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Civil Systems PlanningBenefit/Cost Analysis
Chapters 3 and 4Scott MatthewsCourses: 12-706 and 73-359Lecture 5 - 9/15/2004
12-706 and 73-359 2
Office Hours
Reminder: TA Office Hours (Paulina) Wednesdays 3-5 every week Mon/Wed 3-5 before HWs due (e.g.
today for next Monday’s HW)
12-706 and 73-359 3
Recap: 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)
12-706 and 73-359 4
Maglev Log-Linear Function
q = a*pb - From above, b = -0.3, so if p = 1.2 and q = 20,000; so 20,000 = a*(1.2)-0.3 ; a = 21,124.
If p becomes 1.0 then q = 21,124*(1)-0.3 = 21,124. Linear model - 21,000
Remaining revenue, TWtP values similar but NOT EQUAL.
12-706 and 73-359 5
Making Cost Functions
Fundamental to analysis and policiesThree stages:
Technical knowledge of alternatives Apply input (material) prices to options Relate price to cost
Obvious need for engineering/economics
Main point: consider cost of all partiesIncluded: labor, materials, hazard costs
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Commentary - Externalities
External costs SHOULD be includedMeasurement difficult, maybe impossibleTypically no market transactions to useProxy: cost of eliminating hazard createdBeware transfers / double counting!Example: Construction disrupts
commerce business not lost - just relocated in interim
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Types of Costs
Private - paid by consumersSocial - paid by all of societyOpportunity - cost of foregone optionsFixed - do not vary with usageVariable - vary directly with usageExternal - imposed by users on non-
users e.g. traffic, pollution, health risks Private decisions usually ignore external
12-706 and 73-359 8
Functional Forms
TC(q) = F+ VC(q)Use TC eq’n to generate unit costs
Average Total: ATC = TC/q Variable: AVC = VC/q Marginal: MC = [TC]/ q = TCq
but F/ q = 0, so MC = [VC]/ q
12-706 and 73-359 9
Short Run vs. Long Run Cost
Short term / short run - some costs fixed
In long run, “all costs variable”Difference is in ‘degree of control of
plans’Generally say we are ‘constrained in
the short run but not the long run’So TC(q) < = SRTC(q)
12-706 and 73-359 10
Firm Production Functions
MC
Q
P
What do marginal,Average cost curvesTell us?
AVC
Variable cost showsNon-fixed componentsOf producing the good
Marginal costs show usCost of producing oneAdditional good
Where would firm produce?
12-706 and 73-359 11
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
12-706 and 73-359 12
Supply/Marginal Cost Notes
Quantity
Price Supply=MCAt any given price, determineshow much output to produce tomaximize profit
P*
Q1 Q* Q2
Demand: WTP for each additional unitSupply: cost incurred for each additional unit
12-706 and 73-359 13
Supply/Marginal Cost Notes
Quantity
Price Supply=MCArea under MC is TVC - why?
P*
Q1 Q* Q2
Recall: We always want to be considering opportunity costs (total asset value to society) and not accounting costs
12-706 and 73-359 14
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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Unifying Cost and Supply
Economists learn “Supply and Demand” Equilibrium (meeting point): where S = D
In our case, substitute ‘cost’ for supplyWhy cost? Need to trade-off DemandUsing MC is a standard method
Recall this is a perfectly competitive world!
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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.
12-706 and 73-359 19
Subsidies/Target Pricing
Q*
P*
S
D
QT
a
b
d
c
PT
Price
Quantity
Allocative efficiency only achieved when P = social MC.Assume market for corn below in initial eq’m -> what happens when government guarantees PT to farmers? Social surplus?
12-706 and 73-359 20
Subsidies/Target Pricing
Q*
P*
S
D
QT
a
b
d
e
c
PD
PT
Price
Quantity
At PT, farmers want to supply QT units. At QT , consumers only want to pay PD . This is effective market price. So PT-PD mustbe subsidized by government policy. What is change in CS, PS?
12-706 and 73-359 21
Subsidies/Target Pricing
Q*
P*
S
D
QT
a
b
d
e
c
PD
PT
Price
Quantity
CS increases from aP*b (yellow) to aPDe (yellow+orange).
What about PS?
12-706 and 73-359 22
Subsidies/Target Pricing
Q*
P*
S
D
QT
a
b
d
e
c
PD
PT
Price
Quantity
PS also increases, from P*bc to PTdc. So is overall net benefit tosociety then positive (since PS and CS both increase)?
c
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Subsidies/Target Pricing
Q*
P*
S
D
QT
a
b
d
e
c
PD
PT
Price
Quantity
A cost to society (taxpayers) is the government subsidy -So what is the overall net benefit to society?
12-706 and 73-359 24
Subsidies/Target Pricing
Q*
P*
S
D
QT
a
b
d
e
c
PD
PT
Price
Quantity
Overall net benefit to society is (Increased CS + Increased PS) -Costs = Orange + Yellow - Grey = Triangle bde (loss!).This is a DWL, increases in CS, PS are transfers!Efficiency Measure: Leakage = Area bde/Area PTdePD
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Changes in Demand
There is a difference in ‘change in quantity demanded’ and a ‘change in demand’.
If (only) the price of good changes Change in qty demanded - move along existing D
If something other than price changes (e.g. demand more of good due to advertising) Then entire demand curve shifts (all p,q points) Same things true for supply
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Types of Markets
Primary: directly affected by policySecondary: indirectly affectedExample: new highway
Primary: commuting, traffic, pollution Secondary: change in repairs, gas
Efficient markets (as discussed)Distorted markets: when external effects
occur as a result of market Could be positive or negative
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Benefits in Efficient Market
NSB=CS+ PS + Net Gov’t Revenues
Government adds large quantity of good to market to reduce price Example: surplus food programs
Government intervenes by supplying q’ units into the market Supply curve moves out (right) - more
supplied at each price point
12-706 and 73-359 28
Surplus Food Example
Q
P
Q0
P0
S+q’
D
S
P1
Q1
Initial equilibrium at P0, Q0New eq’m at (lower)P1, (higher) Q1What is change in CS?
a
b
Q2
12-706 and 73-359 29
Surplus Food Example
Q
P
Q0
P0
S+q’
D
S
P1
Q1
Change in CS is P0abP1 (gain)What about PS?
a
b
Q2
12-706 and 73-359 30
Surplus Food Example
Q
P
Q0
P0
S+q’
D
S
P1
Q1
Change in PS is P0acP1 (loss) for the‘original suppliers’ since they stillOperate on supply curve ‘S’What is social surplus?
a
bc
Q2
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Surplus Food Example
Q
P
Q0
P0
S+q’
D
S
P1
Q1
Social surplus is net gain of CS+PS,Or the triangle abc - what isNet Social Benefit?
a
bc
Q2
12-706 and 73-359 32
Surplus Food Example
Q
P
Q0
P0
S+q’
D
S
P1
Q1
Government gains revenue Q2cbQ1, so NSB = Q2cabQ1
a
bc
Q2
12-706 and 73-359 33
Monopoly - the real game
One producer of good w/o substituteNot example of perfect comp!
Deviation that results in DWL There tend to be barriers to entry Monopolist is a price setter not taker
Monopolist is only firm in market Thus it can set prices based on output
12-706 and 73-359 34
Monopoly - the real game (2)
Could have shown that in perf. comp. Profit maximized where p=MR=MC (why?)
Same is true for a monopolist -> she can make the most money where additional revenue = added cost But unlike perf comp, p not equal to MR
12-706 and 73-359 35
Monopoly Analysis
MR D
MC
Qc
Pc
In perfect competition,Equilibrium was at (Pc,Qc) - where S=D.
But a monopolist has aFunction of MR that Does not equal Demand
So where does he supply?
12-706 and 73-359 36
Monopoly Analysis (cont.)
MRD
MC
Qc
Pc
Monopolist supplies where MR=MC for quantity to max.profits (at Qm)
But at Qm, consumersare willing to pay Pm!
What is social surplus, Is it maximized?
Qm
Pm
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Monopoly Analysis (cont.)
MRD
MC
Qc
Pc
What is social surplus?Orange = CS
Yellow = PS (bigger!)
Grey = DWL (from notProducing at Pc,Qc) thusSoc. Surplus is not maximized
Breaking monopolyWould transfer DWL toSocial Surplus
Qm
Pm
12-706 and 73-359 38
Natural Monopoly
Fixed costs very large relative to variable costs Ex: public utilities (gas, power, water)
Average costs high at low outputAC usually higher than MCOne firm can provide good or service
cheaper than 2+ firms In this case, government allows monopoly
but usually regulates it
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Natural Monopoly
MRDQ*
P*
Faced with these curvesNormal monop wouldProduce at Qm and Charge Pm.
We would have sameSocial surplus.
But natural monopoliesAre regulated.
What are options?Qm
Pm
MC
AC
a
bc
d
e
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Natural Monopoly
MR
D
Q*
P*
Forcing the price P*Means that the social surplus is increased.
DWL decreases from abc to dec
Society gains adeb
Qm
Pm
MC
AC
a
bc
d
e
Q0
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Monopoly
Other options - set P = MC But then the firm loses money Subsidies needed to keep in business
Give away good for free (e.g. road) Free rider problems Also new deadweight loss from cost
exceeding WTP
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Pricing Strategies
Highway pricing If price set equal to AC (which is assumed to
be TC/q then at q, total costs covered p ~ AVC: manages usage of highway p = f(fares, fees, travel times, discomfort) Price increase=> less users (BCA) MC pricing: more users, higher price What about social/external costs? Might want to set p=MSC
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