1 civil systems planning benefit/cost analysis scott matthews 12-706 / 19-702
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1
Civil Systems PlanningBenefit/Cost Analysis
Scott Matthews12-706 / 19-702
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Quick demo/recap of TopRank plugin12-706 and 73-359 2
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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
$1000
Given this graph, how canWe describe the ‘set of all Possible splits between 2 peopleThat allocates the entire $100??
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$100
$1000
Line is the ‘set of all possible splits that allocates the entire $100, Also called the potential pareto frontier. Is the line pareto efficient?
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$100
$1000
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
$25
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$100
$1000
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?
$25
$25
$75
$75
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$100
$1000
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
$25
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Pareto Efficiency and CBA
If a policy has NB > 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 MEdges ‘pay off’ middle , still better offOnly 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 Can’t 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 offPotential 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 > 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 EconomicsConceptsPerfect 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
Price
Quantity
P*
0 1 2 3 4 Q*
A
B
Actually an inverse demand curve (whereP = f(Q) instead).
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Social WTP (i.e. market demand)
Price
Quantity
P*
0 1 2 3 4 Q*
A
B
‘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 BenefitsPrice
Quantity
P*
0 1 2 3 4 Q*
A
B
Benefits received are related to WTP - and approximated by the shaded rectangles
Approximated by whole area under demand: triangle AP*B + rectangle 0P*BQ*
P1
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Benefits with WTPPrice
Quantity
P*
0 1 2 3 4 Q*
A
B
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 BenefitsPrice
Quantity
P*
0 1 2 3 4 Q*
A
BA
B
Amount ‘paid’ by society at Q* is P*, so total payment is B to receive (A+B) total benefit
Net benefits = (A+B) - B = A = consumer surplus (benefit received - price paid)
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Consumer Surplus Changes Price
Quantity
P*
0 1 2 Q* Q1
A
BP1
CS1
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
Quantity
P*
0 1 2 Q* Q1
A
BP1
CS2
CS2 is new cons. surplus as price decreases to (P1, Q1); consumers gain from lower price
Change in CS = P*ABP1 -> net benefitsArea : trapezoid = (1/2)(height)(sum of
bases)
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Consumer Surplus Changes Price
Quantity
P*
0 1 2 Q* Q1
A
BP1
CS2
Same thing in reverse. If original price is P1, then increase price moves back to CS1
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Consumer Surplus Changes Price
Quantity
P*
0 1 2 Q* Q1
A
BP1
CS1
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/bLinear curve point elasticity =(1/b)
*p/q = (1/b)*(a+bq)/q =(a/bq) + 1
€
ε =Δqq
Δpp
= pΔqqΔp
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Maglev System Example
Maglev - downtown, tech center, UPMC, CMU
20,000 riders per day forecast by developers.
Let’s 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 - 0.0002*q
Revenue: $1.2*20,000 = $ 24,000 per day
TWtP = Revenue + Consumer Surplus TWtP = pq + (a-p)q/2 = 1.2*20,000 +
(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 -0.3*16.7 = 5.001% to 21,002 (slightly different value)
Change to Revenue = 1*21,000 - 1.2*20,000 = 21,000 - 24,000 = -3,000.
Change CS = 0.5*(0.2)*(20,000+21,000)= 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 firm’s marginal cost curve correspondsto the firm’s SR supply curve. Again, diminishing returns occur.
Quantity
Price
Supply=MCAt any given price, determineshow much output to produce tomaximize profit
AVC
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Market Supply Curves
Quantity
Price Supply=MC
P1
Q1 Q*
• 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
P*
PS1
PS*
TVC1TVC*
Producer Surplus = Economic Profit
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Example
Demand Function: p = 4 - 3qSupply function: p = 1.5qAssume equilibrium, what is p,q?In eq: S=D; 4-3q=1.5q ; 4.5q=4 ;
q=8/9P=1.5q=(3/2)*(8/9)= 4/3CS = (0.5)*(8/9)*(4-1.33) = 1.19PS = (0.5)*(8/9)*(4/3) = 0.6
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Social SurplusSocial Surplus = consumer surplus + producer surplusIs difference between areas under D and S from 0 to Q*Losses in Social Surplus are Dead-Weight Losses!
Q
P
Q*
P*
S
D
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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
Q*
P*
S
D = MB
= MC
Q1 Q2
a
bPrice
Quantity
Is the market equilibrium Pareto efficient?Yes - if increase CS, decrease PS and vice versa.
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Further Analysis
Assume price increase is because of taxTax is P2-P* per unit, tax revenue =(P2-
P*)Q2Tax revenue is transfer from consumers to
gov’t To society overall , no effect Pay taxes to gov’t, get same amount back
But we only get yellow part..
Price
Quantity
P2
0 1 2 Q2 Q*
A
BP*
CS1
C
Old NB: CS2
New NB: CS1
Change:P2ABP*
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Deadweight Loss
Yellow paid to gov’t as taxGreen is pure cost (no offsetting
benefit) Called deadweight loss Consumers buy less than they would w/o
tax (exceeds some people’s WTP!) - loss of CS
There will always be DWL when tax imposed
Price
Quantity
P2
0 1 2 Q* Q1
A
BP*
CS1
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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 don’t get all of CS loss back
OR.. NSB= (-P2ABP*)+ P2ACP* = -ABC