Conclusion of “tools” chapters

Today: More on welfare economics Market failure Various tools of cost-benefit analysis

Today

Conclusion of our “tools” chapters More on Chapter 3

Production economy Two fundamental theorems of welfare economics Market failure

Chapter 8: Cost-benefit analysis Present value Internal rate of return Discount rates and valuing public projects Other issues

More on welfare economics Production economy

Production possibilities curve Efficiency

Two fundamental theorems of welfare economics Market failure

Recall linear production possibility curve Becky has a

given number of hours per day

Feasible bundles: t, v, w, x, y, z Point t does not

use up her time allotment

Point u is infeasible

Efficiency

Efficient points are on the line connecting (0,4) and (20,0)

Examples of efficient points: v, w, x, y, and z

Efficiency

At efficient points, increasing production of one good must result in another good having decreased production

We will typically assume efficient points are chosen No satiation: More is better

See Figure 3.8, p. 39

Marginal Rate of Transformation MRTaf = Marginal rate of transformation of

apples for fig leaves MRTaf = MCa/MCf

Efficiency condition

With apple and fig leaf supply variable, we need the following to get efficiency

MRTaf = MRSaf = MRSaf

MCa/MCf = MRSaf = MRSaf

Adam Eve

Adam Eve

Efficiency condition

Assume that the efficiency condition is not met

Someone could trade to improve utility Trade will continue to occur until efficiency

condition is met

First Fundamental Theorem

With competition and open markets for all commodities, efficiency can occur

This idea is conveyed in the First Fundamental Theorem of Welfare Economics “All producers and consumers act as perfect

competitors” (R/G p. 40) No market power

“A market exists for each and every commodity” (R/G p. 40) Does not happen in real life (No market for the air we

breathe)

Sketch of efficiency conditionsConsumer side:

MRSaf = Pa/Pf

MRSaf = Pa/Pf MRSaf = MRSaf

Producer side:

MC = MB implies

MCa/MCf = Pa/Pf MRTaf = Pa/Pf

Adam

Eve Adam Eve

Efficiency conditions met

Second Fundamental Theorem We return to fairness

Two efficient points are the origins Although these points are efficient, are they “fair?”

Government can play a role in fairness Lump-sum taxes act in the same way as changing

endowments

Efficiency versus equity

A utility possibilities curve can show all of the Pareto efficient points See Figure 3.10, p. 43 Notice that from any point on a utility possibilities

curve, an increase of one person’s utility must cause another’s utility to decrease

Points inside the curve are not Pareto efficient

See Figure 3.9, p. 42, for more on efficiency versus equity

Determining a social welfare function Determining a social welfare function can differ from

person to person Examples

Additive Multiplicative

Which one is “right?” Hard to say Most economists do not try to address this issue

See Figure 3.11, p. 44, for an example of social indifference curves

Maximizing the social welfare function In order to maximize the social welfare

function, find the indifference curve with highest utility that is indifferent to utility possibilities curve See Figure 3.12, p. 44, for an example

Market failure

There are instances in which market efficiency cannot be achieved Market power

Many ways to control price Nonexistence of markets

Asymmetric information Important in health care and retirement: Chapters 9-11

Externalities: Chapter 5 Public goods: Chapter 4

Market failure due to market power How Do Firms Gain Market Power?

Exclusive control over important inputs Patents and copyrights Government licenses or franchises Economies of scale Natural monopoly Networks

Exclusive control over important inputs If a company controls a significant portion of

the important inputs to a product, it can have significant influence on price

Exclusive control over important inputs Example: De Beers

Rough diamond explorer Around 40% of world diamond production by

value Sales and marketing through the Diamond

Trading Company This company sells almost half of the world’s rough

diamonds by value(Information from http://en.wikipedia.org/wiki/De_Beers, checked Feb.

3, 2008)

De Beers

Such large control over the market makes De Beers able to act similarly to a monopolist Marketing of diamond jewelry does not have to be

brand specific "A Diamond is Forever" attempts to prevent old jewelry

from entering the market De Beers does have some control over world

prices

Patents and copyrights

Patents and copyrights prohibit others from copying private work and discoveries Example: Copying songs and movies that are

copyrighted are typically prohibited by law

Government licenses or franchises Government owned property often allows

exclusive operation of the property for various uses

This is to prevent competition that could deteriorate a natural destination

Government licenses or franchises Example: Yosemite National

Park Limited parking Tasteful hotels Most of the park is undeveloped

Most of park development is in only 7 square miles

Park is 1,200 square miles

Bridal Veil Falls

Economies of scale

Some technologies are such that as the quantity produced increases, ATC decreases for all reasonable quantities produced This is due to increasing returns to scale

This happens when ALL inputs double and production MORE THAN doubles

Often happens with large fixed costs and nearly-linear variable costs

One firm could gain market power When a firm gains

market control with economies of scale, it is called a natural monopoly

There are problems with natural monopolies if left uncontrolled

Price ($)

Q

D

ATC

Network economies

What do the following products have in common? Skype Sony IVE Microsoft's MSN Messenger Ojo

Network economies

They are all trying to become the leader in video calling programs

This technology has improved since the PicturePhone was unveiled in 1964

Market failure & government intervention In some of the topics this quarter,

government intervention will be justified by market failure Governments can fail, too

More in Chapter 6

Summary: More on welfare economics Welfare economics

Production possibilities Efficiency

First Fundamental Theorem Second Fundamental Theorem

Efficiency versus fairness Market failure: Market power and

nonexistence of markets

Cost-benefit analysis

We now move on to Chapter 8 for the last “tools” chapter Cost-benefit analysis

Present value Internal rate of return Benefit-cost ratio Discount rates and valuing public projects Valuing intangibles Tactics used to make a project look more or less desirable Distribution and uncertainty

Certainty equivalent value

Present value

Present value shows how much future payments are worth today Example: $100 paid today is not worth the same

as $100 paid a year from now Lost interest in safe investments

Using future value to derive present value Suppose we put $1,000 into the bank today,

earning 1% per year on it Value today: $1,000 Value 1 year from now: $1,010

$1,000 * (1 + 0.01) Value 2 years from now: $1,020.10

$1,000 * (1 + 0.01)2

$1,010 * (1 + 0.01)

Projecting Future Dollars into the Present If we multiply to get future value, we divide to find present

value of a future payment

R0 = $1000

R1 = $1000*(1+.01) = $1010

R2 = $1010*(1+.01) = $1020.10

R2 = $1000*(1+.01)2 = $1020.10

RT = R0*(1+r)T

R0 = RT/(1+r)T Present Value

discount ratediscount factor

Present Value of a Stream of Money

PV RR

r

R

r

R

rT

T

01 2

21 1 1( ) ( ). . .

( )

Present value, permanent annual payment Special case

Present value of an annual payment of R every year forever (starting today), when the annual interest rate is r :

r

RPV

Cost-benefit analysis

Welfare economic theory framework Find present value of benefits and costs If benefits exceed costs, the project should be

done Information for cost-benefit analysis is often

difficult to obtain

Cost-benefit analysis

Present value criteria When there are two mutually exclusive projects,

the preferred project is the one with the highest net present value (assuming it is positive)

What about “fairness?”

Factoring in inflation

Unless otherwise mentioned, we assume costs and benefits are in real terms Real costs and benefits account for inflation

When costs and benefits are in nominal terms, inflation must be factored in

Note that we get same result, once we cancel inflation terms

PV RR

r

R

r

R

r

TT

T T

0

12

22 2

1

1 1

1

1 1

1

1 1

( )

( )( )

( )

( ) ( ). . .

( )

( ) ( )

Private Sector Project Evaluation Comparing two projects

R&D project Advertising project

Choice depends on interest rate (see bolded #s)

Annual Net Return PV

Year R&D Advertising r = R&D Advertising

0 -$1,000 -$1,000 0 $150 $200

1 600 0 0.01 $128 $165

2 0 0 0.03 $86 $98

3 550 1,200 0.05 $46 $37

0.07 $10 -$21

Internal rate of return

The internal rate of return is the discount rate needed to make the present value of a project equal to zero

0)1(

...)1(1 2

221100

TTT CBCBCB

CB

Internal rate of return versus NPV Note that internal rate of return does not necessarily

imply which project to do Project X has the higher internal rate of return Project Y has the higher present value Do Y

Project Year 0 Year 1 ρ Profit PV

X -$100 $110 10% $4 3.77

Y -$1,000 $1,080 8% $20 18.87

Assume 6 percent interest rate in calculating profit

Benefit-cost ratio

Benefit-cost ratio is simply B / C If this ratio is greater than one, then benefits

exceed costs The project is worth considering when the benefit-

cost ratio exceeds one We should only use benefit-cost ratios to

determine if a project is worth considering Use present value criteria to determine which

project gets done

Public projects

What should public discount rate be? Depends on how much private sector consumption and

investment change Example

One-fifth of funds come at the expense of consumption, with discount rate of 10 percent

Four-fifths of funds come at the expense of investment, with discount rate of 15 percent

Public sector discount rate is one-fifth of 10 percent, plus four-fifths of 15 percent, or 14 percent

Public projects in practice

Government conducts two separate analyses to determine costs and benefits 7 percent

More in line with example on previous slide 3 percent

Lower investment rate used to increase concern for: Future generations Individuals with discount rates that are “too high” Externalities of R&D

Valuing public benefits and costs There are many ways to value public benefits

and costs Market prices Adjusted market prices and shadow prices

Problems due to monopoly Problems due to taxes Problems due to unemployment

Consumer surplus Economic behavior

Value of time Value of life

Market prices

Market price is a good measure of marginal social cost if the market is perfectly competitive with no government intervention Problem: Many markets have market power

Adjusted market prices

There are instances in which social marginal cost is not clear Underlying social MC is known as shadow price

Examples where social MC is not clear Monopoly: Market power controls price Taxes: Taxes change price Unemployment: Lack of employment makes

valuing a worker’s skills difficult

Consumer surplus

Decisions by a single firm typically have minimal consequences on a market

Prices often change substantially with some government projects Consumer surplus

can also change substantially with the implementation of government projects

Pounds of avocadosper year

Pric

e pe

r po

und

of a

voca

dos

Da

Sad

A0

Sa’

$1.35

$2.89b

c g

A1

e

Increased CS when price drops from $2.89 to $1.35 per pound

Economic behavior

Some things that are valuable are not formally traded Time

“Time is money” for each person Convenience

Driving versus public transit Life

How much is a life worth? Lost earnings and value of leisure time Probability of death versus wages in dangerous industries

Valuing intangibles

Some consumption is very hard to put a value on Space exploration Beautiful views National security Fireworks shows

Although benefits are difficult to measure, costs can still be minimized given a set of goals

Games cost-benefit analysts play The Chain-Reaction Game

Secondary benefits counted Secondary costs not counted

The Labor Game Some politicians count job creation as a benefit Wages are costs, not benefits

The Double-Counting Game Example: Value of land plus rent from land Only one can be counted as a benefit, since land

can either be sold or rented

Distribution and “fairness”

Hicks-Kaldor criterion A project should be undertaken if it has positive

net present value, regardless of distributional consequences

Social welfare criterion A project should be undertaken if it improves

overall social welfare Bill Gates example

Uncertainty

Actual results of a public project are not certain Errors can occur

Mars orbiter disaster in 1999, due to conversion failure “Earthquake-safe” technology

The benefits are often not known until tested by a big earthquake

Benefits are also uncertain if we don’t know when the next “big one” is

Certainty equivalent

If people were risk neutral, utility would be linear

Most people are risk averse Concave utility function Expected utility of a gamble is less than the utility

of the expected value More on uncertainty in Chapter 9

Calculating the Certainty Equivalent Value

75% probability of gaining y

Summary: Cost-benefit analysis Cost-benefit analysis is used to determine

which projects have higher costs than benefits With limited resources, we do projects with

highest net present values Costs and benefits are not always easy to

calculate Uncertainty is important when people are risk

averse