In this post, I will suggest a model of the delayed effects of investment. A convenient point of entry is the excellent post by Nick Edmonds found at http://monetaryreflections.blogspot.co.uk/2013/07/bank-lending-and-non-bank-lending-model.html .

Edmonds correctly arrives at the equation

ΔL + ΔB + α |
||

1. Y |
= |
------------------ |

Eq |
( 1 - α |

where Y is income, ∆L + ∆B is the change in bank lending plus the change in lending by bonds, aₒ is base consumer spending and a₁ is an adjustment factor relating all the terms. This simple equation has the effect of hiding the long term effects of bank and bond investing.

We can separate and examine the long and short term effects
of bank lending plus lending by bonds by defining *lending* as money that is
borrowed and would result in spending that would count toward national income
as measured by GDP. This is a severe limitation that we enforce by placing a
negative limit on equation 1. To add this limit to equation 1, we would
rewrite it to read

ΔL
+ ΔB + α |
||

2. Y |
= |
------------------- Limit ∆L + ∆B > zero. |

Eq |
(
1 - α |

In other words, bank and bond lending cannot be negative or below zero. If they were negative, they would represent a transaction that is not counted as income but, instead, would be an investment transaction which is not counted as part of GDP.

We will avoid the need for limits by defining our terms carefully. Here, we depart from the definitions of Edmonds, except for the Y term which is commonly used to identify income.

We will narrowly define investment loans from bonds and bank
loans as being *new* loans and bonds, as contrasted to refunding or
roll-over loans or bonds. *New* loans and bonds are anticipated to be
spent on new plant, labor, material or other item that would be counted as
adding to the national GDP calculation. We label new bank loans **NBL** and
new bond issues **NBI**.

We will assume that every income reporting period is
expected to have a different consumer spending base. We label the annual
consumer spending base as **ACSB**.

Up to this point, we have identified two sources of consumer income, borrowing (NBL + NBI) and base spending (ACSB). We will follow Edmonds by ignoring the effects of Government until a later posting. If we also ignore the delayed effects of new loan spending, we can write

3. Y = NBL + NBI + ACSB.

From equation 3, we can see that national consumer income is at least new investment spending plus base consumer spending.

Now we will examine the delayed effects of new money. New
investment spending moves money from the hands of savers into the hands of
workers and materials providers. This movement into new hands is likely to
result in additional spending at some unforeseeable time in the future. New
hands holding new money will change the base consumer spending pattern Y both
in the current time period and future time periods. To model this change in the
most recent time period, equation 3 will be supplemented with the term *a₂
times the value of new loans and new bonds* (a₂ * ( NBL +NBI), where a₂
is the expansion factor for new money . We will write

4. Y = a₂*(NBL + NBI) + NBL + NBI + ACSB .

From equation 4, we can see that national consumer income is at least the factor a₂ times new investment spending, plus new investment spending, plus base consumer spending.

Investment in the next income period may not contain any *new*
investment income but it is highly likely that investment income from the
previous period will carry over into subsequent periods. If equation 4 is used
to predict an income for a future Y₁ with no future investment, we could
write

5. Y₁ = a₃*(NBL + NBI) + ACSB

where a₃ is the revised constant for the no-investment period. NBL, NBI, and ACSB are equal to identical terms from the previous year’s calculation.

More can be done with this model as represented by equation 4. Government can be added to show the effect of changing the base money supply. ACSB can be traced back in time in an attempt to establish a base consumer spending level or find the annual value of a₂. It is expected that these and additional subjects will be covered in future postings.