1 Introduction

This paper describes a very crude macro-economic model in which value producers and value destroyers interact in an economy. It:

1. Classifies possible economies into six different types according to the model.
2. Estimates the parameters of the model for the present economy.
3. Investigates ways in which we can increase the total values in the economy, and the values produced and enjoyed per individual.

2 The Path of a Value

Consider a value v₀, entering (randomly) an economy where the population consists of three types of individual:

1. Value producers, making up a proportion p of the population.
2. Non-producers, making up a proportion n of the population.
3. Value destroyers, making up a proportion d of the population.

1. A value producer uses the input value to create a further value Pv, where P is a (positive) constant of productivity, then sends this randomly to some member of the population.
2. A non-producer absorbs the input value.
3. A value destroyer absorbs the input value, and in addition creates damage of size -Dv, where D is a (positive) constant of destructiveness.

and the total values generated in this situation, including the original v₀, are:

The probability that the initial value v₀ passes through exactly k successive value producers before being absorbed by a value destroyer is p^kd. The total values generated, including the original v₀ and allowing for damage done because the last value in the chain reached a value destroyer, are:

Therefore, if the initial value v₀ passes through exactly k successive value producers (k>=0) before being absorbed, the contribution to the expected value of the total values generated is:

To get the expected value v for the total values generated, we need to sum these contributions over all possible values of k. Thus:

So therefore:

If pP<1, this can be expressed as:

v = v0 (

)

[2]

3 The Total Value in an Economy

Consider an economy where the total amount of values input from external sources (land, past achievements, energy resources etc.) is V₀. We divide this into many small individual values v_i, then follow the path of each v_i through the economy as described in the previous section. Applying equation [1] or (provided pP<1) [2] to each individual v_i, and summing, we can see that the expected value for the total values in the economy is:

If pP< 1, then:

V = V0 (

)

[4]

4 Classification of Economies

Using equations [3] and [4], we can classify economies into six different types according to the values of pP and dD.

1. Where dD > 1, i.e. the value destroyers can destroy values faster than anyone can produce them, V is always negative. Such an economy always destroys every value entering it, and more. This class of economy corresponds to an astronomical "black hole". Note that, in this case, V becomes more negative with increasing p. Therefore all value producers trapped in such an economy will choose to become non-producers (i.e. to set p=0), and/or to suicide.

2. Where dD = 1 and pP < l, i.e. the value destroyers can destroy values just quickly enough to get rid of them all, the value V is zero. Nothing is ever left. This is the limiting case of a "black hole" economy.

3. Where pP < dD < 1, i.e. destruction dominates production, the total value V is positive, but is less than V₀. This type of economy is squandering its resources - in both the "environmental" and human senses. This type of economy is not sustainable for long.

4. Where pP = dD < l, V is exactly equal to V₀. Such an economy is just maintaining its resources - it can just survive, but cannot expand or prosper.

5. In the case where dD < pP < l, the value producers, allowing for their numbers and productivity, are dominating the value destroyers. Here V is larger than - perhaps very much larger than - V₀. This is a prosperous and sustainable economy, and is where we should be today.

6. If pP >= 1, then the right-hand expression in equations [1] and [3] diverges to infinity. This means that, once the productivity and proportion of value producers reach certain levels, the model will no longer apply. Other constraints (such as time available for value production) will take over. However (unless dD > l, when we are in cases 1 or 2 above) the total values generated V will always be positive and extremely large. Such an economy has undergone a quantum leap into a new dimension.

5 Today's Economy

To find in which of the categories above today's economy fits, it is necessary to estimate values for p, P, d and D.

It is easiest first to estimate n, the proportion of non-producers. For simplicity, we classify anyone under about 18 or over about 65 as a non-producer. The proportion of these in the population is a little under 40%, so (allowing for a few unemployed as well) take n=0.40.

Of those who do not fall into this category, approximately 85-90% are value producers and 10-15% value destroyers (estimate by Doug Casey). Taking the mid-points of these ranges gives p=0.525 and d=0.075.

An average value producer generates about 15-20% more values than he or she consumes. (This represents approximately the expected gross profit margin of a well-run service company). Take P=0.175.

The hardest to estimate is D - as a best guess, let us take D=5. This says that, over a long average, a value destroyer destroys about five times as much again as it consumes. (This may be an under-estimate, since some politicians destroy millions of times the values they consume directly. In contrast, the best business leaders generate only hundreds or thousands of times the average).

For the economy today, substituting into equation [4]:

This implies that today's economy fits into the third of the six categories above. Today, the value destroyers are winning by 30% or so.

6 Improving the Economy

From the individual's point of view, what we want to increase is not just the value total V itself, but the value total per individual. A measure, proportional to both values generated and values enjoyed per individual, is the averaged total value per head of population. If N is the total population, we define this as:

The table on page 6 shows the effects on I and on V/V₀ of the following six strategies:

1. Increase the external resources used (i.e. increase V₀).

2. Stop value destructions - turn value destroyers into non-producers, i.e. decrease d while p remains constant.

3. Eliminate value destroyers - decrease d, with a corresponding decrease in N (V₀ remains constant). There is also a corresponding increase in p, since the number of value producers remains constant while the total population decreases.

4. Convert value destroyers into value producers - decrease d, and add the remnants to the pool of producers (p).

5. Make people more productive - increase P. This can be accomplished, for example:
   a. Through providing them with better tools (physical and mental),
   b. Through providing them with a better environment to work in,
   c. Through increasing their satisfaction and happiness,
   d. Through the psychological effects of removing value destructions,
   e. Through making sure that rewards go to those who do produce rather than to those who do not.

6. Implement biological immortality. We assume this is not feasible until there are no value destroyers left, therefore d=O. Then the achievement of biological immortality will decrease n to effectively zero. This is because there will be no-one too old to be productive, and the proportion of those too young to be productive will approach zero. Therefore p will become =1, and the success of the economy becomes a function only of P.

The following are some conclusions which can be drawn from the calculations:

1. Increasing V₀, i.e. using more external resources, lifts I by a corresponding amount. However the value total ratio (V/V₀) does not improve. Therefore this approach cannot cause a transition from the third into the fifth (prosperous and sustainable) category of economy, see above.

2. Stopping value destructions can produce a significant increase in I, with a corresponding increase in V/V₀. Stopping all value destructions would certainly push today's economy over the dividing line into the fifth, prosperous and sustainable, category. Also, there would probably be a further positive "knock-on" effect of an increase in P, due to the psychological effect on value producers.

3. Eliminating value destroyers produces much the same increase in V/V₀ as stopping value destructions. However, I increases significantly, because the decrease in population means that there are more resources V₀ to go round, as well as making p higher. This leads to the interesting conclusion that, given a constant value of V₀, we obtain a greater gain in I by eliminating value destroyers than by letting them exist.

4. Converting value destroyers into value producers produces a greater increase in V/V₀ than eliminating them - but only marginally. It still does not increase I by nearly as much. Any of these three strategies, if applied to all value destroyers, will push the economy into prosperity and sustainability.

5. Increasing individuals' productivity does not have much effect in the short term. A 10% increase in productivity causes only a 1% increase in total values. Thus the current marginal cost of value destructions is of the order of 90%. Even doubling average productivity only produces an 11.3% gain in I and V/V₀. However, the nearer pP gets to 1, the faster the rate of increase in the gain. Multiplying the average productivity by 10 produces an over 1,000% increase, even without getting rid of any value destroyers.

6. Implementing biological immortality is a useful adjunct to increasing individuals' productivity. It approximately halves the productivity gain necessary to produce a 1,000% increase in I and V/V₀.

7 Shortcomings of the Model

The following are some shortcomings of the model:

1. It assumes that values are produced instantaneously, and only on receipt of values from outside. It does not take any account of lag or lead times, or of the evolution of the economy with time.

2. The model only applies to economies with less than a certain critical productivity rate, i.e. with pP less than 1.

3. The model only works with averages. It does not take into account that not all value producers are equal, or that some exceptional individuals have a much higher value of P than the average. Similarly, it does not take into account that not all value destroyers are equally destructive, and that a few are millions of times more destructive than the average.

4. The model does not allow for the natural tendency of a value producer to want to keep the values, which he or she produces, away from value destroyers. Any value producer will prefer to provide values only for his or her fellow value producers, and for voluntary (non-producer) dependents.

5. On the other hand, the model also does not take account of the tendency of wars, terrorism, taxation, bureaucratic oppression and other crimes to concentrate values into the hands of the value destroyers.

6. The estimates for P, and particularly for D, are unverified and may be significantly wrong.

8 Conclusions From the Model

On the assumption that the various shortcomings of the model roughly cancel each other out, the following conclusions may be drawn:

1. The current economy is not sustainable. The "environmentalists" are right (for all the wrong reasons).

2. In the short term, the most effective way to make the economy prosperous and sustainable is to get rid of all value destroyers.

3. Eliminating value destroyers has a greater immediate positive effect than converting them into value producers. Converting them into value producers gives a greater long-term gain, but only marginally.

4. Making productive people more productive is useful, but does not produce a major effect until the average productivity starts to approach something like 5 times its current value.

5. However, if productivity per individual increases by a factor approaching 10, the total of values in the economy starts to show a much greater rate of increase. The economy starts to move into a new dimension.

6. The achievement of biological immortality, and the elimination of all value destroyers, would reduce by half the productivity gain necessary to generate a 1,000% increase in the total values in the economy.

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