Civil Systems Planning
Benefit/Cost Analysis
Scott Matthews
12-706/19-702 / 73-359
Lecture 9
1
Revisiting HW 2, Question 2
(Dam)
Thanks to Ryan and Jenny..
Their argument “should stop doing the project when
the yearly PV goes negative”; year 45 instead of 66
This is a “social cash flow” problem
Should use continuous discounting, but that’s not
concern here
Part a (no concerns) show to keep adding rows until
NPV (cumulative) goes to 0
Use cumulative NPV to automate/avoid doing 25 separate
NPV worksheets
But in reality, what the cumulative says is what NPV “up to
year n” would have been had we done a separate worksheet
Our rule is “select project
as73-359
long as NPV > 0”
12-706 and
2
HW 2, Q2 (cont)
Part b just has different discount rates..
(no big deal)
Still - same basic framework applies. Finding
NPVs to use our “rule”, but using cumulative
NPV to help see when it would have gone to
zero (if had done 45-66 separate worksheets)
12-706 and 73-359
3
Revisiting old problem..
t
At
At
8% (Operation) (Loan 8%)
0
-22,000
10,000
1
10,000
-2,505
2
8,000
-2,505
3
6,000
-2,505
4
2,000
-2,505
5
0
-2,505
1,750
NPV
1542
-2
Dt
It
8,800
5,280
3,168
1,901
851
Tt
800
200
664
1028
516
1158
357
121
185 -18.18
Yt
-12,000
7,295
4,467
2,337
-376
-1,987
1,750
PV of Yt
Cum NPV
-12,000
6,755
3,830
1,855
-276
-161
-12,000
-5,245
-1,416
439
163
2
2
2
I changed At cash streams to be non-uniform, and decreasing
Would we do this project with information above? Eg 5 years?
Does the fact that PV “goes negative” in year 4 matter?
12-706 and 73-359
4
Last thoughts
Had we done separate worksheets to test
NPV for each year 25 to 66, we would
have found a positive NPV.
That is our decision rule for accepting
projects.
12-706 and 73-359
5
Monopoly - the real game
One producer of good w/o substitute
Not 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
6
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
7
Monopoly Analysis
MC
In perfect competition,
Equilibrium was at
(Pc,Qc) - where S=D.
But a monopolist has a
Function of MR that
Does not equal Demand
Pc
So where does he supply?
MR
Qc
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D
8
Monopoly Analysis (cont.)
MC
Pm
Monopolist supplies
where MR=MC for
quantity to max.
profits (at Qm)
But at Qm, consumers
are willing to pay Pm!
Pc
What is social surplus,
Is it maximized?
Qm
MR
Qc
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D
9
Monopoly Analysis (cont.)
MC
What is social surplus?
Orange = CS
Yellow = PS (bigger!)
Pm
Grey = DWL (from not
Producing at Pc,Qc) thus
Soc. Surplus is not
maximized
Pc
Qm
MR
Qc
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Breaking monopoly
D Would transfer DWL to
Social Surplus
10
Natural Monopoly
Fixed costs very large relative to variable costs
Ex: public utilities (gas, power, water)
Average costs high at low output
AC usually higher than MC
One 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
11
Natural Monopoly
Faced with these curves
Normal monop would
Produce at Qm and
Charge Pm.
a
Pm
We would have same
Social surplus.
d
P*
b
Qm
MR
e
AC
c
MC
Q*
12-706 and 73-359
But natural monopolies
Are regulated.
D What are options?
12
Natural Monopoly
Forcing the price P*
Means that the social
surplus is increased.
DWL decreases from
abc to dec
a
Pm
d
P*
b
Qm
MR
e
Society gains adeb
AC
MC
c
D
Q*
12-706 and 73-359
Q0
13
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
14