15.11.2023 Cost Benefit Analysis#

CBA: Comparison of Costs / Benefits of public goods / projects to decide if they should be undertaken

Measuring Costs#

Example Costs:

  • Capital Costs

  • Operation C.

  • Maintenance C.

  • Non-Monetary C.

but very important:

  • Opportunity Costs!

  • Rents

Opprotunity Costs in imperfect markets#

  • Project Hours = 500.000

  • project wage = 25$

  • but real comp. wage = 20$

\[ Opportunity \ Cost = hours * comp. wage = 10.000.000 \]

Discounting#

how to count costs over time? discount value

\[ PDV = \frac{ F_1 }{1+r}+\frac{ F_2 }{(1+r)^2}+\frac{ F_3 }{(1+r)^3}+... \]

Choice of r = very important

  • 1% UBA

  • 7% US Government

Measuring Benefits#

Value of Time Savings#

Approaches;

  • Martket based = wages

    • time savee = valuet at wage

    • problems: nonmonetary aspects of job

  • survey based

    • hypothetical questions

    • embedding effect = difficulty to value things in larger context

    • people dont know their valuations

  • revealed preferences

    • market prices = reveal the individual preferences

    • bias problem

Types of Revealed Preferences

  • Hedonic Market Analysis = regression with a lot of controls

  • Natural Experiments = naturally occuring variation in prices, how much people want to wait

    • e.g.: different prices at gas stations, but longer queues

Value of Lives saved#

= most difficult issue

Approaches:

  • Market based (lifetime wages)

    • poorer people = worth less

    • older people = worth less

  • survey based (value of statistical life)

    • ask for willingness to pay for certain risk

  • revealed preferences

    • compensating differential = higher wages for deadlier jobs (coal miners)

    • Problems:

      • Information

      • Probabilities

      • Bias

      • Heterogenity

Example Project

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Issues#

  • Counting Mistakes

  • Uncertainty (gov prefer certain projects = no risk = lower returns)

  • Distributional Concerns (Costs and Benefits to different people)

Alternative:

Cost-Effectiveness Analysis: projects with immeasurable benefits => most effective project for goal

Critique of CBA#

not part of the lectrúre, but very important (Wiki-Link)

Distribution

  • no account of dsitribution issues

  • only net-benefit for all people (Kaldor Hicks)

  • utilitarian approach (1$ for 1 million people worse than 2 million to one person)

Discounting

  • discounting value of benefits to future generations

  • ignore preferences of future generation

Marginal Utility

  • rich people = lower marginal utility

  • no symmetry in agents

Exercise#

Exercise 3: City of Metropolia

Example:

  • new Metro,

  • Commuters save 15 min driving time, 5 days a week, 50 weeks

  • Housing Price goes up 10000€

  • Discount Rate 5%

Math

  • Hours saved (valued today): \(15*5*50 = 3750 min = 62.5h\)

  • Present Discount Value: \(\frac{ 62.5 }{0.05}\)

  • set equal to house price increase: \(\frac{ 62.5 }{0.5}= 10000 \to 8\)

  • Value of hour saved = 8

Exercise 4

  • Country A: risk of death = 1/20000, Cost = 5000€

  • Country B: risk of death = 1/30000, Cost = 5600€

Value of Life:

  • Risk Difference \(\frac{ 1 }{20000}- \frac{ 1 }{30000} = \frac{ 1 }{60000}\)

  • Willingness to pay: 600$

  • Value of Life: \(\frac{ 600 }{1/60.000} = 36.000.000\)

Exercise 5: Jellystone Park

  • City A: Price=5, Quantity = 10

  • City B: Price= 10, Quantity = 5

Calculate individual demand curve:



a*5+b = 10
a*10+b= 5

a*10+b = a*5+b-5

5a = -5
a = -1

-10 +b = 5 
b = 15

=> -1x+15 = p

img

Consumer Surplus $\( \frac{ (Price_{intercept} - Price_{market}) * Quantity}{2} \)$

  • City A: \(\frac{ (15-5) *10}{2} = 50\)

  • City B: 12.5

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