Cost and Benefit

Cost and Benefit

Avinash Kishore([email protected])

Based on notes from Andrew Foss

Economics 1661 / API-135

February 11, 2011Review Section

mailto:[email protected]

Agenda

Basic Econometrics

– Bi-variate regression

– Multivariate linear regression

– Special cases

Elasticity

Social Welfare Cost

Benefits

– Aggregation of Demand Curves

– Travelling Cost Method

2

Note: A good general reference on costs and benefits is EPA, Guidelines for Preparing Economic Analyses, September 2000 (link), Chapters 7 and 8

http://yosemite.epa.gov/ee/epa/eed.nsf/webpages/Guidelines.html/$file/Guidelines.pdf

Measures of Central Tendency and Dispersion

Measures of Central Tendency: Mean

– Mean = ∑Xi /n

– Mean takes all data points into account

– Mean is sensitive to outliers. Outliers have a lot of weight on

mean

Measures of Dispersion

– Variance = (Xi – mean)2/N

– Standard Deviation =[(Xi – mu)2/N]1/2 = (Variance)1/2

More dispersed data have higher variance

– Like mean, standard deviation is also sensitive to outliers

3

It is possible that two datasets have the same mean but different standard deviations

4From Wikipedia

OLS regression (2 Variables) http://www.ats.ucla.edu/stat/Stata/examples/rwg/rwgstata2/rwgstata2.htm

5Y (wateruse) = 1201.124 + 47.54*income

http://www.ats.ucla.edu/stat/Stata/examples/rwg/rwgstata2/rwgstata2.htm

Bi-variate Regression Model

Yi = β0 + β1Xi + εi

– i = each observation; Y = Dependent Variable (water use); X =

Independent Variable (income); εi = Error term

– β0 = intercept. It tells us the predicted value of Y when X = 0.

– β1 = The coefficient that tells us how Y changes for unit change

in X.

water81 Coef. Std. Err. t P>t [95% Conf. Interval]

income 47.54869 4.652286 10.22 0.000 38.40798 56.6894

_cons 1201.124 123.3245 9.74 0.000 958.8191 1443.43

– N = 496; R-square = 0.1745

3 Sources of Error Term:

– Omitted variables, Measurement error and Chance or

Randomness 6

Multiple Regression

More than one independent variables

– Yi = β0 + β1Xi1 + β2Xi

2 + β3Xi3 + εi

Now, β1 is the change in value of Y for a unit change in

X1 while holding constant (or controlling for) X2 and X3

(the marginal interpretation)

Example:. reg water81 income educat peop81 water81 Coef. Std. Err. t P>t [95% Conf. Interval]

income 32.05796 4.285087 7.48 0.000 23.63864 40.47729

educat -42.61099 17.23512 -2.47 0.014 -76.4745 -8.747484

peop81 480.5194 31.73071 15.14 0.000 418.175 542.8639

_cons 678.8889 245.195 2.77 0.006 197.1305 1160.647

N = 496, R-squared = 0.38

7

The Coefficient and the Confidence Interval (precision)

8

Some Special Cases: binary independent variables

Normally, continuous dependent and independent variables in OLS.

But we can also have binary independents. Also Dummy Variables.

– Βeta coefficient of a dummy variable is not interpreted as its slope.

Let there be a dummy variable Female s.t. Female = 1 for female

employees; 0 for male employees.

Regression equation: Earnings = β0 + β1*Female + εi

– Earnings = 16.99 – 3.45*Female + εi

Interpretation: Constant, β0 = Mean earning of men = 16.99

β1 = Difference in mean earnings of men and women. Here, β1 = -3.45. So,

mean earning of women = 16.99 – 3.45 = 13.44.

Multivariate Example:

– Earnings = β0 + β1 Years of Education + β2Female + εi

– Earnings = 15.55 + 3.00* Years of Education –3.55*Female

Show graphically 9

Special Cases: Interaction Terms

It is possible that both intercepts and slopes (returns per year of

education in this case) are different for two groups.

e.g. Earnning = β0 + β1Years of Education + β2Female + β3

Female*Years of Education + εi

So, for females: Earnings = β0 + β1Years of Education + β2*1 +

β3*1*Years of Education+ εi

= (β0 + β2) + (β1+ β3)*Years of Education+ εi

for males: Earnings = β0 + β1Years of Education + β2*0 + β3*0*

Years of Education + εi

= β0 + β1Years of Education + εi

So, for females, Slope = (β1+ β3) and Intercept = β0 + β2

For males, Slope = β1 and intercept = β0 10

We can also capture non-linear relations through linear regression

Quadratic: If the dependent variable is a parabolic

function of the independent, we can still capture the

relationship by adding a squared term, e.g.

Environmental Kuznets Curve hypothesis:

– Pollution = β0 + β1GDPPC + β2 (GDPPC)2 + εi

Categorical Dependent Variable (as in RUM)

– We get estimates of probability

– OLS is not appropriate in such cases

– Logit or probit models

11

Cost and Benefits

12

Costs Estimation Methods and Elasticity

Direct Compliance Cost Method

Partial Equilibrium Analysis (behavioral response)

General Equilibrium Analysis

Want to know how consumers and firms will react to

changes in prices for the good/service being regulated

Depends on price elasticity of supply and demand

Elasticity = % ΔQ/% ΔP = (ΔQ/Q)/ (ΔP/P) =

(ΔQ/ΔP)*(P/Q) = (1/Slope)*(P/Q)

Higher the elasticity, greater the behavioral response

to regulation and greater the social welfare cost.

13

If demand is very responsive to change in price, good is price elastic. If demand does not respond much to price changes, demand is price inelastic

14

Elasticity = ∞ Elasticity = 0

Social Welfare Costs

Illustration of social welfare costs

– Losses in consumer and producer surplus from increased

marginal cost across regulated industry

15Quantity

Price

D

MC0 = S0CS0

PS0

Quantity

Price

MC0 = S0

CS1

PS1

MC1 = S1

P0

Q0

P0

Q0

P1

Q1

Welfare Effects of Industry-Wide Increase in Marginal Cost

D

Benefits: Aggregation of Demand Curves (Private Goods)

16

Let’s say Q is a private good. Person 1 demand for Q is: Q1 = 100 – PPerson 2 demand for Q is : Q2 = 100 – PSo, what is the aggregate market demand for Q?

Algebraically, it is

QT = 200 – 2P

Note: The algebra and the graph won’t be this simple if demand functions are different

Benefits: Aggregation of Demand Curves (Public Goods)

17

Now assume Q is a public good (non-rivalrous and non-excludable)

Does that change how we aggregate demand curves?

Algebraically, it is

P = 200 – 2Q

You work with inverse demand curve

One more example: public park provision

There are 500 people in a locality

Each has demand function: Q = 100 – P

– P = $ price per unit area of park people are willing to pay for

Q sq. yards of the park preserved

– MC = $ 10,000/sq. yard

How many sq yard of park area should be preserved?

– P = 100 – Q

– Aggregate demand: P =500[100 – Q]

– or P = 50,000 – 500Q

50,000 – 500Q = 10,000, Q* = 80 sq. yards

What is the total benefit @ Q*? Net benefit = ? 18

Travel Cost Method:Example Problem

Ruritania is a country with three cities and a beautiful

park at its center

Environmental economists in Ruritania have collected

the following data on park visitors from the three cities

The environmental economists want to estimate the

recreational value (i.e., non-market use value) of the

park to the people of Ruritania

19

Origin Population Visitors Travel Cost

1 100,000 15,000 $12.50

2 750,000 75,000 $25.00

3 1,000,000 50,000 $37.50


First calculate the visitation rate for each origin

20

Origin Population Visitors Visit Rate Travel Cost

1 100,000 15,000 0.15 $12.50

2 750,000 75,000 0.10 $25.00

3 1,000,000 50,000 0.05 $37.50


Next plot the relationship between visitation rate and

travel cost and express it in an equation

21

TC = - (50 / 0.20) * R + 50 = -250 * R + 50

or

R = - (0.20 / 50) * TC + 0.2

= -0.004 * TC + 0.2$0

$10

$20

$30

$40

$50

0.00 0.05 0.10 0.15 0.20

Tra

ve

l Co

st

(TC

)

Visitation Rate (R)

Origin 3

Origin 2

Origin 1


Suppose a fee were charged to enter the park

Calculate the relationship between Origin 1’s visitation

rate and the hypothetical fee

22

R = -0.004 * (TC + Fee) + 0.2

TC1 = 12.5

R1 = -0.004 * (12.5 + Fee) + 0.2

= -0.004 * Fee + 0.15

or

Fee = -250 * R1 + 37.5

$0

$10

$20

$30

$40

0.00 0.05 0.10 0.15 0.20

Hy

po

the

tic

al F

ee

Visitation Rate (R)

Origin 1




23

R = -0.004 * (TC + Fee) + 0.2

TC2 = 25

R2 = -0.004 * (25 + Fee) + 0.2

= -0.004 * Fee + 0.10

or

Fee = -250 * R2 + 25

$0

$10

$20

$30

$40

0.00 0.05 0.10 0.15 0.20

Hy

po

the

tic

al F

ee

Visitation Rate (R)

Origin 2




24

R = -0.004 * (TC + Fee) + 0.2

TC3 = 37.5

R3 = -0.004 * (37.5 + Fee) + 0.2

= -0.004 * Fee + 0.05

or

Fee = -250 * R3 + 12.5

$0

$10

$20

$30

$40

0.00 0.05 0.10 0.15 0.20

Hy

po

the

tic

al F

ee

Visitation Rate (R)

Origin 3


Calculate the relationship between all three origins’

visitation rate and the hypothetical fee

25

R = -0.004 * (TC + Fee) + 0.2

R1 = -0.004 * Fee + 0.15

R2 = -0.004 * Fee + 0.10

R3 = -0.004 * Fee + 0.05$0

$10

$20

$30

$40

0.00 0.05 0.10 0.15 0.20

Hy

po

the

tic

al F

ee

Visitation Rate (R)

Origin 1 Origin 2 Origin 3


Calculate the relationship between the number of

visitors from Origin 1 and the hypothetical fee

26

Per capita demand function:

R1 = -0.004 * Fee + 0.15

Population = 100,000

So, demand function is: = 100,000*(-0.004 * Fee + 0.15)

= -400 * Fee + 15,000

$0

$10

$20

$30

$40

0 30,000 60,000 90,000 120,000 150,000

Hy

po

the

tic

al F

ee

Visitors (Q)

Origin 1


Calculate the relationship between the number of visitors

from Origin 2 and the hypothetical fee

27

Per capita demand function:R1 = -0.004 * Fee + 0.10

Population = 75,000

So, total demand function is: = 75,000*(-0.004 * Fee + 0.10)

Q2 = -3,000 * Fee + 75,000$0

$10

$20

$30

$40

0 30,000 60,000 90,000 120,000 150,000

Hy

po

the

tic

al F

ee

Visitors (Q)

Origin 2


Calculate the relationship between the number of

visitors from Origin 3 and the hypothetical fee

28

Per capita demand function:R1 = -0.004 * Fee + 0.05

Population = 50,000

So, total demand is: = 50,000*(-0.004 * Fee + 0.05)Q3 = -4,000 * Fee + 50,000

$0

$10

$20

$30

$40

0 30,000 60,000 90,000 120,000 150,000

Hy

po

the

tic

al F

ee

Visitors (Q)

Origin 3


– Aggregate curve (from horizontal summation) represents total

recreational demand as a function of hypothetic park fee

– 1st kink @ Fee = $25, Qagg = 5000

– 2nd kink @ Fee = $ 12.50, Qagg = 10,000 + 37,500 = 47,500

– X-intercept = 15,000 + 75,000 + 50,000 = 140,000

–

29

Q1 = -400 * Fee + 15,000

Q2 = -3,000 * Fee + 75,000

Q3 = -4,000 * Fee + 50,000

$0

$10

$20

$30

$40

0 30,000 60,000 90,000 120,000 150,000

Hy

po

the

tic

al F

ee

Visitors (Q)

Origin 1 Origin 2 Origin 3 Aggregate


Calculate recreational value as area under the

aggregate curve

– The recreational value of the park is $1,531,250

30

Area A = ½ * (37.5 - 25) * 5,000 = 31,250

Area B = ½ * (25 - 12.5) *(5,000 + 47,500)

= 328,125

Area C = ½ * (12.5 - 0) *(47,500 + 140,000)

= 1,171,875

Total Area = 1,531,250

$0

$10

$20

$30

$40

0 30,000 60,000 90,000 120,000 150,000

Hy

po

the

tic

al F

ee

Visitors (Q)

Aggregate

Area A

Area B

Area C


Calculate recreational value as area under each of the

origin-specific demand curves (alternative method)

– The recreational value of the park is $1,531,250

31

Area 1 = ½ * 37.5 * 15,000 = 281,250

Area 2 = ½ * 25 * 75,000 = 937,500

Area 3 = ½ * 12.5 * 50,000 = 312,500

Total Area = 1,531,250

$0

$10

$20

$30

$40

0 30,000 60,000 90,000 120,000 150,000

Hy

po

the

tic

al F

ee

Visitors (Q)

Origin 1 Origin 2 Origin 3

Area 1

Area 2Area 3


Calculate the number of visitors and consumer surplus

if no fee were charged to enter the park

– Total park visitation is 15,000 + 75,000 + 50,000 = 140,000

– CS is equal to recreational value: $1,531,250

32


Calculate the number of visitors and consumer surplus

if a fee of $20 were charged to enter the park

– Total park visitation is 7,000 (Or. 1) + 15,000 (Or. 2) = 22,000

– CS is area below demand curve and above price: $98,750

33

Area A = ½ * (37.5 - 25) * 5,000 = 31,250

Area D = ½ * (25 - 20) * (5,000 + 22,000) = 67,500

Total Area = 98,750$0

$10

$20

$30

$40

0 30,000 60,000 90,000 120,000 150,000

Hy

po

the

tic

al F

ee

Visitors (Q)

Aggregate

Area A

Area DFee = $20

Benefits: Mid-term 2005

The City of Miami, Florida proposes to invest in a new water reservoir for its public water

system, and estimates its cost. To justify this substantial expenditure of public funds, the

Mayor explains that if the new reservoir is not constructed then the next most costly way to

increase Miami’s water supply will be to invest in a desalinization plant, which will be even

more expensive. Hence, the Mayor explains, the social benefits of building the new reservoir

clearly exceed its social costs. There are no environmental or other externalities involved with

either alternative. How would you assess this reasoning from an economic perspective?

34

– This is the “avoided cost” method of evaluating benefits.

It is incorrect because it ignores demand for the public good

(water), i.e., water’s real benefits to the society.

AvoidedCosts

Willingnessto Pay

Willingnessto Accept

To Be Continued…

Next time: More on benefit estimation methods

35

Cost and Benefit

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