Wednesday, January 27, 2010

Availability of capital - modeling aggregate investment levels

Given persistent payments on business investment I and loans (at interest) L, aggregate fixed costs F, quantity sold Q, expected revenue per unit R, and per-unit cost V, profit in time period t is:

profit(t) = (R-V)Q - F - L - I

Ceteris Paribus, a business that shows profit could in theory pay down its loans and buy back its stock over time, increasing long run profits. Such a business could also continually fail to meet profit expectations, in which case expenses will be paid in left to right order. One can expect investors to receive dividends or other benefits only if a surplus reaches them. Thus, they are in the highest risk position. One can also expect corporations in particular to generally be unable to pay down investments, instead maintaining constant investment levels and paying out dividends in lieu of buying back, as this is a more lucrative path for the controlling shareholders to take.

A start-up will have a risk position that is a point within the bounded range between the maximum expected profit and minimum expected profit (negative being loss) that determines interest rates and total loan credit available. A business proposal does not give an incentive to the prospector (for purposes of this essay the prospector will be the person who creates the business proposal) to safeguard investments or loans received. Rather, the prospector's primary incentive is his own desire to attract the investment, meaning he is interested in making a convincing argument regarding the business venture. The prospector enters into negotiations with investors and banks in which he will make an argument regarding his risk position within the minimum-maximum range.

Similarly, any business looking to either expand operations or replace depreciated equipment may have need for temporary capital. The same process will take place, but in models featuring incomplete information, more complete information than in the prospector case should be assumed.

This negotiation is best modeled by empirical data. In a theoretical sense, such a negotiation is irresolvable due to it being empty of a priori content. Games or market models that may be superficially similar show similarity only insofar as they make assumptions about the players that are grounded in empirical reasoning.

The risk position is dilated or contracted when aggregate demand changes. An economic decline will generally shift the minimum expectation down slightly and the maximum expectation down greatly. Similarly an economic recovery will shift the minimum up slightly and the maximum up greatly. Typically, the level of aggregate demand is a significant determinant of the risk position of any business. This in turn determines the results of negotiations and the aggregate investment level. The loan offerings available to a business will also change based on the state of the economy. Generally, loans are more secure during economic downturns due to their lower risk position than investments, and will expand less during upswings due to bank attitudes regarding speculation - meaning they will generally have a higher price than investors during good times and a lower price than investors during bad times.

The distribution of business financing between investments and loans will also depend on the interest rates offered on loans. Businesses and prospects will each have both a credit rating (which partially determines loan offerings) and a risk position (which partially determines investment offerings). Thus, businesses can be divided into three categories:
  1. Businesses which attract loans at a lower interest than investments
  2. Businesses which attract loans and investments at the same interest
  3. Businesses which attract investments at a lower interest than loans
An important psychological factor comes into play in this distribution: the desire of investors and businessmen to maintain various degrees of control over businesses. For this reason, loans and other indirect investment mechanisms will have some edge over the introduction of new investors who could conceivably interfere with existing leadership structures. This means that even in boom times where there are many investors, institutions will still feature loans as a significant part of their portfolio.

Looking specifically at economic downturns, on the supply side investors will generally move assets into "safe" financial instruments. This will reduce the potential investor pool, driving up the price of each investment (in the form of dividend payouts). Therefore, loans will become a greater portion of business portfolios - meaning more businesses will be in category 1. This is accompanied by an increase in interest rates that is somewhere in between previous term interest rates and the new price of investment. Generally businesses become saddled with higher costs and less repayment flexibility during recessions.

Economic conditions may also prevail in which speculative investment increases in real estate, commodities, and other factors of production. This has the effect of driving up other aspects of business cost. Ceteris paribus, this forces businesses to seek additional investment, loans, or curtail operations. In fact, general decreases in prices seem to reach real estate last - meaning that real estate proportionally increases in cost during recession periods even as it shows no net increase in investments. Such changes bring about a long-term shift in the profit functions of businesses and force a decrease in hiring.

Arguably, it is these two effects which have the largest role in explaining the business cycle. Before venturing on, it is worth reviewing a key concept described in a previous blog entry regarding the distribution of money between the financial and real parts of the economy. Ignoring possible increases in the money supply, even if divided in a totally arbitrary fashion, it is clear that a two sector economy will have a relationship in which one sector gains money only as another loses it. If one takes the position, as I do, that loans do not actually increase the money supply, the following points will hold true.

Economies display a certain degree of stability. This stability is the result of the stimulus effect of incidental profits and losses. Within any given time period, some businesses will fail and investors will lose their money. However, so long as these failures are not interpreted by investors (or economists!) as a sign of changes in aggregate demand, average investor behavior will not change. These incidental losses must exist to balance against the unexpected successes (incidental profits) of other investors. Each time such an event occurs, aggregate demand is either stimulated beyond its equilibrium (in the case of incidental losses) or drawn below equilibrium (in the case of incidental profits). This follows from analysis of the relative stimulus effect of dollars in the financial relative to the real sector: since a failing business must by definition inject net dollars into the hands of noninvestors and a profitable one must do the opposite.

Paradoxically, the stability described above can only be maintained in an economy where there is a great deal of uncertainty among investors. Typically, the stability itself will lead to the perception of greater certainty as investors look to specific examples as test cases (regardless of the actual significance of these tests) and investors will turn toward a new strategy. It is extremely unlikely that investors will allow the economy to move toward a higher aggregate demand position through their own changes, as this would entail, in the short term, a higher risk position in the context of an average expected investment profit that is close to zero in the long term. In the event that mistakes are made and investors make bad investments, the immediate stimulus effect may roll the economy over to a new equilibrium. If mistakes are not made, investors will precipitate a recession because the opening time periods of the recession will promise them the largest profits. It is likely that some increased investment has occurred in commodities and real estate, further deteriorating the risk position of businesses.

Economic recoveries (and the prevention of recessions) generally occur through a combination of four factors:
  1. Increased spending by Governments
  2. Collapse of commodity and real estate markets
  3. Significant expansions in the dollars available to the poorest (perhaps through welfare or other deficit income transfers).
  4. An exogenous increase in the propensity to spend by consumers
Each of these, in sufficient magnitude, will produce a stimulus that has the potential to push the economy back to a new equilibrium.

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