<h3>Lecture 12. THE &ldquo;BREAK-EVEN&rdquo; MULTIPLIER</h3>

Does Size Really Matter?
The formula M* = 1 / [DR / 5) + TB] states that the minimum 
value of the multiplier that would decrease the DR is equal 
to the reciprocal of the sum of (DR / 5) + TB and is 
therefore inversely proportional to that sum.

It is interesting to note that the stimulus, S, is canceled 
out and does not appear in the formula.  In theory, the 
size of the stimulus does not affect the value of M*.  In 
practice, the size of the stimulus is limited by the 
availability of idle resources.  When the stimulus 
competes with consumer spending for resources, it causes 
inflation.

The immediate consequence of the formula is that the 
larger the DR, the smaller the multiplier needed to justify 
a stimulus. The formula can be best understood by 
considering numerical examples, starting with a low DR. We
will consider several cases,numbering each as we increase 
the DR. We will assume that TB = 30%.

1. With the DR equal to 50% (Mr. Greenspan’s nightmare), 
the multiplier would have to exceed

   1 / [(0.5 / 5) + 0.3]
 = 1 / (0.1 + 0.3)
 = 1 / 0.4
 = 2.5

   to reduce the DR.

2. When Greenspan can get to sleep with a DR equal to 60%     
   or more, the multiplier would have to exceed

   1 / [(0.6 / 5) + 0.3]
 = 1 / (0.12 + 0.3)
 = 1 /.42
 = 2.38

   to reduce the DR.

3. With the DR equal to 100% (approximately our current DR),
   the multiplier would only have to exceed
 
   1 / [(1.0 / 5) + 0.3]
 = 1 / (0.2 + 0.3)
 = 1 / 0.5
 = 2.0

   to reduce the DR.

4. Finally, when the DR is equal to 200% (Japan's DR), the
   multiplier would only have to exceed

   1 / [(2.0 / 5) + 0.3]
 = 1 / (0.4 + 0.3)
 = 1 / 0.7
 = 1.43 

   
This raises an interesting question: Why not keep the
economy at a high DR to take advantage of the ease of
justifying a stimulus? With the Fed's ability to borrow
at 1% interest rates (or at any pegged rate!), a $1T
stimulus has an annual cost of $10B. The productivity
gain would easily be worth the cost.

Conclusion I: Given a DR greater than 60% (to appease
Mr. Greenspan’s worry that the Treasury bond market 
will run short of supply), federal debt policy should be 
to use as much of the idle resources as possible to 
improve infrastructure without concern for the budget. The
multiplier will be large enough to reduce the DR. Tax 
revenue due to full employment will always pay for the 
infrastructure.

Conclusion II: Given a DR less than 60%, federal 
investment in infrastructure will raise the DR above 60% 
to appease Mr Greenspan. Infrastructure investment is 
always justified when using idle resources. Economic 
policy is always correct when GDP rises. while the DR 
declines.  

We have shown that, during a recession, stimulus that uses
idle resources to build useful infrastructure is available 
at very low or zero cost. The tax proceeds gained by the 
GDP growth and additional benefits listed below pay
for the stimulus.

And even if the stimulus adds a small amount to the ND, it
cannot increase our indebtedness or decrease our
creditworthiness.  Our bond-holders will always be pleased
if our GDP rises while our DR declines and we add to the 
national infrastructure that we bequeath to our posterity.
That is how we outgrow our debt, even with annual 
deficits.
ADDITIONAL BENEFITS
Please note that in our theoretical discussion above we do
not include the following additional economic benefits of
federal deficit spending during a recession:

1. Decreased public expense due to social problems caused by 
   unemployment.
 
2. Decreased administration of Medicaid, unemployment, and 
   food stamp benefits.

3. Increased productivity (and future GDP growth) through 
   infrastructure improvement.

The last point is most important.  Prosperity and progress
depend entirely upon productivity, measured as annual GDP 
per worker-hour.  The gain in productivity due to 
government-created infrastructure such as the first 
continental railway, public schools, Land-grant 
universities, the Veteran's Education  Bill, the Veteran's
Housing Bill, the National Institute of Health, the 
interstate highways, and the internet has set us on top of
the world.  Our posterity depend upon the maintenance and 
advancement of our infrastructure.

Productivity becomes critical when we consider the rapidly
approaching effect of the baby boom.  If fewer workers are
to support more non-workers, productivity must begin to 
rise immediately.  Infrastructure improvement is not a 
luxury we can defer.  It is an absolute necessity that 
should not wait another day.
Proceed to:
Lecture 13. DEPRESSION, WAR, AND POST-WAR
Thanks for your interest.
  Marvin Sussman, retired engineer

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