) while theline would shift in to lineCD if revenue targets fell inhalf or prices doubled.

The iso-revenue line wouldshift out to line EF if therevenue target doubled (orprices fell in half) while theline would shift in to lineCD if revenue targets fell inhalf or prices doubled.



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Change in price of fruit Change in price of vegetablesThe iso-revenue line wouldshift out to line BC is the price of fruit fell in halfbut shift in to line BD ifthe price of fruit doubled

The iso-revenue line wouldshift out to line BC is the price of fruit fell in halfbut shift in to line BD ifthe price of fruit doubled



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Change in price of fruit Change in price of vegetablesThe iso-revenue line wouldshift out to line AD if the price of vegetables fell in halfbut shift in to line AC is theprice of fruit doubled.

The iso-revenue line wouldshift out to line AD if the price of vegetables fell in halfbut shift in to line AC is theprice of fruit doubled.



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Profit Maximizingcombination ofProduct Prices



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Combination of ProductsThe profit maximizing combination of two productsis found where the slope of the production possibilitiesfrontier (PPF) is equal to the slope of the iso-revenueCurve, or where:

Canned fruit Price of vegetablesCanned vegetables Price of fruit= –

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Slope of an PPF curve

Slope of an PPF curve

Slope of iso- revenue line

Slope of iso- revenue line



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Assume Line AB representsrevenue for $1 million.

Assume Line AB representsrevenue for $1 million.



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We want to find the profit maximizing combination to “can”given the current prices of canned fruitand vegetables.

We want to find the profit maximizing combination to “can”given the current prices of canned fruitand vegetables.



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Page 124

Canned fruit Price of vegetables

Canned vegetables Price of fruit


Canned vegetables Price of fruit= –

Shifting line AB out in a parallel fashion holds both prices constant at their current level

Shifting line AB out in a parallel fashion holds both prices constant at their current level



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18,000 cases of vege-tables


MRPTequals-0.75

MRPTequals-0.75

125,000 cases of

fruit

125,000 cases of

fruit



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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



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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


Canned vegetables Price of fruit


Canned vegetables Price of fruit= –

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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



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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.



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Effects of a Changein the Price of One Product



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If the price of canned fruit fell in half, the firm must sell twice as many cases ofcanned fruit to earn $1 million if it focused solely on fruit production.

If the price of canned fruit fell in half, the firm must sell twice as many cases ofcanned fruit to earn $1 million if it focused solely on fruit production.



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Page 125

This gives us a new iso-revenue curve… line CB.

This gives us a new iso-revenue curve… line CB.



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Page 125

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….

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….



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Page 125

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.

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.



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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.

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.



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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.



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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 equals the ratio of the product prices



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

Technology

Agri 2312 chapter 7 economics of input and product substitution