Econ 101: Principles of Microeconomics · Econ 101: Principles of Microeconomics Chapter 9: Making...

Econ 101: Principles of MicroeconomicsChapter 9: Making Decisions

Fall 2010

Herriges (ISU) Ch. 9: Making Decisions Fall 2010 1 / 37

Outline

1 Opportunity Cost and Decisions

2 The Role of Marginal AnalysisMarginal CostMarginal Benefits

3 Sunk Cost

4 The Concept of Present Value

The Focus of This Chapter

In the remainder of the course, we will look in detail about thedecisions made by firms and consumers.

While the issues will vary from case to case, there are severalconcepts that will arise over and over again.

This chapter highlights four key concepts to keep in mind whenstudying the decision-making process:

1 Opportunity Costs: what you give up in making a choice.2 Marginal Analysis: studying the impact of small changes in the

“how-much” decision.3 Sunk Costs: costs that have already been incurred and cannot be

recovered.4 Present Value: The value today of a future cost or benefit.

1 Opportunity Costs: what you give up in making a choice.

2 Marginal Analysis: studying the impact of small changes in the“how-much” decision.

3 Sunk Costs: costs that have already been incurred and cannot berecovered.

4 Present Value: The value today of a future cost or benefit.

“how-much” decision.

3 Sunk Costs: costs that have already been incurred and cannot berecovered.

recovered.

Opportunity Cost and Decisions

We have already talked about the notion of opportunity cost

- In considering whether to make a fancy breakfast before class.- In considering the cost of attending college.

The opportunity cost of an action is the value of what we give up bytaking that action.

These costs can be broken down into two main components:1 The explicit cost; i.e., the actual money spent as a result of the action.2 The implicit costs; i.e., the non-monetary costs (opportunities

foregone) by the action.

In many cases, the implicit costs can be substantial.

- In considering whether to make a fancy breakfast before class.

- In considering the cost of attending college.

These costs can be broken down into two main components:

1 The explicit cost; i.e., the actual money spent as a result of the action.2 The implicit costs; i.e., the non-monetary costs (opportunities

These costs can be broken down into two main components:1 The explicit cost; i.e., the actual money spent as a result of the action.

2 The implicit costs; i.e., the non-monetary costs (opportunitiesforegone) by the action.

The Cost of Raising a Child

What is the cost of raising a child, excluding college?

The estimates vary substantially, but figures close to $250-300,000are typical

The site http://www.babycenter.com/cost-of-raising-child-calculatorprovides estimates that vary by region, whether it is a single- ortwo-parent household, and the region in which you live.

Some of the categories they consider are:- Housing- Food- Transportation- Clothing- Healthcare- Childcare and Education

What other costs might we be missing here?

Is the cost of raising children less if one parent decides to stay athome?

Some of the categories they consider are:

- Housing- Food- Transportation- Clothing- Healthcare- Childcare and Education

Some of the categories they consider are:- Housing

- Food- Transportation- Clothing- Healthcare- Childcare and Education

Some of the categories they consider are:- Housing- Food

- Transportation- Clothing- Healthcare- Childcare and Education

Some of the categories they consider are:- Housing- Food- Transportation

- Clothing- Healthcare- Childcare and Education

Some of the categories they consider are:- Housing- Food- Transportation- Clothing

- Healthcare- Childcare and Education

Some of the categories they consider are:- Housing- Food- Transportation- Clothing- Healthcare

- Childcare and Education

Accounting Profit versus Economic Profit

These same issues arise when economists talk about profit.

Economists distinguish between1 Accounting profit: The total revenues of the firm minus the firm’s

explicit costs and capital depreciation.2 Economic profit: The total revenues of the firm minus the opportunity

costs of the resources it uses.

Accounting profits are important, particularly for tax purposes.

However, economic profits are more important in terms of guiding thedecisions made by firms.

Economists distinguish between

1 Accounting profit: The total revenues of the firm minus the firm’sexplicit costs and capital depreciation.

2 Economic profit: The total revenues of the firm minus the opportunitycosts of the resources it uses.

explicit costs and capital depreciation.

2 Economic profit: The total revenues of the firm minus the opportunitycosts of the resources it uses.

Example: John’s Woodworking Firm

Suppose John own’s a woodworking operation, which he runs out ofhis home basement and starts by purchasing $10,000 in equipmentusing money he has saved over the years.

During his first year of operations, he

- paid an assistant $30,000 to work for him,- purchased $50,000 in lumber and supplies,- paid $10,000 in utilities, and- sold $150,000 in furniture.

A local cabinet-maker had offered John the opportunity to work forher instead, at an annual salary of $60,000.

John’s accounting and economic profits will differ substantially.

- paid an assistant $30,000 to work for him,

- purchased $50,000 in lumber and supplies,- paid $10,000 in utilities, and- sold $150,000 in furniture.

- paid an assistant $30,000 to work for him,- purchased $50,000 in lumber and supplies,

- paid $10,000 in utilities, and- sold $150,000 in furniture.

- paid an assistant $30,000 to work for him,- purchased $50,000 in lumber and supplies,- paid $10,000 in utilities, and

- sold $150,000 in furniture.

John’s Accounting and Economic Profits

Revenues: $150,000

Costs:Cost of Equipment 10,000Lumber,etc. 50,000Utilities 10,000Wages 30,000

Total Costs: 100,000

Accounting Profit: $50,000

Revenues: $150,000

Costs:Cost of Equipment 10,000Lumber,etc. 50,000Utilities 10,000Wages 30,000Foregone interest 500Foregone salary 60,000

Economic Profit: -$10,500

Revenues: $150,000

Costs:Cost of Equipment 10,000

Lumber,etc. 50,000Utilities 10,000Wages 30,000

Revenues: $150,000

Costs:Cost of Equipment 10,000Lumber,etc. 50,000

Utilities 10,000Wages 30,000

Revenues: $150,000

Costs:Cost of Equipment 10,000Lumber,etc. 50,000Utilities 10,000

Wages 30,000

Revenues: $150,000

Costs:Cost of Equipment 10,000

Lumber,etc. 50,000Utilities 10,000Wages 30,000Foregone interest 500Foregone salary 60,000

Revenues: $150,000

Costs:Cost of Equipment 10,000Lumber,etc. 50,000

Utilities 10,000Wages 30,000Foregone interest 500Foregone salary 60,000

Revenues: $150,000

Costs:Cost of Equipment 10,000Lumber,etc. 50,000Utilities 10,000

Wages 30,000Foregone interest 500Foregone salary 60,000

Revenues: $150,000

Foregone interest 500Foregone salary 60,000

Revenues: $150,000

Costs:Cost of Equipment 10,000Lumber,etc. 50,000Utilities 10,000Wages 30,000Foregone interest 500

Foregone salary 60,000

Revenues: $150,000

The Difference in Profits

In John’s case, while he made an accounting profit, economists wouldsay he had an economic loss.

The difference between his accounting profits and his economic profitslies in the “implicit costs” of his capital

Capital includes his

- Physical capital: the equipment, buildings, tools, inventory, andfinancial assets used by the firm.

- Human capital: the education and knowledge embodied in theworkforce.

For John, there are two implicit costs of his capital that are ignoredwhen computing accounting profits:

- The foregone interest John could have earned on the money he used tobuy the equipment.

- The foregone salary he could have earned working for the othercabinetmaker.

The Role of Marginal Analysis

Marginal Analysis

A second important economic concept is that of marginal analysis

:the comparison of the benefit of doing a little more of some activitywith the cost of doing a little more of that activity.

While we do often make “either or decisions,”such as whether to

buy a car or not,attend to college or not,take a vacation or not,. . .

. . . many of our decisions involve “how much” decisions (or whateconomists often refer to as “decisions at the margins”)

For example, we have to decide

How many packages of Ramen noodles to buy,How large a house to buy,How many hours to study for an examHow much money the government should allocate to the“Cash-for-clunkers” program.

Marginal Analysis

A second important economic concept is that of marginal analysis:the comparison of the benefit of doing a little more of some activitywith the cost of doing a little more of that activity.

Marginal Analysis

While we do often make “either or decisions,”

such as whether to

Marginal Analysis

buy a car or not,

attend to college or not,take a vacation or not,. . .

Marginal Analysis

buy a car or not,attend to college or not,

take a vacation or not,. . .

Marginal Analysis

How many packages of Ramen noodles to buy,

How large a house to buy,How many hours to study for an examHow much money the government should allocate to the“Cash-for-clunkers” program.

Marginal Analysis

How many packages of Ramen noodles to buy,How large a house to buy,

How many hours to study for an examHow much money the government should allocate to the“Cash-for-clunkers” program.

Marginal Analysis

How many packages of Ramen noodles to buy,How large a house to buy,How many hours to study for an exam

How much money the government should allocate to the“Cash-for-clunkers” program.

Marginal Analysis

Choosing How Many Rocking Chairs to Build

Let’s revisit John’s woodworking shop.

For simplicity, suppose that

- John only builds rocking chairs.- He already owns all his equipment and has decided to work alone.- He no longer has a job offer from any other firm.

If we know that John could make $500 in profit by building 10rocking chairs, does that mean

- that he should build those 10 rocking chairs?- that he should build more rocking chairs?

We can’t tell.

What we need to be able to compare is the

- Marginal cost (i.e., the additional cost) of building each chair to- Marginal benefit (i.e., the additional benefit) from building each chair.

We can’t tell.

- John only builds rocking chairs.

- He already owns all his equipment and has decided to work alone.- He no longer has a job offer from any other firm.

We can’t tell.

- John only builds rocking chairs.- He already owns all his equipment and has decided to work alone.

- He no longer has a job offer from any other firm.

We can’t tell.

- that he should build those 10 rocking chairs?

- that he should build more rocking chairs?

We can’t tell.

- Marginal cost (i.e., the additional cost) of building each chair

to- Marginal benefit (i.e., the additional benefit) from building each chair.

We can’t tell.

The Role of Marginal Analysis Marginal Cost

Marginal Costs

In general, the marginal cost of producing a good is the additionalcost of producing one more unit of the good.

For John, suppose the marginal cost of building a rocking chair is$100, regardless of how many chairs he builds.

This includes the cost of lumber and the electricity used in production.

This is an example of constant marginal cost

Marginal Costs

John’s Total Costs (TC) and Marginal Costs(MC)

Number of Chair Total Cost Marginal Costs (per chair)0 0

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

1 100100

2 200100

3 300100

4 400100

5 500100

6 600100

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

1001 100

2 200100

3 300100

4 400100

5 500100

6 600100

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

1001 100

1002 200

3 300100

4 400100

5 500100

6 600100

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

1001 100

1002 200

1003 300

4 400100

5 500100

6 600100

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

1001 100

1002 200

1003 300

1004 400

5 500100

6 600100

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

1001 100

1002 200

1003 300

1004 400

1005 500

6 600100

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1001 100

1002 200

1003 300

1004 400

1005 500

1006 600

1007 700

Marginal Cost Curve

Increasing and Decreasing Marginal Costs

With John’s woodworking shop, we assumed that each additionalchair cost the same amount to produce.

Marginal costs, however, are often not constant.Decreasing marginal costs (i.e., with the additional cost of producinga good declining as more goods are produced) can arise due to:

- Learning effects: with individual workers getting more efficient atproducing as they produce more.

- Specialization:* With a single worker, this may take the form of working on parts in

batches.* With multiple employees, individual workers focus on only a part of the

production process.

Increasing marginal costs (i.e., with the additional cost of producing agood increasing as more goods are produced) can arise due to:

- Fixed inputs: Limits on currently available equipment make it costly, ifnot impossible, to produce more.

- The gains from specialization have been exhausted and may in facthinder productivity.

Marginal costs, however, are often not constant.

Decreasing marginal costs (i.e., with the additional cost of producinga good declining as more goods are produced) can arise due to:

production process.

- Specialization:

* With a single worker, this may take the form of working on parts inbatches.

* With multiple employees, individual workers focus on only a part of theproduction process.

batches.

* With multiple employees, individual workers focus on only a part of theproduction process.

production process.

The Role of Marginal Analysis Marginal Benefits

Marginal Benefit

The other half of the story is the Marginal Benefit of an action.

The marginal benefit of a good or service is the additional benefitfrom producing one more unit of that good or service.

Suppose, in the case of John’s rocking chairs, that eight people areinterested in buying a rocking chair, and they are willing to pay:

Individual Willingness-to-Pay

Marginal Benefit

John’s Total Benefits (TB) and Marginal Benefits (MB)Number of Chair Total Benefits Marginal Benefits

4001 400

3002 700

2253 925

1504 1075

1105 1185

806 1265

607 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

3002 700

2253 925

1504 1075

1105 1185

806 1265

607 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

1 400300

2253 925

1504 1075

1105 1185

806 1265

607 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

1 400300

2 700225

1504 1075

1105 1185

806 1265

607 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

1 400300

2 700225

3 925150

4 1075

1105 1185

806 1265

607 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 1185

806 1265

607 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 1265

607 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 1325

408 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

0 0400

1 400300

2 700225

3 925150

4 1075110

5 118580

6 126560

7 132540

8 1365

Marginal Benefits Curve

Combining the Pieces

We can use the above information to determine the optimal quantityfor John to produce.

We do this by comparing the marginal benefits of producing each unitof the good (in this case a chair) to the marginal cost of producingthat unit.

1 If the MB ≥ MC, then we should produce the good.2 If the MB < MC, then we should not produce it.

Another way to say the say thing is that we should produce the goodas long as the marginal net benefit (MNB ≡ MB - MC) is positive.

1 If the MB ≥ MC, then we should produce the good.

2 If the MB < MC, then we should not produce it.

Finding the Optimal QuantityQ TB TC TNB MB MC MNB

0 0 0 0400 100 300

1 400 100 300300 100 200

2 700 200 500225 100 125

3 925 300 625150 100 50

4 1075 400 675110 100 10

5 1185 500 68580 100 -20

6 1265 600 66560 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

Finding the Optimal QuantityQ TB TC TNB MB MC MNB0 0 0 0

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 300

1 400 100 300300 100 200

2 700 200 500225 100 125

3 925 300 625150 100 50

4 1075 400 675110 100 10

5 1185 500 68580 100 -20

6 1265 600 66560 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 200

2 700 200 500225 100 125

3 925 300 625150 100 50

4 1075 400 675110 100 10

5 1185 500 68580 100 -20

6 1265 600 66560 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 125

3 925 300 625150 100 50

4 1075 400 675110 100 10

5 1185 500 68580 100 -20

6 1265 600 66560 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 50

4 1075 400 675110 100 10

5 1185 500 68580 100 -20

6 1265 600 66560 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 10

5 1185 500 68580 100 -20

6 1265 600 66560 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -20

6 1265 600 66560 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -40

7 1325 700 62540 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -60

8 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

400 100 3001 400 100 300

300 100 2002 700 200 500

225 100 1253 925 300 625

150 100 504 1075 400 675

110 100 105 1185 500 685

80 100 -206 1265 600 665

60 100 -407 1325 700 625

40 100 -608 1365 800 565

The Optimal Quantity

The optimal quantity for John to produce is 5 rocking chairs.

For any higher level of production, the marginal benefits of productionare less than the marginal cost of production.

For example, when considering whether or not to produce an 8throcking chair, John should compare:

The marginal benefit of the 8th chair ($40)To the marginal cost of the 8th chair ($100)

Even though John would still be making an overall profit of $565 bymaking a total of 8 chairs, he would make even more ($685) byproducing only 5 chairs.

With discrete quantities of production, the principle of marginalanalysis says to produce each quantity as long as MB≥MC.

With continuous quantities of production, this same principle says toproduce up to the point where MB=MC

The marginal benefit of the 8th chair ($40)

To the marginal cost of the 8th chair ($100)

Optimal Coffee Production

Using the Principle of Marginal Analysis

We’ve applied the principle of marginal analysis to thedecision-making of a producer (John’s woodworking)

But the same idea applies to a variety of settings, such as1 The decision of individuals choosing how large a house to buy2 The decision of the Iowa government as how much money to spend on

lake restoration3 The dosage level to set for a medication (trading off efficacy versus

side effects)4 The size of the “Cash-for-Clunkers” program.5 How much time a student spends studying for an exam.6 How much money the government allocates to cancer research

Sometimes it is difficult to quantify the MB and MC’s of an action,but implicitly our decisions are making such trade-offs, whether welike it or not.

But the same idea applies to a variety of settings, such as

1 The decision of individuals choosing how large a house to buy2 The decision of the Iowa government as how much money to spend on

But the same idea applies to a variety of settings, such as1 The decision of individuals choosing how large a house to buy

2 The decision of the Iowa government as how much money to spend onlake restoration

3 The dosage level to set for a medication (trading off efficacy versusside effects)

4 The size of the “Cash-for-Clunkers” program.5 How much time a student spends studying for an exam.6 How much money the government allocates to cancer research

lake restoration

3 The dosage level to set for a medication (trading off efficacy versusside effects)

4 The size of the “Cash-for-Clunkers” program.5 How much time a student spends studying for an exam.6 How much money the government allocates to cancer research

side effects)4 The size of the “Cash-for-Clunkers” program.

5 How much time a student spends studying for an exam.6 How much money the government allocates to cancer research

side effects)4 The size of the “Cash-for-Clunkers” program.5 How much time a student spends studying for an exam.

6 How much money the government allocates to cancer research

Sunk Cost

Sunk Costs

The third concept we want to focus on in this chapter is that of sunkcost; i.e., a cost that has been incurred and cannot be recovered.

Consider the following example:- A popular music group is coming to town and you are able to buy 50

tickets at $25 each.- Two hours prior to the concert, you stand outside and sell 30 tickets

for $40 each.- An hour later you sell 10 tickets for $25 each.- Just a few minutes before the concert starts, you sell the last 10 tickets

for $20 each.

Did it make sense to sell those last 10 tickets for $20 each?- Yes! You had already spent the money on the tickets and could not get

it back.- The earlier money you had spent buying them is now irrelevant and

should no longer impact your decision-making.

What was the marginal cost of selling those last 10 tickets at timeyou sold them? 0

Sunk Cost

Sunk Costs

The third concept we want to focus on in this chapter is that of sunkcost; i.e., a cost that has been incurred and cannot be recovered.Consider the following example:

- A popular music group is coming to town and you are able to buy 50tickets at $25 each.

- Two hours prior to the concert, you stand outside and sell 30 ticketsfor $40 each.

- An hour later you sell 10 tickets for $25 each.- Just a few minutes before the concert starts, you sell the last 10 tickets

for $20 each.

Sunk Cost

Sunk Costs

for $20 each.

Sunk Cost

Sunk Costs

for $20 each.

Sunk Cost

Sunk Costs

- An hour later you sell 10 tickets for $25 each.

- Just a few minutes before the concert starts, you sell the last 10 ticketsfor $20 each.

Sunk Cost

Sunk Costs

for $20 each.

Sunk Cost

Sunk Costs

for $20 each.

Did it make sense to sell those last 10 tickets for $20 each?

- Yes! You had already spent the money on the tickets and could not getit back.

- The earlier money you had spent buying them is now irrelevant andshould no longer impact your decision-making.

Sunk Cost

Sunk Costs

for $20 each.

it back.

- The earlier money you had spent buying them is now irrelevant andshould no longer impact your decision-making.

Sunk Cost

Sunk Costs

for $20 each.

Sunk Cost

Sunk Costs

for $20 each.

What was the marginal cost of selling those last 10 tickets at timeyou sold them?

Sunk Cost

Sunk Costs

for $20 each.

Sunk Cost

Ignoring Sunk Costs

Ignoring sunk costs can be hard.

We often feel guilty if we do so:

- When we buy a membership in a health club and fail to attend.- When we buy a river-rafting tour and, when it turns out to be a rainy

day, we fail to attend- When we stop spending money repairing a car after it continues to not

However, ignoring sunk costs is the appropriate decision: “There’s nopoint in throwing good money after bad.”

Sunk Cost

Ignoring Sunk Costs

Sunk Cost

Ignoring Sunk Costs

- When we buy a membership in a health club and fail to attend.

- When we buy a river-rafting tour and, when it turns out to be a rainyday, we fail to attend

- When we stop spending money repairing a car after it continues to notwork.

Sunk Cost

Ignoring Sunk Costs

day, we fail to attend

- When we stop spending money repairing a car after it continues to notwork.

Sunk Cost

Ignoring Sunk Costs

Sunk Cost

Ignoring Sunk Costs

The Concept of Present Value

Comparing Values over Time

There are many situations in which we have to compare the benefitsand costs of an action over time.

If you had a choice between getting paid a $1000 bonus today or 1year from now, would you care?

If ISU allowed you to postpone paying your tuition for a year, wouldyou care?

Hopefully, the answer your answer would be yes in both cases, butwhy?

There is an opportunity cost of time; e.g., having to wait to get paid.

In this last section, we will discuss the notions of present value andfuture value in comparing values over time.

Other Examples

1626, Peter Minuit bought Manhattan from the Man-a-hat-a Indiansfor goods valued at $24

- The 12800 acres are now valued at $627 million/acre or $8 trillionunimproved

- Claim: This was a heck a deal for the Dutch. Is this true?

Furnace Advertisement:

- Furnace costs $2,000- Energy Savings = $200/year- Claim: The furnace will pay for itself in 10 years. Is this true?

Powerball Lottery

- Current Prize is worth $20 million- Payout is $800,000 per year for 25 years- Claim: The state will make money on the lottery, even if it only sells

$20 million in tickets for the $20 million prize. Is this true?

Other Examples

Powerball Lottery

Other Examples

- Claim: This was a heck a deal for the Dutch.

Is this true?

Powerball Lottery

Other Examples

Powerball Lottery

Other Examples

Powerball Lottery

Other Examples

- Furnace costs $2,000

- Energy Savings = $200/year- Claim: The furnace will pay for itself in 10 years. Is this true?

Powerball Lottery

Other Examples

- Furnace costs $2,000- Energy Savings = $200/year

- Claim: The furnace will pay for itself in 10 years. Is this true?

Powerball Lottery

Other Examples

- Furnace costs $2,000- Energy Savings = $200/year- Claim: The furnace will pay for itself in 10 years.

Is this true?

Powerball Lottery

Other Examples

Powerball Lottery

Other Examples

Powerball Lottery

Other Examples

Powerball Lottery

- Current Prize is worth $20 million

- Payout is $800,000 per year for 25 years- Claim: The state will make money on the lottery, even if it only sells

Other Examples

Powerball Lottery

- Current Prize is worth $20 million- Payout is $800,000 per year for 25 years

- Claim: The state will make money on the lottery, even if it only sells$20 million in tickets for the $20 million prize. Is this true?

Other Examples

Powerball Lottery

$20 million in tickets for the $20 million prize.

Is this true?

Other Examples

Powerball Lottery

The Role of Interest Rates

The issue for all of these examples: $1 today is not equal to $1 oneyear from now

We need a way to create equivalencies between dollars received atdifferent times

The Mechanism: Interest rates (r)

- The opportunity cost of spending $1 today = $1 + $1 ×r = $1(1 + r);At r = 0.1 (10%) the opportunity cost is $1.10 next period

- The opportunity cost of spending $1 today = $1 + $1 ×r = $1(1 + r);

At r = 0.1 (10%) the opportunity cost is $1.10 next period

Future Value

Future Value: refers to the value in dollars at a future point in time ofa given sum of money today.

Compounding: refers to the successive application of interestpayments to generate future values.

A $1 today have a future value of

Period Future Value

1 $1(1 + r)2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

Generally, $1 today is worth $(1 + r)T T periods from now.

Future Value

Period Future Value

1 $1(1 + r)2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

Future Value

Period Future Value

1 $1(1 + r)

2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

Future Value

Period Future Value

1 $1(1 + r)2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

Future Value

Period Future Value

1 $1(1 + r)2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

Future Value

Period Future Value

1 $1(1 + r)2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

Future Value

Period Future Value

1 $1(1 + r)2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

Future Value

Period Future Value

1 $1(1 + r)2 $1(1 + r)(1 + r) =$1(1 + r)2

3 $1(1 + r)3

4 $1(1 + r)4

5 $1(1 + r)5

The Man-a-hat-a Indians Example

How much would the $24 in 1626 be worth today if they justcollected interest?

$1 in 1626 is worth $1(1 + r)T now, where $T = 2009-1626 = 383

r Future Value

0.10 $1,712,420 trillion0.09 $5,183 trillion0.08 $152 trillion0.07 $4.3 trillion0.06 $118 billion0.05 $3.1 billion

The break-even point r=0.072 (7.2%)

US 30-year Treasury Bonds have averaged 7.7% over the past 32years.

r Future Value

0.10 $1,712,420 trillion

0.09 $5,183 trillion0.08 $152 trillion0.07 $4.3 trillion0.06 $118 billion0.05 $3.1 billion

r Future Value

0.10 $1,712,420 trillion0.09 $5,183 trillion

0.08 $152 trillion0.07 $4.3 trillion0.06 $118 billion0.05 $3.1 billion

r Future Value

0.10 $1,712,420 trillion0.09 $5,183 trillion0.08 $152 trillion

0.07 $4.3 trillion0.06 $118 billion0.05 $3.1 billion

r Future Value

0.10 $1,712,420 trillion0.09 $5,183 trillion0.08 $152 trillion0.07 $4.3 trillion

0.06 $118 billion0.05 $3.1 billion

r Future Value

0.10 $1,712,420 trillion0.09 $5,183 trillion0.08 $152 trillion0.07 $4.3 trillion0.06 $118 billion

0.05 $3.1 billion

r Future Value

Present Value

Present Value: The value in current (i.e., present) period dollars of asum of money to be received at some point in the future.

The notion of present value is essentially the opposite of the notion offuture value

Instead of asking how much a dollar today is worth in the future. . .. . . we are asking how much a dollar promised in the future would beworth today.

Well, if$1 Today = $1(1 + r) Next Period, (1)

then we just divide both sides of this equality to get that

1 + rToday = $1 Next Period, (2)

Present Value

Instead of asking how much a dollar today is worth in the future. . .

. . . we are asking how much a dollar promised in the future would beworth today.

Present Value

Making Sense of Present Value

So, does this make sense intuitively?

Well, if I am given $11+r today and invest it in the bank, how much will

I have in one period?

- I’ll have my original principal: $11+r

- Plus the interest I earn on that principal: r × $11+r ,

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

For example, if the interest rate is 10% (i.e., r=0.10), then thepresent value of $1 one period from now is $1

1+r = $11.1 = 0.91

This is because if I took that $0.91 and invested it in the bank, Iwould earn $0.09 in interest and end up with $1 total next period.

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

for a total of

+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

for a total of

1 + r+ r × $1

= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

= $1 (3)

1+r = $11.1 = 0.91

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

for a total of

1 + r+ r × $1

1 + r= (1 + r)× $1

1 + r= $1 (3)

1+r = $11.1 = 0.91

Present Value for Two PeriodsHow does this result change if we want to know the present value of$1 promised two periods from today.

The idea is the same.The PV of this $1 future payment would be

(1 + r)2(4)

This is because I would earn compound interest on the money overtwo years, giving me back a total of $1 in two years.For example, the PV of $1 promised 2 years from now given a 10%interest rate would be

(1 + r)2=

1.21= $0.862 (5)

- After one year in the bank I would have (1.1)($0.862)=$0.91 inprincipal and interest.

- After the second year I would have (1.1)($0.91)=$1 in principal andinterest.

Present Value for Two PeriodsHow does this result change if we want to know the present value of$1 promised two periods from today.The idea is the same.

The PV of this $1 future payment would be

(1 + r)2(4)

(1 + r)2=

1.21= $0.862 (5)

Present Value for Two PeriodsHow does this result change if we want to know the present value of$1 promised two periods from today.The idea is the same.The PV of this $1 future payment would be

(1 + r)2(4)

(1 + r)2=

1.21= $0.862 (5)

(1 + r)2(4)

This is because I would earn compound interest on the money overtwo years, giving me back a total of $1 in two years.

For example, the PV of $1 promised 2 years from now given a 10%interest rate would be

(1 + r)2=

1.21= $0.862 (5)

(1 + r)2(4)

(1 + r)2=

1.21= $0.862 (5)

(1 + r)2(4)

(1 + r)2=

1.21= $0.862 (5)

(1 + r)2(4)

(1 + r)2=

1.21= $0.862 (5)

(1 + r)2(4)

(1 + r)2=

1.21= $0.862 (5)

More Than Two Periods

In general, the PV of $1 promised T periods from today is

(1 + r)T(6)

This is known as discounting: successive application of interest ratesto generate present values.

In general, the longer into the future we go, that smaller (in presentvalue) will be any promise of payment.

For example, the PV of $1 promised in 40 periods with r=0.1 is givenby

(1 + 0.10)40≈ $0.02 (7)

This is because there is a high opportunity cost associated with thatwaiting.

(1 + r)T(6)

(1 + 0.10)40≈ $0.02 (7)

(1 + r)T(6)

(1 + 0.10)40≈ $0.02 (7)

(1 + r)T(6)

(1 + 0.10)40≈ $0.02 (7)

(1 + r)T(6)

(1 + 0.10)40≈ $0.02 (7)

The Furnace Example

Consider our furnace example.

The cost of the furnace today is $2,000

If the furnace saved you $200 over the next ten years, is worth theinvestment?

Your answer should be no, because, while the costs are all today, youhave to wait for the benefits for up to 10 years.

Discounting provides a way to compare all the costs and benefits intoday’s dollars (i.e., in present value terms)

The cost of $2,000 already in PV terms.

The PV of the benefits (with r=0.1) is

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3

+ · · ·+$200

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82

+ $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29

+ $150.26 + · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26

+ · · ·+ $77.11 = $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11

= $1, 429

The Furnace Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)10

= $181.82 + $165.29 + $150.26 + · · ·+ $77.11 = $1, 429

The Lottery Example

The same arguments explain why the lottery can make money selling$20 million in tickets and paying out $800,000 per year for 25 years($20 million total).

The present value of the benefits to the state is $20 million today!.

The present value of its costs, the payments over 25 years, (withr=0.10) is:

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

Essentially, the lottery is making money off the interest it earns byspreading the payments over 25 years.

The Lottery Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

The Lottery Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

The Lottery Example

(1 + 0.1)

+$0.8m

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

The Lottery Example

(1 + 0.1)+

(1 + 0.1)2

+$0.8m

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

The Lottery Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3

+ · · ·+$0.8m

(1 + 0.1)25

= $7.26 million

The Lottery Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

The Lottery Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

The Lottery Example

(1 + 0.1)+

(1 + 0.1)2+

(1 + 0.1)3+ · · ·+

(1 + 0.1)25

= $7.26 million

Econ 101: Principles of Microeconomics · Econ 101: Principles of Microeconomics Chapter 9: Making...

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