APPLICATIONS OF LOGARITHMIC &EXPONENTIAL FUNCTIONS IN ECONOMICS AND GENERAL COMMERCE

“Mathematics is everywhere”: a phrase that we find ubiquitously thrown around is agreed upon by the masses. The field of commerce is no exception to this, and often mathematical tools are essential to understanding and implementing various concepts in Economics, business and finance. Economics and Mathematics are complementary disciplines. The use of Mathematics allows modern economists to construct specific models and analyse the effects of changing variables of the real world. Higher-level math courses, including Statistics and Calculus, are almost always mandatory for students pursuing business, finance or economics degrees. Consequently, we are intrigued by the real-world applications of Mathematical concepts in the field of commerce. This article pens down some of the many applications of logarithmic and exponential functions in Economics and general commerce.

Finance

Calculating compound interest is not exclusive to those in finance; instead, it is a task that one will inevitably come across while managing personal finances. When interest is earned on an individual’s investment, it is relatively easy to compute as a linear function; however, compound plans for interest are also available in modern banking systems. These include adding interest on the interest that the depositor has already earned. The exponential function models this: A(t) = P(1 + r/n)nt, where P is the principal, r is the interest rate, n is the number of times the interest is compounded each year, and t is the number of years since the investment was made.

Compounding functions are especially vital for investment decision making. Investors will want to analyse an investment; the cash outflows and the expected future receipts must be transformed into units of standardised value and then compared. An amount received in the future is not equivalent to an amount held in the present because money, if invested at some rate of interest, grows to a more significant amount. Compounding interest permits the conversion of future values into present values, hence aiding decision making. Therefore, logarithmic and exponential functions are used to calculate the various variables in the compound interest function and are an integral part of modern finance.

Economics

Logarithmic and exponential functions are commonly used to model exponential growth and decay. In economics, these functions are used to construct models like population growth and population growth rate, allowing economists to make calculated predictions and aid policymaking. The population growth rate for a region goes through phases of growth, decline and stagnation. These can be computed for the period t2 - t1 by the formula: PGR=ln(P(t2))−ln(P(t1))/(t2−t1). For instance, as estimated by the United Nations, the world population graph is modelled as an exponential graph that shows the projected population until the year 2100.

In addition to this, the study of microeconomics involves analysing and evaluating different demand curves that are modelled exponentially. Without such functions, economists or firms would not be able to predict the quantity demanded at specific prices. Furthermore, an entire economy’s aggregate demand would also be graphically depicted as an exponential function and help economists consider various economic scenarios and build policies accordingly.

Conclusion

In hindsight, it is beyond the scope of a short article to elucidate all the applications of logarithmic and exponential functions in economics and general commerce, but it is safe to conclude that the field of commerce in our modern world can not be stripped of these mathematical concepts. Moreover, it is likely that in the near future, we will see more such applications of logarithmic and exponential functions in economics and general commerce.

Ananya Singh