## Sunday, May 6, 2018

### How does EX/IM money circulate?

Our evidence is persistent import surpluses accompanied by increasing foreign ownership of domestic debt. Can we justify speculation that unbalanced imports move capital from the ownership of (probably) eager buyers into the ownership of postponing buyers?

President Trump is concerned about foreign imports reducing the number of available domestic jobs. It is easy to see that foreign made products can have that effect by replacing domestic made products but what is the effect on the internal domestic flows of financial capital? We will find a plausible answer using logic and a mathematical relationship.

The Five Sector Rhythm Production Equation

The rhythm equation describes the productive evolution from initial labor to final product consumption in terms of capital and ownership. The five sectors are household $$c,$$ government $$g,$$ [both consumers] labor $$n,$$ private firm $$k_p,$$ and capital (money) $$k_k.$$The precedes-equals symbol $$\preceq$$ replaces the familiar equality symbol $$=$$ to remind us that production precedes consumption. The term $$f_w$$ relates labor hours to the unique currency of the domestic economy. $(1+k_k) n f_w \preceq c + g \pm k_p.$ The left side of the equation describes sectors that produce product for sale. The right side describes consumer sectors and the owning firm's profit. Product and time moves to the right with capital returned to owners at sale completion.

Figure 1. may help the reader understand the worker-to-consumer evolution.
 Figure 1. The equation's left side represents worker's time, conversion of time to capital, and the production of product. The right side represents consumption and a return of capital to the productive firm.
The 'Catastrophic Transfer Dilemma'

A quick glance at this equation might leave the reader thinking that all of the capital in the economy could end up in the ownership of the left side of the equation. Well, that won't happen if the owners and producers (who are mostly workers) are actually consumers (shown in Figure 1). If we assume that people receiving money also spend money, there will never be a 'catastrophic transfer dilemma'.

What about foreign trade, particularly unbalanced trade, where external economies acquire considerable ownership of domestic capital? As of February18, 2018, offshore investors have invested $6291.6B in United States Government debt, or about 31.5% of current GDP. China ($1176.7B) and Japan ($1059.5B) have accumulated combined debt valued at about 11.2% of current GDP ($19965B). Do we have a slow moving catastrophe here?

We can model foreign production with a generalized production equation. This is easily done by denoting net imports $$k_\text{ni}$$ and writing $(1+k_k) n f_w + k_\text{ni}\preceq c + g \pm k_p.$Now the equation shows foreign imports with a share of the domestic production marketplace. Foreign production will be purchased with domestic currency. While in the case of domestic production, we assumed that 'money earned will be money spent', that condition is glaringly absent in the case of unbalanced imports. Therefore, alarmingly, the equation gives us cause to predict that a catastrophic transfer dilemma is possible should importers continue to delay spending the monetary resource.

Any value received from sale of imports (which were initially produced using a foreign currency) is pure profit in terms of the domestic currency. The implication from this knowledge is that imports should be modeled exactly like the finished domestic product, which is what we have done. Both domestic production and imports are forms of 'capital' at this point of entry into the equation.

Imports Counter Stimulus Efforts

Imports are recognized as a transfer of capital between two currency systems. This type of transfer will leave a capital hole in the exporting economy and (after sale) create a newly filled deposit account in the importing economy. A natural (and probably safe) place to invest this new deposit is into the debt of the importing nation's national government (which seems to have happened in the United States).

To the extent that domestic workers buy imported goods, the pool of consumer money eagerly awaiting spending is reduced. To the extent of the reduction, the demand for government bonds is increased. Hence, government stimulus activity is directly countered by import purchases when not balanced by exports (Figure 2.).

 Figure 2. Net Federal Government Saving less Net Exports of Goods and Services. The remaining stimulation to the economy has varied widely over the last 20 years.

Conclusion

We have a coherent model that supports speculation of capital migration from eager spenders into a postponing ownership.  Perhaps we should be gratified that actual data confirms that possibility as an actual event, albeit as a slow moving evolution.

Domestic money flowing into unbalanced import accounts can be cycled through the lending process while awaiting permanent decisions. A loan to government is one of several possible money absorbing possibilities.

(c) Roger Sparks 2018