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Conclusion of “tools” chapters
Today: Welfare economics
Some cost-benefit analysis tools
Certainty equivalent value
Administrative issues
Crashers? I do have add codes (updated from posted lecture
slides) Talk to me after class
Administering tests If you qualify for an exception on taking any of the
tests, see syllabus for more details
Last week
Introduction to Econ 130 and public finance Read syllabus if you have not done so
Chapter 1 What is public finance?
Parts of Chapter 2 Empirical tools to test theory
Tiebout model “Voting with your feet”
Today
Conclusion of our “tools” chapters Welfare economics
Pure exchange economy Pareto improvements
Market failure Common in markets we will be examining this quarter
Cost-benefit analysis What projects should be done?
Certainty equivalent value How much money are risk-averse people willing to give
up to get a sure thing?
Before we start…
Why is trade beneficial? Econ 1 answer: Comparative advantage Another possibility
You did not get the right bundle allotted to you
Welfare economics
Begin study using Edgeworth boxes Pure exchange economy
R/G chapter 3 For an in-depth look, see also Varian’s Intermediate
Micro book, chapters 30-33
Edgeworth boxes
Simple study of distribution We will make extensive use of Edgeworth boxes,
Pareto efficiency, and Pareto improvements Edgeworth boxes are used for a two-person
economy Bottom left of Edgeworth box is origin for one person Top right of Edgeworth box is origin for other person
Edgeworth Box
Edgeworth Box
Adam
Eve
0
0’
s
r
Apples per year
Fig
leav
es p
er y
ear
vwu
y
x
Indifference curves in Edgeworth Box
Edgeworth Box
Adam
Eve
0
0’
s
r
Apples per year
Fig
leav
es p
er y
ear
A1
A2
A3
E1
E3
E2
Pareto efficiency
Nobody can be made better off without making another person worse off
In cases with “standard” indifference curves (ICs), the two ICs will be tangent to each other when Pareto efficiency is achieved
Pareto improvement
Reallocation of goods or resources that meets the following requirement At least one person is made better off without
anybody else being made worse off
Pareto efficient point: p
Edgeworth Box
Adam
Eve
0
0’
s
r
Apples per year
Fig
leav
es p
er y
ear
Ag
Ah
Ap
Eg
gh
p
A Pareto Efficient
Allocation
Points g and h are not optimal, since Adam can be made better off without making Eve worse off
Another efficient point: p1
Edgeworth Box
Adam
Eve
0
0’
s
r
Apples per year
Fig
leav
es p
er y
ear
Ag
Eg
g
p1
pEp1
A Pareto Efficient
Allocation
Here, by going from point g to point p1, Eve is being made better off without making Adam worse off
Point p2 is also Pareto efficient
Edgeworth Box
Adam
Eve
0
0’
s
r
Apples per year
Fig
leav
es p
er y
ear
Ag
Eg
g
p1
p
Ep2
Ap2
p2
• Pareto efficient
• Pareto improvement
Point p2 makes both Adam and Eve better off, relative to g
Starting from a different initial point
Edgeworth Box
Adam
Eve
0
0’
s
r
Apples per year
Fig
leav
es p
er y
ear
Ag
Eg
g
p1
p
Ep2
Ap2
p2
p3
p4
k
Contract curve
The set of all Pareto efficient points Usually goes from one person’s origin to the
other person’s origin Origin of each person is Pareto efficient
Note that efficient points may or may not be “fair” in your mind Fairness is often not a topic brought up by
economists More on “fairness” later
The Contract Curve
Edgeworth Box
Adam
Eve
0
0’
s
r
Apples per year
Fig
leav
es p
er y
ear
Ag
Eg
g
p1
p
Ep2
Ap2
p2
p3
p4
The contract curve
Moving on to production
We have found the efficient points on the consumption side
Now, let’s do the same on the production side Production possibilities curves
Production possibilities: Linear example 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 assumption: More is better
New example
Apples per year
Fig
leav
es p
er y
ear
C
C0
w
y
x z
│Slope│ = marginal rate oftransformation
A more realistic example of production possibilities is a curve with increasing marginal cost
Why increasing marginal cost Let’s go from the
vertical intercept to the horizontal intercept
As the slope gets steeper, we must give up more figs for each additional apple we can consume Opportunity cost
increases as more apples are consumed
Apples per year
Fig
leav
es p
er y
ear
C
C0
w
y
x z
¦ Slope¦ = marginal rate oftransformation
A more realistic example of production possibilities is a curve with increasing marginal cost
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 example
Picture phones Each company in this
industry is trying to become the leader in video calling programs
This technology has improved since the PicturePhone (at right) 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
Cost-benefit analysis/CE value We now move on to Chapter 8 for the last
“tools” chapter Cost-benefit analysis
Present value Internal rate of return Benefit-cost ratio Valuing public projects
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
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
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
CE Value: An example
Let our two possible incomes be $6,400 (E) and $10,000 (E + y) Each possible income has probability of 0.5 of occurring
U(x) = x½
A gamble versus a sure thing
Let our two possible incomes be $6,400 (E) and $10,000 (E + y) Each possible income has probability of 0.5 of
occurring U(x) = x½ How much money am I willing to take to be
indifferent to the above gamble?
Expected income of the gamble Recall expected value from last Wednesday’s
lecture ½ ($10,000) + ½ ($6,400) = $8,200
Expected utility of the gamble U($10,000) = 100 U($6,400) = 80 Expected utility of the gamble
½ (100) + ½ (80) = 90
Certainty equivalent value
This risk averse person will be indifferent between the following two options $10,000 with probability 0.5 and $6,400 with
probability 0.5 Some amount of money with certainty
How much?
Notice that the first option has an expected utility of 90 How much money (paid with certainty) will lead to
a utility of 90?
Certainty equivalent value
We need to find some y such that U(y) = 90 y½ = 90 y = 8100 The certainty equivalent value is 8100
Recall that the expected income of the gamble is 8200 This risk-averse person is willing to lose $100 in
expected income to remove all risk
Summary
Welfare economics is important in determining what outcomes are efficient
Market failure can occur when there are not competitive and complete markets
Cost-benefit analysis helps to determine which projects are most useful to society
Certainty equivalent value determines how much money a risk-averse person is willing to give up in order to remove risk
End of Unit 1
This concludes our tools lectures Beginning Wednesday: Unit 2
Public goods Externalities Voting Government growth Education
For Wednesday: Read Ch. 4 Public goods
See you Wednesday
What type of utility function do you think gamblers have?