Civil Systems Planning Benefit/Cost Analysis

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Civil Systems PlanningBenefit/Cost Analysis

• Scott Matthews
• 12-706 / 19-702

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Why these Lectures?

• Very important to know who the benefits, costs
  accrue to in public (policy) analysis
• Benefit-cost analysis a simple and useful
  framework to assist with this

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Efficiency Definitions/Metrics

• Allocative - resources are used at highest value
  possible
• But welfare economics uses another..
• An allocation of goods is Pareto efficient if no
  alternative allocation can make at least one
  person better off without making anyone else
  worse off.
• Inefficient if can re-allocate to make better
  without making anyone else worse
• Assumed that decisions made with this in mind?

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A Pareto Example

• Try splitting between 2 people
• Get total (100) if agree on how to split
• No agreement, each gets only 25
• Pareto efficiency assumptions
• More is better than less
• Resources are scarce
• Initial allocation matters

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100
Given this graph, how can We describe the set of
all Possible splits between 2 people That
allocates the entire 100?
?
100
0
6
100
Line is the set of all possible splits that
allocates the entire 100, Also called the
potential pareto frontier. Is the line pareto
efficient?
100
0
7
100
No. Could at least get the status quo result
of (25,25) if they do not agree on splitting. So
neither person would accept a split giving them
less than 25. Is status quo pareto efficient?
25
100
0
25
8
100
No. They could agree on splits of (25, 30) or
(30, 25) if they wanted to - all the way to
(25,75) or (75,25). All would be pareto
improvements. Which are pareto efficient?
75
25
0
100
25
75
9
100
The pareto frontier is the set of allocations
that are pareto efficent. Try improving on
(25,75) or (50,50) or (75,25) We said initial
alloc. mattered - e.g. (100,0)?
25
100
0
25
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Pareto Efficiency and CBA

• If a policy has NB gt 0, then it is possible to
  transfer value to make some party better off
  without making another worse off.
• To fully appreciate this, we need to understand
  willingness to pay and opportunity cost in light
  of CBA.

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Willingness to Pay

• Example how much would everyone pay to build a
  mall in middle of class
• Near middle may not want traffic costs
• Further away might enjoy benefits
• Ask questions to find indifference pts.
• Relative to status quo (no mall)
• E.g. middle WTP -2 M, edges 3 M
• Edges pay off middle , still better off
• Only works if Net Benefits positive!

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Opportunity Cost

• Def The opportunity cost of using an input to
  implement a policy is its value in its best
  alternative use.
• Measures value society must give up
• What if mall costs 2 M?
• Total net WTP 1M, costs 2M
• Not enough benefits to pay opp. cost
• Cant make side payments to do it

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Wrap Up

• As long as benefits found by WTP and costs by OC
  then sign of net benefits indicated whether
  transfers can make pareto improvements
• Kaldor-Hicks criterion
• A policy should be adopted if and only if gainers
  could fully compensate losers and still be better
  off
• Potential Pareto Efficiency (line on Figure)

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Three Legs to Stand On

• Pareto Efficiency
• Make some better / make none worse
• Kaldor-Hicks
• Program adopted (NB gt 0) if winners COULD
  compensate losers, still be better
• Fundamental Principle of CBA
• Amongst choices, select option with highest net
  benefit

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Welfare EconomicsConcepts

• Perfect Competition
• Homogeneous goods.
• No agent affects prices.
• Perfect information.
• No transaction costs /entry issues
• No transportation costs.
• No externalities
• Private benefits social benefits.
• Private costs social costs.

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(Individual) Demand Curves

• Downward Sloping is a result of diminishing
  marginal utility of each additional unit (also
  consider as WTP)
• Presumes that at some point you have enough to
  make you happy and do not value additional units

Actually an inverse demand curve (where P f(Q)
instead).
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Social WTP (i.e. market demand)

• Aggregate demand function how all potential
  consumers in society value the good or service
  (i.e., someone willing to pay every price)
• This is the kind of demand curves we care about

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Total/Gross/User Benefits
P1

• Benefits received are related to WTP - and
  approximated by the shaded rectangles
• Approximated by whole area under demand triangle
  APB rectangle 0PBQ

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Benefits with WTP

• Total/Gross/User Benefits area under curve or
  willingness to pay for all people Social WTP
  their benefit from consuming sum of all WTP
  values
• Receive benefits from consuming this much
  regardless of how much they pay to get it

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Net Benefits
A
B

• Amount paid by society at Q is P, so total
  payment is B to receive (AB) total benefit
• Net benefits (AB) - B A consumer surplus
  (benefit received - price paid)

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Consumer Surplus Changes
Price
A
CS1
P
B
P1
0 1 2 Q
Q1
Quantity

• New graph - assume CS1 is original consumer
  surplus at P, Q and price reduced to P1
• Changes in CS approximate WTP for policies

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Consumer Surplus Changes
Price
A
CS2
P
B
P1
0 1 2 Q
Q1
Quantity

• CS2 is new cons. surplus as price decreases to
  (P1, Q1) consumers gain from lower price
• Change in CS PABP1 -gt net benefits
• Area trapezoid (1/2)(height)(sum of bases)

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Consumer Surplus Changes
Price
A
CS2
P
B
P1
0 1 2 Q
Q1
Quantity

• Same thing in reverse. If original price is P1,
  then increase price moves back to CS1

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Consumer Surplus Changes
Price
A
CS1
P
B
P1
0 1 2 Q
Q1
Quantity

• If original price is P1, then increase price
  moves back to CS1 - Trapezoid is loss in CS,
  negative net benefit

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Elasticity - Some Formulas

• Point elasticity dq/dp (p/q)
• For linear curve, q (p-a)/b so dq/dp 1/b
• Linear curve point elasticity (1/b) p/q
  (1/b)(abq)/q (a/bq) 1

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Maglev System Example

• Maglev - downtown, tech center, UPMC, CMU
• 20,000 riders per day forecast by developers.
• Lets assume price elasticity -0.3 linear
  demand 20,000 riders at average fare of 1.20.
  Estimate Total Willingness to Pay.

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Example calculations

• We have one point on demand curve
• 1.2 a b(20,000)
• We know an elasticity value
• elasticity for linear curve 1 a/bq
• -0.3 1 a/b(20,000)
• Solve with two simultaneous equations
• a 5.2
• b -0.0002 or 2.0 x 10-4

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Demand Example (cont)

• Maglev Demand Function
• p 5.2 - 0.0002q
• Revenue 1.220,000 24,000 per day
• TWtP Revenue Consumer Surplus
• TWtP pq (a-p)q/2 1.220,000
  (5.2-1.2)20,000/2 24,000 40,000 64,000
  per day.

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Change in Fare to 1.00

• From demand curve 1.0 5.2 - 0.0002q, so q
  becomes 21,000.
• Using elasticity 16.7 fare change (1.2-1/1.2),
  so q would change by -0.316.7 5.001 to 21,002
  (slightly different value)
• Change to Revenue 121,000 - 1.220,000
  21,000 - 24,000 -3,000.
• Change CS 0.5(0.2)(20,00021,000) 4,100
• Change to TWtP (21,000-20,000)1
  (1.2-1)(21,000-20,000)/2 1,100.

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BCA Part 2 CostWelfare Economics Continued
The upper segment of a firms marginal cost curve
corresponds to the firms SR supply curve. Again,
diminishing returns occur.
Price
At any given price, determines how much output to
produce to maximize profit
SupplyMC
AVC
Quantity
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Market Supply Curves
? Producer surplus is similar to CS -- the
amount over and Above cost required to produce a
given output level ? Changes in PS found the
same way as before
SupplyMC
Price
P
PS
P1
PS1
TVC
TVC1
Quantity
Q1 Q
Producer Surplus Economic Profit
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Example

• Demand Function p 4 - 3q
• Supply function p 1.5q
• Assume equilibrium, what is p,q?
• In eq SD 4-3q1.5q 4.5q4 q8/9
• P1.5q(3/2)(8/9) 4/3
• CS (0.5)(8/9)(4-1.33) 1.19
• PS (0.5)(8/9)(4/3) 0.6

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Social Surplus
Social Surplus consumer surplus producer
surplus Is difference between areas under D and S
from 0 to Q Losses in Social Surplus are
Dead-Weight Losses!
P
S
P
D
Q
Q
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Allocative Efficiency
Allocative efficiency occurs when MC MB (or S
D) Equilibrium is max social surplus - prove by
considering Q1,Q2
S
MC
Price
b
P
D MB
a
Q
Q1
Q2
Quantity
Is the market equilibrium Pareto efficient?
Yes - if increase CS, decrease PS and vice versa.
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Further Analysis
Price
Old NB CS2 New NB CS1 ChangeP2ABP
A
CS1
P2
B
C
P
0 1 2 Q2
Q
Quantity

• Assume price increase is because of tax
• Tax is P2-P per unit, tax revenue (P2-P)Q2
• Tax revenue is transfer from consumers to govt
• To society overall , no effect
• Pay taxes to govt, get same amount back
• But we only get yellow part..

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Deadweight Loss
Price
A
CS1
P2
B
P
0 1 2 Q
Q1
Quantity

• Yellow paid to govt as tax
• Green is pure cost (no offsetting benefit)
• Called deadweight loss
• Consumers buy less than they would w/o tax
  (exceeds some peoples WTP!) - loss of CS
• There will always be DWL when tax imposed

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Net Social Benefit Accounting

• Change in CS P2ABP (loss)
• Government Spending P2ACP (gain)
• Gain because society gets it back
• Net Benefit Triangle ABC (loss)
• Because we dont get all of CS loss back
• OR.. NSB (-P2ABP) P2ACP -ABC