1 Civil Systems Planning Benefit/Cost Analysis Chapter 4 Scott Matthews Courses: 12-706 and 73-359 Lecture 6 - 9/20/2004.

1

Civil Systems PlanningBenefit/Cost Analysis

Chapter 4Scott MatthewsCourses: 12-706 and 73-359Lecture 6 - 9/20/2004

12-706 and 73-359 2

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 3

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 4

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 5

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

12-706 and 73-359 6

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 7

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

12-706 and 73-359 8

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

12-706 and 73-359 9

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

12-706 and 73-359 10

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

12-706 and 73-359 11

Pollution (Air or Water)

Q

P

Q#

P#

S*: marginalPrivate costs

D

S#:marginalSocial costs

P*

Q*

Typically supply (MC) only private, not social costs. Social costs higher for each quantity

What do these curves, Equilibrium points tell us?

12-706 and 73-359 12

What is WTP by society to avoid?

Q

P

Q#

P#

S*: marginalPrivate costs

D

S#:marginalSocial costs

P*

Q*

Typically supply (MC) only private, not social costs. Social costs higher for each quantity

12-706 and 73-359 13

What is WTP by society to avoid?

Q

P

Q#

P#

S*: marginalPrivate costs

D

S#:marginalSocial costs

P*

Q*

Differences in cost functions represent thealternative ‘valuations’ of the product -Thus difference between themWTP to avoid costs

12-706 and 73-359 14

Pollution (Air or Water)

Q

P

Q#

P#

S*: marginalPrivate costs

D

S#:marginalSocial costs

P*

Q*

Relatively too much gets produced,At too low of a cost - how to Reduce externality effects?

DWL

12-706 and 73-359 15

Pollution (Air or Water)

Q

P

Q#

P#

S*: marginalPrivate costs

D

S#:marginalSocial costs

P*

Q*

Government can charge a tax ‘t’ on Each unit, where t = distance betweenWhat are CS, PS, NSB?

t

12-706 and 73-359 16

Pollution (Air or Water)

Q

P

Q#

P#

S*: marginalPrivate costs

D

S#:marginalSocial costs

P*

Q*

CS = (loss) A+BPS=(loss) E+F

t

P# - t

A B

E F

12-706 and 73-359 17

Pollution (Air or Water)

Q

P

Q#

P#

S*: marginalPrivate costs

D

S#:marginalSocial costs

P*

Q*

Third parties: (gain) B+C+F(avoided quantity between S curves) Govt revenue: A+ETotal: gain of C

t

P# - t

B

F

CA

EC is reduced DWLof pollution eliminated by tax**

**This cannot be a perfect reduction in practice - need to consideradministrative costs of program

12-706 and 73-359 18

Distorted Market - Vouchers

Example: rodent control vouchers Give residents vouchers worth $v of cost Producers subtract $v - and gov’t pays

themLikely have spillover effects

Neighbors receive benefits since less rodents nearby means less for them too

Thus ‘social demand’ for rodent control is higher than ‘market demand’

12-706 and 73-359 19

Distortion : p0,q0 too low

Q

P

Q0

P0

S-v

DM

S

DS: represents higher WTPfor rodent control

P1

Q1

What is NSB? What are CS, PS?

SocialWTP

12-706 and 73-359 20

Social Surplus - locals

Q

P

Q0

P0

S-v

DM

S

DSP1

Q1

B

P

E

P1+vA C

Make decisions based on S-v, DmWhat about others in society, e.g. neighbors?

Because of vouchers,Residents buy Q1

12-706 and 73-359 21

Nearby Residents

Q

P

Q0

P0

S-v

DM

S

DS

P1

Q1

B

P

E

P1+vA C

Added benefits are area between demandabove consumption increaseWhat is cost voucher program?

F

G

12-706 and 73-359 22

Voucher Market Benefits

Program cost (vouchers):A+B+C+G+E ----

Gain (CS) from target pop: B+EGain (CS) in nearby: C+G+FProducers (PS): A+C---------Net: C+F

12-706 and 73-359 23

Notes about Public Spending

Resource allocation to one project always comes at a ‘cost’ to other projects E.g. Pittsburgh stadium projects “Use it or Lose it” There is never enough money to go around

Thus opportunity costs exist Ideally represented by areas under supply curves Do not consider ‘sunk costs’ Three cases (we will do 2, see book for all 3)

12-706 and 73-359 24

Opportunity Cost: Land

Q

P

D

b

Price

• Case of inelastic supply (elastic supply in book, trivial)• Government decides to buy Q acres of land, pays P per acre• Alternative is parceling of land to private homebuyers• What is total cost of project?

S Can assume quantityof land is fixed (Q)

12-706 and 73-359 25

Opportunity Cost: Land

Q

P

D

b

Price

Government pays PbQ0, but society ‘loses’ CS that theywould have had if government had not bought land. This lostCS is the ‘opportunity cost’ of other people using/buying land.• Total cost is entire area under demand up to Q (colored)

S

0

12-706 and 73-359 26

Example: Change in Demand for Concrete Dam Project

If Q high enough, could effect market Shifts demand -> price higher for all buyers Moves from (P0,Q0) to (P1,Q1).. Then??

Q0

P0

D

a

Price

Quantity

D+q’

S

P1

Q1

12-706 and 73-359 27

Another Example: Change in Demand

Original buyers: look at D, buy Q2 Total purchases still increase by q’ What is net cost/benefit to society?

Q0

P0

D

a

Price

Quantity

D+q’

S

P1

Q1Q2

12-706 and 73-359 28

Another Example: Change in Demand

Project spends B+C+E+F+G on q’ units Project causes change in social surplus! Rule: consider expenditure and social surplus change

Q0

P0

DPrice

Quantity

D+q’S

P1

Q1Q2

E

B C FA

GG

G

12-706 and 73-359 29

Dam Example: Change in DemandDecrease in CS: A+B (negative) Increase in PS: A+B+C (positive)

Net social benefit of project is B+G+E+F

Q0

P0

DPrice

Quantity

D+q’S

P1

Q1Q2

E

B C FA

GG

G

12-706 and 73-359 30

Final Thoughts: Change in Demand

When prices change, budgetary outlay does not equal the total social cost Unless rise in prices high, C negligible

So project outlays ~ social cost usually Opp. Cost equals direct expenditures adjusted by social surplus changes

Quantity

12-706 and 73-359 31

Secondary Markets

When secondary markets affected Can and should ignore impacts as long

as primary effects measured and undistorted secondary market prices unchanged

Measuring both usually leads to double counting (since primary markets tend to show all effects)

12-706 and 73-359 32

Primary: Fishing Days

Q1

P

D

Price

Government decides to buy Q acres of land, pays P per acreWhat is total cost of project?

b

a

Q0

MC0

MC1