1 Civil Systems Planning Benefit/Cost Analysis Chapters 3 and 4 Scott Matthews Courses: 12-706 and 73-359 Lecture 5 - 9/15/2004

1

Civil Systems PlanningBenefit/Cost Analysis

Chapters 3 and 4Scott MatthewsCourses: 12-706 and 73-359Lecture 5 - 9/15/2004

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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)

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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)

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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.

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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

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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

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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)

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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?

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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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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

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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

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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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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.

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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?

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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?

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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?

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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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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?

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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

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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

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Q

P

Q0

P0

S+q’

D

S

P1

Q1

Change in CS is P0abP1 (gain)What about PS?

a

b

Q2

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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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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

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Q

P

Q0

P0

S+q’

D

S

P1

Q1

Government gains revenue Q2cbQ1, so NSB = Q2cabQ1

a

bc

Q2

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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

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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

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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?

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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

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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

Documents

1 Civil Systems Planning Benefit/Cost Analysis Chapters 3 and 4 Scott Matthews Courses: 12-706 and 73-359 Lecture 5 - 9/15/2004