In his classic book “The Wealth of Nations”, Adam Smith coined the term “invisible hand” to describe the mysterious force that drives the market economy toward optimal efficiency without any central planning. He wrote:

“Every individual … intends only his own gain, and he is in this, led by an invisible hand to promote an end which was no part of his intention … By pursuing his own interests, he frequently promotes that of the society more effectually than when he really intends to promote it.”

It has been 240 years since the publication of “The Wealth of Nations”, and the “invisible hand” along with free market efficiency has been widely accepted by economists. However, the “invisible hand” was accepted almost like an axiom without a formal proof. Little was known about what is the “invisible hand” and how it works the magic to benefit the economy.

So a while ago I set out to find out what is the nature the “invisible hand”. It turned out that the “invisible hand” is real and can be proved mathematically. Among the findings:

- It can be formally proved that a free market economy in which producers (manufacturers) compete for limited resources will eventually reach optimal resource allocations if and only if the following conditions are met:
- There is a free market in which the prices of the resources are determined by the law of supply-and-demand.
- The producers and resources owners act in their own best interest and try to maximize their profits.
- The producers and resource owners are forward-looking and plan their activity to maximize their future profits.

- If all three conditions above are met, it can be proven that the economy will eventually approach the optimal equilibrium in which the Gross National Product (GDP) is maximized given the limited resources.
- The math also predicts the economic cycles as a side-effect of the “invisible hand”. Before the economy reaches its equilibrium, it will go through many up and down cycles in which productions and prices increase and decrease along with the GDP.
- If the third condition above are not met, i.e. the producers and resource owners do not plan ahead and instead only focus on immediate profits, then the economy will be in a perpetual cycle of ups and downs without converging to the optimal efficiency.
- As the economy approach the optimal equilibrium, the resource owners are the ones who pocket most of the moneys, while the producers will see their profit margins approach zero.
- The formal proof involves a new algorithm to solving the Linear Programing problem. Unlike the Simplex method, the new method is distributed and can be run on multiple processors in parallel. Each processor represents a producer or a resource owner who interacts with others via the resource commodity market. The producers determine the production rates of their products (primal variables) based on the resource costs, while the resource owners set the prices of their resources (dual variables) based on their demands.
- The algorithm can be implemented using a Recurrent Neural Network in which each producer is a primal neuron, and each resource owner is a dual neuron.

This finding was presented at the 17th International Symposium on Mathematical Programming in Georgia Institute of Technology, Atlanta. Here is the full paper:

A Nonlinear Neural Network for Solving Linear Programming Problems

Now that the “invisible hand” has been unveiled, is there a way to manipulate it so that the economy can reach the optimal equilibrium faster and with less side effect. Please share your thoughts. Thank You.