1. Civil Systems Planning Benefit/Cost Analysis
Scott Matthews /

2. Admin Issues
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Installation in CEE cluster continues
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Quick demo/recap of TopRank plugin
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3. 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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4. 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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5. 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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6. ? Given this graph, how can We describe the ‘set of all
$100
Given this graph, how can
We describe the ‘set of all
Possible splits between 2 people
That allocates the entire $100? ?
$100
and

7. $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
and

8. $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
$25
and

9. $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
$25
$75
$100
and

10. We said initial alloc. mattered - e.g. (100,0)?
$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
$25
and

11. 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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12. 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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13. 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
and

14. 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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15. Three Legs to Stand On Pareto Efficiency Kaldor-Hicks
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
and

16. Welfare Economics Concepts
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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17. (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* Q* A B
Actually an inverse
demand curve (where
P = f(Q) instead).
and

18. Social WTP (i.e. market demand)
Price
Quantity P* 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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19. Total/Gross/User Benefits
Price
Quantity P* Q* A B P1
Benefits received are related to WTP - and approximated by the shaded rectangles
Approximated by whole area under demand: triangle AP*B + rectangle 0P*BQ*
and

20. Benefits with WTP
Price
Quantity P* 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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21. Net Benefits
Price
Quantity P* Q* A B A 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)
and

22. Consumer Surplus Changes
Price
CS1 A P* B P1
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
and

23. Consumer Surplus Changes
Price A
CS2 P* B P1
Q* Q1
Quantity
CS2 is new cons. surplus as price decreases to (P1, Q1); consumers gain from lower price
Change in CS = P*ABP1 -> net benefits
Area : trapezoid = (1/2)(height)(sum of bases)
and

24. Consumer Surplus Changes
Price A
CS2 P* B P1
Q* Q1
Quantity
Same thing in reverse. If original price is P1, then increase price moves back to CS1
and

25. Consumer Surplus Changes
Price A
CS1 P* B P1
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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26. 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)*(a+bq)/q =(a/bq) + 1
and

27. 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 $ Estimate Total Willingness to Pay.
and

28. 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 = or 2.0 x 10^-4
and

29. Demand Example (cont) Maglev Demand Function:
p = *q
Revenue: $1.2*20,000 = $ 24,000 per day
TWtP = Revenue + Consumer Surplus
TWtP = pq + (a-p)q/2 = 1.2*20,000 + ( )*20,000/2 = 24, ,000 = $ 64,000 per day.
and

30. Change in Fare to $ 1.00
From demand curve: 1.0 = q, 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, *20,000 = 21, ,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.
and

31. BCA Part 2: Cost Welfare Economics Continued
The upper segment of a firm’s marginal cost curve corresponds
to the firm’s SR supply curve. Again, diminishing returns occur.
Price
At any given price, determines
how much output to produce to
maximize profit
Supply=MC
AVC
Quantity
and

32. 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
Supply=MC
Price P*
PS* P1
PS1
TVC*
TVC1
Quantity
Q Q*
Producer Surplus = Economic Profit
and

33. Example Demand Function: p = 4 - 3q Supply function: p = 1.5q
Assume equilibrium, what is p,q?
In eq: S=D; 4-3q=1.5q ; 4.5q=4 ; q=8/9
P=1.5q=(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
and

34. 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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35. Allocative Efficiency
Allocative efficiency occurs when MC = MB (or S = D)
Equilibrium is max social surplus - prove by considering Q1,Q2
Price S
= MC b P*
D = MB a Q1 Q* Q2
Quantity
Is the market equilibrium Pareto efficient?
Yes - if increase CS, decrease PS and vice versa.
and

36. Further Analysis Assume price increase is because of tax
Old NB: CS2
New NB: CS1
Change:P2ABP* A
CS1 P2 B C P*
Q 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 gov’t
To society overall , no effect
Pay taxes to gov’t, get same amount back
But we only get yellow part..
and

37. Deadweight Loss Yellow paid to gov’t as tax
Price A
CS1 P2 B P*
Q* Q1
Quantity
Yellow paid to gov’t as tax
Green 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
and

38. 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
and