How economies develop over time is a very complex issue that has continued to evade our true understanding of. One approach to this question is through the use of models from systems dynamics, which is a systems-based approach that tries to look at and model whole complex systems through understanding the types of relations between the parts and the feedback dynamics that create the system’s overall behavior.[1] For systems dynamics, the main concern is to understand how structure – variables and causal links – generates behavior in a world of continuous process, rather than discrete events.[2]

The model of causal links and feedback loops is fundamental to understanding the dynamics of complex systems as they capture and describe the different types of relations between components within nonlinear systems. Causal links and feedback loops are one of the best examples of the key premise of complexity theory; the idea that complex phenomena can, in fact, be the product of simple rules.[3] But it cannot be a direct product of these simple rules. We can only get this complex emergent phenomenon out of the nonlinear interactions between these simple rules, as they are iterated upon over many cycles and give rise to emergent outcomes.

### Causal Links

A causal loop diagram (CLD) is a causal diagram that aids in visualizing how different variables in a system are interrelated. The diagram consists of a set of nodes and edges. Nodes represent the variables and edges are the links that represent a connection or a relation between the two variables.[4] A link marked positive indicates a positive relation and a link marked negative indicates a negative relation. A positive causal link means the two nodes change in the same direction, that is, if the node in which the link starts decreases, the other node also decreases. Similarly, if the node in which the link starts increases, the other node increases as well. An example of this might be the relation between manufacturing output and electrical consumption within an economy. They will both move together; the more of one, the more of the other.

A negative causal link means the two nodes change in opposite directions, that is, if the node in which the link starts increases, the other node decreases, and vice versa. An example of this might be the relationship between the amount of driving one does and the amount of fuel in your car. The more driving the less fuel will remain. Negative links are additive in nature, whatever we add or subtract from one side, we add or subtract the same from the other side. Positive links are compounding effects, where more of one thing begets more of the other within the relationship; both variables in the relationship move in the same direction, going up or down together. With positive links, in contrast, when we add or subtract from one element, we also add or subtract from another. Thus, they will not sum up to zero and we cannot create an equation around them. They will give us nonlinear solutions. Positive links and positive feedback are behind almost all nonlinear phenomena. Thus, they are very important to understanding the dynamics of nonlinear systems.

Because negative links are linear and sum up to zero, they can be used to model zero sum dynamics. If we have a cake and divide it up between two people, the more one gets the less the other will get. Negative links are what we might call neutral. The interaction itself does not add or subtract from the whole. In these zero-sum games the whole pie is staying the same, what is changing is who gets what. In contrast, positive links define non-zero sum games. A non-zero sum game is a situation in which the interacting parties’ aggregate gains and losses can be less than or more than zero. Thus, it is nonlinear. Through positive links, the whole pie that is being divided up between agents can grow or diminish, that is to say, the interaction is not neutral. The interaction itself is adding or subtracting something from the whole pie. In such a circumstance it is necessary to understand the type of relation between elements.

### Synergy & Interference

If the interaction between the two components adds value to the whole, this is called a synergy.[5] If the interaction subtracts value from the whole, it is called interference. A synergy is a constructive interaction, meaning the output to the interaction will be more than the sum of its parts. There are many examples of synergies in our world, from the cooperation of cells and organs in the human body to many different kinds of synergies produced by social organizations. Trade is thought to be positive sum for example, because if you are prepared to part with something you must value what you are exchanging it for more. And if both value what they are getting more than what they are giving up, then some value has been added to the entire system through this interaction.

The word synergy comes from the Greek word meaning ‘working together.’ This working together involves the constituent components differentiating their activities with respect to each other and also coordinating these activities towards a common end. One of the best examples of this is our global economy. Many millions or even billions of people perform different specialized functions, but these functions are then coordinated within firms and markets so that we can get something like a laptop computer that no one person could create. It is only through this process of differentiation and then reintegration that value is added to the system. Synergistic relations are pervasive phenomena in our universe as they are part of all complex organizations, and of course, they are nonlinear. The whole will be more than the sum of its parts because value is being added by these synergistic interactions.

Synergies are just one type of positive link where both components’ values will move in the same positive direction as the whole pie grows, but we can also get the inverse phenomenon. They can both move in the negative direction due to what is called interference, the classical example of this being the interference between two sound waves as they cancel each other out. Interference is the opposite of a synergy, that is to say, the failure to differentiate and coordinate. If a society doesn’t provide proper education and training for its people or they don’t choose to take it, there will be too few high skilled specialized workers and too many people looking for undifferentiated unskilled labor. Because of the failure to differentiate, there will be a failure to coordinate and we will get interference and crowding-out. Because of this destructive relation of interference, the whole pie will get smaller and the variables associated with all the components in the relation will go down together.

### Positive & Negative Externalities

Negative links define closed systems. As such, they are representative of dynamics surrounding rival goods. The more that one person uses of a rival good the less another can. Value is excludable. Thus, we get a well-bounded, well- defined system. Marginal cost will approximate marginal benefit with a trade-off between agents and an equilibrium, out of which we can create the market mechanism of supply and demand. Because nothing is being added or subtracted to the entire system, negative links have no externalities. Non-rival goods are goods that have externalities. With non-rival goods, marginal cost or benefit approaches zero. The benefit to the additional consumer may be substantial, thus resulting in a non-zero interaction and positive externalities.

Because positive links are non-zero sum, they have externalities – both positive externalities where through synergies the system becomes greater than its parts and thus adds value to its environment. And inversely, through interference, it can subtract value from its environment, what are called negative externalities. When a company achieves internal synergies between employees or departments, it will be able to deliver a better product that will be of more value to the economy and society, which is a positive externality. With synergies and positive externalities, social value is higher than the private value.

With interference, the system will be less than the sum of its parts, and thus the input of resources to the system must be more than the output in order to maintain the system, meaning the system’s environment is paying the cost for running the system. The social cost is higher than the private cost. Some of the cost is being externalized to the environment, a negative externality. Thus, the system will over-produce because the marginal cost to the system will be less than the marginal benefit.

### Market Mechanism

A negative link can be used as a description of the market mechanism, where the benefits and costs of each agent in the relation are balanced against each other, giving an equilibrium of supply and demand through which to regulate the quantity of goods and services produced and consumed and their allocation; it is a self-regulating system. The market mechanism breaks down when we have both positive and negative externalities; because the marginal cost and marginal benefit are out of equilibrium. The two are not moving in opposite directions or there is a weak correlation between them. As for example might be the case with digital

products where the marginal cost of producing one more copy is very small and the marginal benefit can be very large, thus, the two are not directly correlated. This is even more extreme with the network effect where both the producer and the consumer can be gaining value at only a very small marginal expense to one, meaning both variables are moving in the same direction. Civil war is another example of a positive link. We have interference in the system as the two components are in conflict. The marginal cost to one of waging war is also a marginal cost to the other. Here, the two variables are moving in the same direction that is not balanced and thus it can’t be regulated through the market mechanism.

### Nonlinearity

Causal link diagrams help us to focus on nonlinear phenomena in that they divide the world into linear additive interactions as described by negative feedback, and nonlinear interactions as described by positive links that look specifically at relations that add or subtract value from the entire system through synergies or interference between the agents. They can be used as a basic formal language for capturing many game theoretical microeconomic phenomena such as non-zero sum games, externalities, and non-rival goods or market failures. It is in causal loop diagrams that involve the interaction between many causal links that we can see how complexity may emerge from very simple local rules and their nonlinear interaction over time.

Reference

1. (2017). Systemdynamics.org. Retrieved 26 May 2017, from https://goo.gl/XHtMK3

2. (2017). Systemdynamics.org. Retrieved 26 May 2017, from https://goo.gl/UtbbEP

3. (2017). Complex-systems.com. Retrieved 26 May 2017, from http://www.complex-systems.com/pdf/22-2-2.pdf

4. (2017). Nutritionmodels.com. Retrieved 26 May 2017, from https://goo.gl/s0wcTr

5. Synergy – organization, system, company, business, system, History of synergy, Individuals and synergy. (2017). Referenceforbusiness.com. Retrieved 26 May 2017, from http://www.referenceforbusiness.com/management/Str-Ti/Synergy.html