Economics 151 The Economics of the Public Sector: Expenditure

1
Economics 151 The Economics of the Public
SectorExpenditure

• Professor Nora Gordon
• Fall 2004
• Lecture 15

2
Outline for today

• Finish cost-benefit analysis
• Review for midterm 2

3
How to measure value of individuals time using
revealed preference?

• Preferences revealed through actual economic
  decisions
• Ex. Airline flight delays
• Compare prices on flight routes (ex. NY-LA) as
  delays increase
• Otherwise identical flights
• Difference in price attributed to delay
• Hedonic pricing
• One study finds ticket price falls about 3 per
  minute of delay

4
How can we value a human life?

• Market-based
• wages
• Contingent valuation
• Est. 825,000 to 22.3 million per life saved
• Revealed preference
• Airbag example
• Costs 350
• Reduces prob of death by 1 in 10,000
• Implies life valued at least 3.5 million by
  those who buy airbags
• Revealed preference consensus estimate 7
  million

5
Midterm 2 review

• Public goods
• Definition
• Efficient allocation
• Voluntary contribution equilibrium
• Political economy
• Lindahl taxes
• Majority voting Arrow, MVT
• Government failure
• Cost-benefit analysis
• Assessing costs and benefits with
• Market prices
• Contingent valuation
• Revealed preference
• Valuing future costs and benefits
• Choosing the appropriate discount rate

6
Two properties of pure public goods

• 1. Non-rival in consumption
• My consuming the public good does not affect your
  ability to consume it
• Marginal cost of another person consuming the
  good (once it is already provided) is zero
• Congestion can affect rivalry.
• 2. Non-excludable in consumption
• It is impossible to prevent anyone from consuming
  the good
• Technology can affect excludability.

7
Pareto-efficient level of public good
Pm
6
Leahs D for rockets
DLr
rockets
20
Pm
Taras D for rockets
4
DTr
rockets
Pm
Sr
10
Leah Taras D for rockets
DTLr
rockets
20
8
Conditions for Pareto optimality

• MSB MSC for public and private goods
• Private goods
• MRSLbc MRSTbc MSB
• MRTbc MSC
• so MRSLbc MRSTbc MRTbc
• Public goods
• MRSLbc MRSTbc MSB
• MRTbc MSC
• so MRSLbc MRSTbc MRTbc

9
Efficient allocation of public good

• Two roommates (A and B), identical preferences
  over carrots (pvt good) and lava lamps (pub good)
• U(C,L) ln(C) ln(L)
• Identical budget constraints
• Each has income100
• PC5, PL5.
• Total BC 5(CA CB) 5L 200
• Efficient allocation requires
• MRSALCMRSBLC MRTLC

10
Efficient allocation of public good

• MRSALCMRSBLC MRTLC
• MRSALCMUAL/MUAC
• Recall U(C,L) ln(C) ln(L)
• MUAC1/C, MUAL1/L
• MRSALCCA/L
• MRSBLCCB/L
• MRTLC PL/PC 1
• Pareto optimum CA/LCB/L 1
• BC 5(CACB)5L 200
• Rewrite BC CACB40-L
• Subst BC into PO condition to solve for L
• (CACB)/L 1
• (40-L)/L1
• 40-LL
• L20, CACB10

11
Voluntary contribution eqm

• Think of As decision as a response to Bs
• Now max Uln(20-LA)ln(LBLA)
• FOC

• This is As best response function to B.
• We know A and B are identical, so Bs best
  response to A is LB 10-LA/2
• Substitute to find eqm where both conditions
  hold
• LA 10 (10-LA/2)/2
• LA 5LA/4
• ¾LA 5 ? LA 20/3LB

12
Voluntary contribution eqm

• LA 20/3LB CACB40/3
• Is this efficient?
• Check if SMRSMRT
• Remember MRSALCCA/L and MRSBLCCB/L
• Tip MRSxyMUx/MUyf/g, meaning would trade f
  units of good y for g units of good x.
• MRSALC

? A would trade 2 carrots for a lava lamp.
SMRS224 ? together A and B would trade 4
carrots for one lava lamp MRT1 ? a lava lamp
only costs one carrot So level of lava lamps is
inefficiently low.
13
Lindahl equilibrium

• Best case scenario people reveal preferences
  truthfully given Lindahl taxes
• Announce set of tax prices (indiv-specific)
• Get all indiv i to report D for G at those tax
  prices
• Individually adjust tax prices so that all indiv
  want the same amt of G
• This is the Lindahl equilibrium (Ch. 9).
  SMRSMRT.

14
Arrows impossibility theorem

• No preference aggregation rule will translate
  individual preferences into a consistent social
  choice without either
• Restricting preferences, or
• Imposing a dictatorship
• How to restrict preferences?
• Require single-peaked preferences preferences
  with only a single local maximum, or peak, so
  that utility falls as choices move away in any
  direction from that peak

15
Why didnt voting work in case 2?
U(spending)
Jill
1st choice U
Karen
2nd choice U
Paula
3rd choice U
Spending level
L
M
H
16
Median Voter Theorem

• MVT If preferences are single-peaked, majority
  voting will yield the choice of the median voter,
  which will be the socially efficient outcome.
• Shortfall Does not reflect intensity of
  preferences