Joker Curve Implies Chaos

     Joker Curve Implies Chaos

 

          The “Joker Curve” is a graphical representation of the Quadratic Theory of Economic Value. The linear theory of value says that more is better; the quadratic Joker curve says that too much is as bad as too little.

          This is the Joker Curve:

 

Value                         “Sage’s Peak”

Received                  the golden mean

|                ***   

|            *        *

|         *             *

|       *                 *    

|     *                     *

|    *                       *

|   *                         *

|  *                           *

| *                             *  Value spent

|*_______________________________*_________

 “Miser’s Misery”                                “Fool’s Price”               

There is no free lunch                           Caveat Emptor

 

          Not the similarity between the Joker curve and the Laffer curve. The difference is that the Laffer curve is a macro-economic theory with micro credibility; but the Joker curve is a micro-economic theory with macro credibility.

          At the Sage’s Peak, the marginal value of value is zero! Each additional dollar spent is entirely wasted. The Sage’s Peak is the “point of vanishing returns”, a.k.a. “marginal folly”.

          At the Fool’s Price, the buyer and his money are soon parted. Excessively conspicuous wealth attracts lean, hungry, and thoughtful predators; eventually these dangerous folk outsmart the rich Fool. This Iron Law of Irony is well known to the common people. Note how, in the folktales, the Devil always demands the highest possible price, and always returns zero value. The Fool’s Price is the “point of no return”.

          Wealth deludes, and infinite wealth deludes infinitely.

          Merely to possess the Fool’s Price is enough to activate this market mechanism. Its owner needn’t try to spend it; others will attend to that chore. Three cases in point:

1)   Pharaoh’s pyramids, now stripped bare by graverobbers and archeologists.

2)   Donald Trump’s real-estate career.

3)   Donald’s Trump’s America.

Consider what happens when we apply the Joker Curve recursively. Suppose that the value returned after a round with the return curve were re-invested, and so on? If the return curve is linear, then such a recursion causes exponential growth or decay of value. But in a non-linear theory, equilibrium is possible. Note this graph:

          

       |

Value         |       ***      * 

Next    |    *      X

Cycle   |  *    *     *

             | * *          *

       |*______________*____

                  Value this cycle  

          X marks the spot where this year’s wealth equals next year’s wealth; an equilibrium. The stability of this equilibrium depends on the steepness of the Joker curve.

          If the Joker curve is shallower than the diagonal line, then the economy stabilizes at zero. A higher equilibrium appears if the Joker pokes above the diagonal. If the marginal value of value at the upper equilibrium is more than negative one dollars per dollar, then it is stable; but if not, then wealth must oscillate; first at period 2, then (for steeper Jokers) period 4, then 8, and so on, culminating in economic chaos.

          In the steepest possible Joker curves, the Sage’s Peak equals the Fool’s Price. Call such an economy a “Sage’s Folly”, for it is an economy in which planning, moderation, and frugality can win you so much money that you must lose it all one year later.

          Such an economy is necessarily chaotic. Its future size is unpredictable in principle due to its sensitive dependence on initial conditions; the “Butterfly Effect”. Within a Sage’s Folly, a single butterfly fluttering past a single stockbroker can start an exponentially increasing economic fluctutation.

          Within a Sage’s Folly, does the sage control the butterfly, or does the butterfly control the sage?