Chemical Kinetics & Rate of Production: An Interesting Analogy

Introduction

Through this article, I am delighted to put forward a parallelism that enraptured my curious intellect. Blending scientific and economic theories is my passion. I think about a scientific topic, a law or a formula and try to use it as a foundation for an economic ideology. It was during this thought process, that I discovered the correlation. I have also tried to use this correlation to answer some of the most fundamental questions in economics. So, let’s start.

Chemical kinetics is the branch of chemistry that deals with rates of chemical reactions. A chemical reaction is essentially a chemical process that transforms reactants into products. And the rate of a chemical reaction is quite simply, the speed at which such a process can occur under a given set of conditions.

Similar to a chemical reaction is production, which is the economic process of converting physical resources (like land, minerals, seeds) into goods and services (like buildings, cars, food). This allows us to define, a new term ‘rate of production’. It is the speed at which the production process can occur under a given set of constraints (constrained optimization). In economics, variables that are defined concerning a marginal change in another variable are called marginal variables. So, we may refer to the ‘rate of production’ as the ‘marginal rate of production’.

Mathematics

Now we’ll use some mathematics. There are two ways to express the rate of a reaction:

1) Average rate of a reaction: It is defined as the change in concentration of the products (or equivalently reactants) for a unit change in time. The concentration of the product is the amount of product (in terms of moles) present in a unit volume of solution. You may simply think of it as the amount of product produced per unit time. It is expressed as follows:

Here, P refers to the product, and [P] refers to the concentration of the product. t refers to time. [P] is the concentration at time t and [P] is the concentration at time t (t < t).

2) Instantaneous rate of a reaction: It is just the average rate of reaction, as the time interval becomes infinitesimally small. Using differentiation, we can express it as follows:

Now, let’s apply the same to the process of production. So, there should be two types of rates of production:

1) Average rate of production: Just as before, the average rate of production will be the total monetary value of output produced in a unit time period. The expression is shown below:

Here Y refers to the total production output and t refers to the time. Y is the output at time t and Y is the output at time t (t < t).

2) Instantaneous rate of production: Again, make the time interval infinitesimally small. So, the following equation is obtained:

Thus, a basic analogy has been obtained. It is very important to note that the rate of a reaction measures only the speed of the reaction, not the extent of its completion. In other words, we are not concerned about the amount of product formed, we are concerned with the speed at which the transformation of reactants to products occurs. Similarly, here, our focus will be on the rate of production, not on the amount or magnitude of production. We shall now explore some more concepts to strengthen the correlation between reaction and production.

Determinants

Various factors affect the rate of a chemical reaction. These include the concentration of the reactants, temperature, catalyst, surface area, etc. I’ll first describe the concentration of reactants.

In chemical kinetics, there’s a very popular law called the rate law, which states that the rate of a reaction is proportional to the concentration of the reactants raised to certain powers. In other words,

Here, k is a constant called the rate constant, [R] is the concentration of reactants, and x refers to the order of the reaction. The law is pretty intuitive. If you have a greater concentration of reactants at any given point, the rate of the reaction would also be higher. Now, I’ll try using the above law in economics.

Logically, the rate of production must also be proportional to the amount of resources available in the economy. That is,

Here k is the rate constant, Q is the quantity of input/resources available for production, and x is another constant (which I can perhaps call ‘the order of production’).

I may not have proper proof for the above expression as it just based on an analogy, but I do have an intuitive explanation. Consider a chocolate factory, which transforms raw materials such as cocoa, sugar, milk, nuts, etc into tasty chocolates. Now, suppose due to natural factors such as favourable weather conditions or man-made factors such as better harvesting technologies or favourable government initiatives, the supply of cocoa beans increases. Microeconomically, this will cause a dip in the prices of cocoa beans. The reduction in the cost of inputs would cause producers of chocolate to increase their production. Back to our factory. As our factory increases its production, it will require more capital and better infrastructure. It would use the money that it saved (due to a fall in the price of cocoa) to purchase the required capital. Better technology would eventually hasten the process of production. So, there it is. But, one problem is that I can only explain the impact of an increase in input on average production rates. Providing a just explanation for instantaneous rates would be much more difficult and may require rigorous math. But I do hope, I have been quite successful to provide a decent intuition for the theory.

Now, coming to temperature. An increase in temperature can increase the rate of reaction significantly (better say, exponentially). What happens is that a rise in temperature increases the kinetic energy of reactant molecules, causing the molecules to vibrate more rigorously, and collide at a faster pace, thereby increasing the reaction rate. So, in other words, it increases the ability of the molecules to carry out the reaction faster.

What about production? What correlates with temperature? The answer lies in the government policies, primarily business policies that affect the ‘ease of doing business’. Consider an example. Suppose the government comes out with a new taxation policy that seeks to simplify a large number of complicated procedures involved in paying taxes. This will make it so much easier for entrepreneurs to conduct business. It’ll remove a problem or a barrier that was slowing them down. It would also allow them to pay more attention to the process of production and channel efforts to improve its efficiency and pace. Amazing, right?

Lastly, I’ll like to talk about my favourite- catalyst. A catalyst provides an alternating path /route by which a reaction can occur. Such a path has lower activation energy (activation energy is the minimum energy that reactant molecules must have to collide and form products) than the previous path. As the requirement for activation energy is lowered, a greater number of molecules will have the required energy. More molecules will be able to collide per unit time, and products will be formed at a greater rate.

Finding the economic parallelism for catalyst was a tough choice. Many factors can be correlated with it. However, I chose the best fit- Technological innovation. New ideas, initiatives and innovations, particularly the ones related to production technologies can significantly alter production. Their development can provide ‘alternate routes/substitutes’ for archaic production methods, allowing firms to expedite production.

The Bottom Line

The above theory can help us view a few basic, but essential economic concepts through scientific lenses. Some fundamental questions such as ‘Why is it important for countries to improve their Ease of Doing Business (EODB) Rankings?’, ‘What is the role of technological innovation in production?’, etc can be answered using the theory. There is a lot that can still be done. For example, understanding the role of investments and credit in boosting production pace, using graphical and mathematical rigour, and applying some interesting physical laws (Maxwell-Boltzmann Distribution). I hope to be able to come up with suitable models and theories to explain some of these in my upcoming articles!

Economics Enthusiast