Constraint Theory

By Paras Sharma and Dhruv Sharma

Biography of Author/Contact Information:

Paras Sharma is an economist and distinguished anthropologist who graduated from the University of Virginia. His specialty is in economic scenarios, future thinking, enacting rapid positive change, anthropology of intuition, public choice economics, demand revelation. Paras has worked at Arlington Court System, The Arlington Institute, a leading think tank, and also in the Private Sector Office of the Department of Homeland Security.


Dhruv Sharma is an independent scholar in Arlington VA with a background in risk management, artificial intelligence, organizational behavior, and systems engineering.


The failure of markets in 2008 is an interesting phenonemenon as it relates to deregulation, highlights the effect of acting on the long standing complaints by economists that there have been too many constraints on free markets.  Constraints are essential to well being and long term utility.  Constraints chosen wisely are good and can lead to greater utility in the long run.  The goal of this paper is to outline the importance of constraint(s) to economics and its central role in shaping prevalent economic principles.  Constraints are important and the goal of economics is not to eliminate them in a quest for short sighted utility.  The key question for economists and humans is to understand the importance of constraints.


The aim of this paper is to outline an important construct that can help unify economic theory and optimization science.  This construct has been tacitly in existence in certain key economic principles such as diminishing return, niche strategy, and comparative advantage.  This articles fleshes out the theory and makes it explicit.  This will allow practitioners alike to change the assemblage points of economic theory application and be able to increase utility maximization even more by revealing it to be a rich domain which benefits from creative thinking and self-knowledge.


Maximization of utility is the centerpiece of economic theory.  In the current incarnation of utility maximization this goal is considered falsely as an unconstrained optimization problem.  This means that a firm or individual should take actions to unequivocally maximize utility in a given setting with given resources, or what is here termed natural constraints.  Thus more is better given all existing natural constraints. 


To truly maximize utilities the rational agent must create self imposed constraints.  These self imposed constraints must be carefully constructed to maximize long term utility. By imposing constraints an agent can maximize utility further than with no constraint. This is an important and counterintuitive concept missing in economics. In other words, scarcity does not necessitate choice; choice necessitates scarcity.


Three relevant economic examples will be analyzed to show the important of constraint theory to economics along with a brief discussion of statistical/optimization examples of constraint theory.  The idea of constraints have the promise to be contribute across disciplines such as economics, anthropology, management science, statistics, and complexity science.  Constraints may be the answer to the puzzle of complexity where simple (constrained rules) may result in complex phenonemenon.


One example will be of a firm which has enough resources to produce multiple goods, another example will deal with choices faced by an individual, and stock investment.  We then conclude by throwing in a spiritual example.


Strategy & the Individual Firm

Imagine a firm which produces two products: paper napkins and paper plates.  It may indeed be possible to expand production to the creation of paper plates and paper forks.  However, if the costs do not exceed the benefits, then the company is better off producing less.  The firm is better off producing less, than more.  More is not better.  In fact the entire assumption of diminishing marginal utility to any decision is based on the fact that by imposing self constraints, the individual optimizes the particular allocation.  


A bigger example is that of a firm that can produce multiple products or choose to create a single niche product and result in higher profitability strategy than trying to sell as many products as it can.  By focusing on fewer targeted products with higher margins the firm can in the long run be more profitable resulting in greater long term utility due to a carefully chosen constraint-the niche product and customer base. 





Comparative Advantage


Not only does constraint theory explain how firms maximize profits, it also underlies the basis of trade and specialization.  Traditional economic theory states that the law of comparative advantage is the basis of all trade and specialization.  Even if you are superior at producing something, you should produce what you’re best at, and trade for the rest.  By constraining your production possibilities, you can optimize your time in a way that makes everyone better off. 


Individual Choice


In addition to comparative advantage another staple construct of economics, diminishing returns can also be viewed from the constraint theory perspective.  If a student drinks multiple bottles of soda they will find each subsequent soda bottle to be less tasty.  This simple construct can be altered with constraint theory as saving the bottles and drinking them at latter times one can enjoy each can just as much or if not more.  For example if the soda is enjoyed on a hot day after working in the yard.  More apocryphal examples are the hot chewy fritter or the golden goose principle.  If you eat a hot chewy fritter it will burn your tongue. But if you wait the rewards are just splendid.  Also you can kill the goose now or place a constraint to only produce one golden egg a day and be happy forever.



Stock Market Example


Another key example of constraint theory at work is Markowitz’s mean-variance portfolio theory.  By holding a small number of stocks, about 10, randomly chosen an investor can maximize return than by holding a larger quantity.



A promising future extension of constraint theory would be applications of holographic worldview and fractal theory to develop a stochastic constraint that each agent can use to maximize everyone’s returns.  This is in a sense what Markowitz’s work has laid the ground for along with Mandelbrot’s pioneering work on fractals.  Reframing portfolio optimization as a multiagent search for fractal investment strategies that result in a robust and stable market providing consistent compounding returns is an important problem that needs to be researched.  Adopting the lens of constraint theory allows portfolio optimization to be seen as the general problem that it is.  Markowitz’s solution is a good one but not complete to the problem being framed here as constraint theory allows us to extend the scope of the problem to seek a more optimal solution.


Another interesting application of this would be to place an a priori constraint of maximal expected return from an asset.  In this example an investor would liquidate positions which earn abnormal returns and rebalance to risk free assets to avoid the risk of being caught in a bubble asset market.



Anthroposophy: Economics and Spirituality?


This is in a sense another example of the personal choice flavor.  If happiness is a form of utility it is clear that each religion has important spiritual lessons for economics. Instead of doing what makes one feel good all the time all religions derived from spiritual knowledge urge people to constraint their utility maximization by thinking of others, making them happy, performing penance, sacrifice, and meditation to live lives of meaning and fuller and holistic utility.




Interdisciplinary Extensions

The idea of constraints has been fruitfully employed in statistical and engineering disciplines.  A powerful example of constraint creating more utility in the statistics arena is Tibshirani’s Lasso regression technique.  This method produces an improved regression by introducing a constraint on the sum of beta coefficients in the regression estimation process.  This has traditional been done as an error minimization optimization problem but Tibshirani’s novel constraints results in counterintuive performance aka utility.


Another innovative use of constraints in the engineering domain is Bart Kosko’s work on stochastic resonance where addition of noise makes the image classification better.  Instead of removing all possible noise to form pattern recognition, Kosko highlights that some noise improves certain nonlinear signal classification.


These diverse examples highlight the potential of rigorous study of constraints to human endeavors. If Stephen Hawkings is correct and the 21st century is one complexity science then constraints may offer key insights in this domain.




            Constraints have to be chosen carefully. Constraints have different sensitivities and diminishing returns.   The goal of research is to find how to choose, set and change constraints.  Constraints offer a fresh view of classic economic theory.  The applications and scope of research is rich and deserves attention of economists and engineers alike as this domain can result a greater amount of utility and welfare for all.

            This article makes constraints visible and shows the counterintuitive importance of having and selecting constraints instead of trying to remove constraints at all costs.  If we step back we can see evolution of progress as changes in constraints over time.  By being aware of constraints we can do better long term planning.  Examples of this phenomena abound in architecture, urban planning, and large scale technology projects.  A simple example from IT is the fact that in the past computer programs were optimized for memory and space, a constraint.  Now memory is cheap and this is not a real constraint.  Also data can travel at the speed of light on fiber cables.  Despite this we have not developed algorithms to process at the speed of light yet.  Yesterday’s constraint on space is gone and now we are left with a bottleneck of not being able to process the sheer quantity of information that we can easily transmit.  Thus constraints are important to impose when appropriate and it is also equally important to imagine if constraints we face are lifted and see the next bottlenecks or problems down the horizon.  Thus the use of constraints and the impact of removals of constraints deserve much more focus in economic and all major human system focused domains.  This is an area which futurists and long term scenario planners acknowledge the importance of.  Also the interdisciplinary nature of this domain is important to recognize as complexity science grapples with the hard task of identifying simple rules, or constraints, which result in complex phenomena of interest.  Nature like humans solves unconstrained problems by imposing constraints that result in diversity and evolutionary combinations.  It is nowhere else evident the power of carefully chosen constraints than in the development of life and nature.  This is a lesson economists and anthropologists can learn from.











Kosko, Bart, Mitaim, S. (2003) “Stochastic Resonance in Noisy Threshold Neurons.”  Neural Networks. Volume 16.


Markowitz, H. (1959), Portfolio Selection: Efficient Diversification of Investments, New York: John Wiley & Sons


Tibshirani, R. (1994). “Regression shrinkage and selection via the lasso”. Retrieved from


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