profit when reporting income of proprietorships. I would rather trust an expert in national accounts to tease them apart, and to judge whatever pay should be imputed
to people in the household sector not literally employed.
The Level Payment Mortgage (A2.5) gives
V(x)=F [F@eror dz . (A7.1)
Consider the level payment mortgage. F(z) is the constant level payment while r(x)
is the constant interest rate Here (A2.5) simplifies to
V(x)= Ff-et™ dz=Fe™ im e"dz= “[1 —e@ ex) | (A7.2)
As there is no self-invested output, and no negative cash flow after initial investment
at time 0, decapitilization (amortization) simplifies to -V(x). Thus
, _ dF —r@ 1x _F -ro YX 1X D@)=-V'x)=-_-[1-e e |r ax =— e’, (A7.3)
confirming that amortization increases exponentially over the term of the mortgage.
Depreciation Theory
Depreciation can be defined as decapitalization which is a function of time since capitalization alone. When assets change hands, depreciation continues unchanged. Depletion and liquidation in sale, by contrast, are options available at any asset age.
Amortization can be given the same definition as depreciation, but is customarily
APPENDIX A: The Argument in Notation 3/7/16 16
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