1

Civil Systems PlanningBenefit/Cost Analysis

Chapters 3 and 4Scott MatthewsCourses: 12-706 and 73-359Lecture 4 - 9/9/2002

12-706 and 73-359 2

Unifying Cost and Supply

Economists learn Supply and Demand Equilibrium: where S=D

In our case, substitute cost for supply Econ: S = MC under perfect competition Perfect competition => no profits Thus market price = cost of producing

Why cost? Need to trade-off DemandUsing MC is a standard method

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Meaning of Cost Curves

Highway pricing p = f(fares, fees, travel times,

discomfort) p ~ AVC: manages usage of highway Price increase=> less users (BCA) MC pricing: more users, higher price

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Welfare Economics Continued

The upper segment of a firm’s marginal cost curve correspondsto the firm’s supply curve. Again, diminishing returns occur.

Quantity

Price Supply=MCAt any given price, determineshow much output to produce tomaximize profit

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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: additional 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

We always want to be considering opportunity costs (total asset value to society) and not accounting costs

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Supply/Marginal Cost Notes

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*

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Equilibrium Example

Demand Function: p=4-3qSupply function: p=1.5qAssume equilibrium, what is p,q?Eq=> S=D; 4-3q=1.5q ; 4.5q=4 ;

q=8/9P=1.5q=1.5*(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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Allocative Efficiency

Allocative efficiency occurs when MC = MB

Q*

P*

S

D = MB

= MC

Q1 Q2

a

bPrice

Quantity

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Social Surplus

Social Surplus = consumer surplus + producer surplusLosses in Social Surplus are Dead-Weight Losses!

Q

P

Q*

P*

S

D

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Subsidies/Target Pricing

Q*

P*

S

D

QT

a

b

d

c

PT

Price

Quantity

Allocative efficiency can only be achieved when P=MC.Assume market for corn, in initial eq’m -> what happens when government guarantees PT to farmers?

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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. But at QT , consumers only want to pay PD . This is effective market price. So PT-PD issubsidized by government policy. What is change in CS, PS?

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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?

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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. 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

The cost to society (taxpayers) is the government subsidy -So what is the overall net benefit to society?

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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, orange and yellow areas are transfers!Leakage of program is 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 D

If something other than price changes (e.g. demand more of good) Then entire demand curve shifts 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

See related problems on p. 73

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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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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

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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

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Surplus Food Example

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

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, usuallyProduce where D=ACWhy?

Qm

Pm

MC

AC

a

bc

d

e

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Natural Monopoly

MRDQ*

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