1. Look over the ranges of marginal net benefit among the projects and alternatives you are considering starting from the left hand side of the chart.
1. Initially we are at zero total investment and zero on all projects.
1. What initial investment opportunities are presented by this particular set of projects?
Four projects have a smallest scale version that comes in at $25,000: branding, cleanup, pedestrian zone, and advertising. This amount represents the smallest "chunk" of resources that we can allocate at this point. The smallest scale for three other projects is $50,000: police, trolley, and beautification. Finally, the parking garage has a smallest scale version that comes in at $125,000. Let's look at the MNB for each of these investments:

'''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at zero investment'''
Advertising 25 6
Cleanup 25 3.4
Branding 25 2.6
Pedestrian 25 2
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
Garage 125 1.4
1. What is the best return we can get for the first bit that we invest?
The highest marginal net benefit facing us WHERE WE CURRENTLY STAND (having allocated nothing to any project) is the 6 for advertising. Our research has suggested that just a little bit of expenditure on advertising will increase retail sales (and hence sales tax collection) significantly (in fact, we estimated $150,000 net benefit for a $25,000 investment). So this is where we allocate our first $25,000.
Currently, then:
'''Project''' '''Investment''' '''Net Benefit''' <rowspan="10">[[Image(MNB-all-detail-01.gif, noborder)]]
Police 0 0
Branding 0 0
Garage 0 0
Cleanup 0 0
Pedestrian 0 0
Trolley 0 0
Advertising 25 150
Clean Up 0 0
<rowbgcolor="black" colspan="3">
TOTAL 25 150
1. What are the investment opportunities we face at this point?
If we put another $25,000 into ADVERTISING we are looking at a marginal net benefit of 3, but we could do better with this $25 by investing it in CLEANUP which has a MNB of 3.4 at this point. Examination of the graph suggests there is no better place to put this next $25,000 and so our next expense is for CLEANUP. Here's a summary of the opportunity we are looking at:
<rowalign="center" tableborder="1">'''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at zero investment'''
Cleanup 25 3.4
Advertising 25 3
Branding 25 2.6
Pedestrian 25 2
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4

When we put the next $25,000 into clean up, our total investment so far looks like this:

<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit''' <rowspan="10">[[Image(MNB-all-detail-02.gif, noborder, thumb, 200)]]
Cleanup 25 85
Advertising 25 150
<rowbgcolor="black" colspan="3">
TOTAL 50 235

1. Once again, we look at the opportunities we face at this point. The highest marginal net benefit belongs to investing another 25,000 in advertising.

<rowalign="center" tableborder="1">'''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
Advertising 25 3
Branding 25 2.6
Pedestrian 25 2
Cleanup 25 1.6
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
We can expect to achieve a net benefit of $75,000 from this investment and so we make this investment and find ourselves in the following situation:
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 25 85
Advertising 50 225
<rowbgcolor="black" colspan="3">
TOTAL 75 310

1. What kind of opportunities are we looking at now?

<rowalign="center" tableborder="1"> '''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
<rowalign="center" rowspan="10">[[Image(MNB-all-detail-03.gif, noborder, thumb, 400)]] align="left">Branding 25 2.6
Pedestrian 25 2
Cleanup 25 1.6
Advertising 25 1.2
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
From the chart we see that branding is the best place for my next dollar of investment and that I should spend an initial $25,000 on this with an expected net benefit of $80,000. My tally of where my money has gone now looks like this:
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 25 85
Advertising 50 225
Branding 25 80
<rowbgcolor="black" colspan="3">
TOTAL 100 390
And the marginal net benefit rates we are looking at is this:
<rowalign="center" tableborder="1"> '''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
<rowalign="center" rowspan="10">[[Image(MNB-all-detail-04.gif, noborder, thumb, 400)]] align="left">Pedestrian 25 2
Cleanup 25 1.6
Advertising 25 1.2
Branding 25 1
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
1. What now?
The best place for the next dollar is the pedestrian zone project where a $25,000 investment looks like it will return a net benefit of twice what we invest or $50,000 in sales tax revenue. After we allocate this money our tally is
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 25 85
Advertising 50 225
Branding 25 80
Pedestrian 25 50
<rowbgcolor="black" colspan="3">
TOTAL 125 440
and we are left looking at this
<rowalign="center" tableborder="1"> '''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
<rowalign="center" rowspan="10">[[Image(MNB-all-detail-05.gif, noborder, thumb, 400)]] align="left">Pedestrian 25 2.4
Cleanup 25 1.6
Advertising 25 1.2
Branding 25 1
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
1. There something "special" about what we are looking at. What is it?
The MNB line for the pedestrian zone project is above all the others for the next $175,000 of investment! This means that each of our next several decisions are going to be in favor of the pedestrian zone project.
[[Image(MNB-all-detail-06.gif, noborder)]]
And when we've done this, here is where things will stand:
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 25 85
Advertising 50 225
Branding 25 80
Pedestrian 200 600
<rowbgcolor="black" colspan="3">
TOTAL 300 990
1. So where do things stand now? What should we do next? Let's look at the entire chart and write down what our next investment opportunities look like.
[[Image(MNB-all-full-12.gif, noborder)]]
There is a temptation to look at the peak in the trolley line — it's a promising marginal net benefit of 3. BUT, that's not "where we are" on that project. At this point we have allocated nothing to the trolley project and so the MNB we are looking for it is all the way over on the left side of the chart. The initial investment in the trolley actually has a negative marginal net benefit — it costs more than it will net in increased tax revenues. If we write down all of our "next dollar invested" numbers here's what we see:
<rowalign="center" tableborder="1">'''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
Pedestrian 25 2
Cleanup 25 1.6
Advertising 25 1.2
Branding 25 1
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
It turns out the next investment should still be in the pedestrian zone project. When we allocate another $25,000 to this project here's how things will stand:
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 25 85
Advertising 50 225
Branding 25 80
Pedestrian 225 650
<rowbgcolor="black" colspan="3">
TOTAL 325 1040
<rowalign="center" tableborder="1"> '''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
<rowalign="center" rowspan="10">[[Image(MNB-all-detail-07.gif, noborder, thumb, 400)]] align="left">Cleanup 25 1.6
Advertising 25 1.2
Branding 25 1
Pedestrian 25 1
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
Another $25,000 for clean up is called for. It will yield $40,000 in additional net benefit (MNB = 1.6). After we allocate these funds, here's our budget so far
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 50 125
Advertising 50 225
Branding 25 80
Pedestrian 225 650
<rowbgcolor="black" colspan="3">
TOTAL 350 1080
and here is what our opportunities look like.
<rowalign="center" tableborder="1"> '''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
<rowalign="center" rowspan="10">[[Image(MNB-all-detail-08.gif, noborder, thumb, 400)]] align="left">Advertising 25 1.2
Branding 25 1
Cleanup 25 1
Pedestrian 25 1
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
So, the best place for our next dollar is actually the parking garage, but the smallest scale at which we can do parking garage is $125,000. Since we still have that much before we are over our budget constraint, that's the next allocation we make.
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 50 125
Advertising 50 225
Branding 25 80
Pedestrian 225 650
Parking 125 175
<rowbgcolor="black" colspan="3">
TOTAL 475 1255
And now we are faced with an interesting situation. More garage promises the higher bang for buck but the garage comes in $125,000 chunks and our budget only has another $100,000 in it. Therefore, even tough it means accepting a lower marginal net benefit, we put our next allocation into advertising.
<rowalign="center" tableborder="1"> '''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
<rowalign="center" rowspan="10">[[Image(MNB-all-detail-09.gif, noborder, thumb, 400)]] <align="left" bgcolor="yellow">Advertising <bgcolor="yellow">25 <bgcolor="yellow">1.2
Branding 25 1
Cleanup 25 1
Pedestrian 25 1
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
Our allocations now look like this
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 50 125
Advertising 75 255
Branding 25 80
Pedestrian 225 650
Parking 125 175
<rowbgcolor="black" colspan="3">
TOTAL 500 1285
1. We have, at this point, exhausted our 500,000 budget constraint and so here we would stop. But a few considerations before continuing. Suppose our budget constraint had been $600,000 instead. Let's look at where things stood when we'd allocated $500,000:
[[Image(MNB-all-detail-10.gif, noborder)]]
Now we are down to several "next steps that have the same MNB and they are all 1. [[Image(stop-and-think-small.gif, noborder)]] What does a MNB of 1 mean? Does it mean "even money" (you get what you give) and so suggest there is not point in investing?
No. Remember, it's marginal NET benefit. If it is above 0 then the net benefit line is sloping upward and we are getting something back for our investment. MNB of 1 just means that for a dollar invested you NET a dollar of beneft (in other words, the dollar produces $2 of benefit).
So, what are we looking at here? We have 5 different options all with the same MNB. In principle that means that spending the next dollar on any of them is the same. But, we've mucked up the works here. The last $25k we spent on the way to 500 could be coupled with this "new" 100 and it should be spent on the next scaling up of the parking garage since that has a MNB of 1.4.
<rowalign="center" tableborder="1">'''Project''' '''Investment[[br]]($000)''' '''Marginal Net Benefit[[br]]at current project scale'''
<rowalign="center" align="left" bgcolor="yellow">Advertising <bgcolor="yellow">25 <bgcolor="yellow">1
Branding 25 1
Cleanup 25 1
Pedestrian 25 1
<colspan="3">
Beautification 50 1
Trolley 50 -0.4
Police 50 -0.8
<colspan="3">
Garage 125 1.4
1. OK, let's see where we stopped on each of our projects.
<rowalign="center" tableborder="1">'''Project''' '''Marginal Net Benefit[[br]]of last dollar spent''' '''Marginal Net Benefit[[br]]of next dollar to be spent'''
Pedestrian 2 1
Cleanup 1.6 1
Advertising 1.2 1
Branding 1.6 1
<colspan="3">
Beautification
Trolley
Police
<colspan="3">
Garage 1.4 1.4
1. If our method is sound, it should be the case that we cannot do anything with that last $25,000 that would increase our net benefit. Let's take a look. Here's where we are with each of our allocations again:
<rowalign="center" tableborder="1">'''Project''' '''Investment''' '''Net Benefit'''
Cleanup 50 125
Advertising 75 255
Branding 25 80
Pedestrian 225 650
Parking 125 175
<rowbgcolor="black" colspan="3">
TOTAL 500 1285

Let's take the $25 away from advertising. We lose that last $30K net benefit. Let's just go down the list and see how we would do re-allocating it to each of the other options:

Pedestrian at 225. If we move to 250 our net benefit goes from 650 to 675, a gain of 25 but that's less than 30.
Clean up is at 50. Move to 75 and net benefit goes from 125 to 150, again, a gain of 25.
Branding is at 25. If we go to 50 net benefit goes from 65 to 90, again 25.
Parking we can't afford the next increment
Police we cannot afford.
Beautification we cannot afford.
Trolley we cannot afford.
Conclusion. Our last 25 was best where it was.