A parameterize, continuous function of the form h(t, 0) = f(t), h(t, 1) = g(t) and h(0, t) = x(0) = h(1, t) where h[0, 1]. I will keep this simple and assume there is a fundamental group. If one attaches time to the parameter t, then the functions describes “products” of value with a velocity.
Defining the interaction between producers and consumers, as a transfer of value, implies the existence of at least one producer and one consumer (from the stand point of Homotopy there exist a self interaction which, by my definition, transfer no value). My definition also implies the existence of at least one unit of labor and one unit of capital.
PROOF:
- f1, g1 : X -> Y are homotopic, and f2, g2 : Y -> Z are homotopic. Their composition f2 o f1 and g2 o g1 : X -Z are also homotopic. My working principle is to let X -> Y represent the transfer of value due to labor and Y -> Z represents the transfer of value due to capital to produce the final product. Z represents the final output space for this example. Two different processes are represented by f’s and g’s (no self interaction). It is require that the “length” of the path in Z not be zero (no transfer of value with self interaction) and its length be the same for f‘s and g‘s. From an economic point of view the value of a product can be consider a constant for the period in question. End Points are fixed in Homotopy.
I define the process as an interaction between capital and labor as a sanity preserving mechanism.
We can use the composition mechanism for production to analysis the effects of Home Equity Credit Lines on a local economy. I’m going to take a stance and state the House is the Laborer and the Homeowner is the Capital. Equity -> Cash is the process the House does and capital (the homeowner) is needed to pay off the loan. The Homeowner needs a value such that payment is made and the house is in their procession, acquiring equity (replacement cost for the equity build). In order to remain in business, from a firm point of view, inputs must be used efficiently (productivity gain) and the capital must come at the lowest price. The output of this firm must have a value such that it can be sold to the community. If your house was a fractional bank or the cash was used in some other firm or you have a home based business, your community will experience economic growth.
Reality check
- The Federal Reserve will never allow housing to become a fractional banking system.
- Vast majority of home owners do not have a home based business.
- The Equity -> Cash process, for the vast majority of home owners, is a lost.
- Local communities can fall into a poverty trap if none of cash was used to create new jobs.
