By Shloka Satish

26 August 2025

Its no doubt that in our quest for attaining sustainability, individuals must compromise on various other features like cost, quality, and time. However, sometimes there are those golden solutions which propel us towards being a more environmentally friendly society. Switching from incandescent lighting to LED lights is one of them. So, with reference to economics, sustainability, and mathematics, this article will touch on why and how we can make this small change to create a large, worthwhile impact. 

The Economics Behind the Decision:

In purchasing a product, consumers look for the item with has minimised opportunity cost and maximised consumer satisfaction, the latter can be measured via quality and cost-effectiveness. In terms of durability and quality, LEDs last 15,000–25,000 hours, a significantly longer lifespan than that of incandescent bulbs, which burn out in about 1,000 hours. This means fewer replacements, less hassle, and lower waste. LEDs also provide steadier lighting quality, reduce flicker, and come in a range of brightness levels that improve comfort and productivity, giving them superior quality.

In terms of cost, it can be seen that an LED lighting upgrade, though costing more upfront, can also save a fixed amount per year on electricity. However, is this enough to consider the product cost-effective? The answer is no. Seeing as these savings occur over time while the cost is immediate, people can use the idea that the time value of money tells us that a dollar saved in the future is worth less today, because it could have been invested elsewhere. To resolve this, economists use the idea of use the idea of present value. By using mathematics, we will calculate the we need to calculate the present value (PV) of all future savings, and then compare it with the upfront cost. If PV exceeds the cost, the investment is worthwhile in terms of cost-effectiveness, making LED lighting an economically viable decision.

The Math of it All:  

If savings arrive steadily over time, we can treat them as a continuous function. At any point in time t (measured in years), the value of a dollar saved must be discounted because future money is worth less now. Mathematically, this discount factor is:

Where r is the discount rate (say, 5% = 0.05).

In terms of initial cost, an incandescent bulb has a 2 $ startup cost as compared to the 5 $ startup cost of LED lighting. Thus, if one were to purchase 200  units of LED lighting rather than incandescent lighting, the increased startup cost would be  600 $. It is also said that the savings of an average household switching to LED lighting are about 225 $ per year. 

If this savings rate is constant, then the present value of all savings over 10 years (a hypothetical case) is the integral:

This is equal to $1770.61, which rounds up to $1771

The Result

In solving this sum, it can be concluded that the present value of savings is about $1771. Since this is almost three times greater than the upfront cost of $600, the upgrade is not only sustainable, but also economically rational. Even if the LED dims slightly over time (reducing S(t)S(t)S(t)), the PV would still likely remain positive.

Sustainability Beyond the Wallet

The environmental benefit is equally important. Saving $225 per year corresponds to about 400 kWh of electricity avoided. At an emission factor of 0.4 kg CO₂ per kWh, this means 1.6 tonnes of CO₂ avoided over 10 years. Thus, through the integral function, we can understand that this solution comes with captures both a financial and environmental payoff: money saved and emissions prevented.

In conclusion, through mathematically modelling the savings of switching to LED light bulbs, we can see that the present value of savings outweighs the cost, while emissions fall significantly. Hence, it is clear that LEDs pay off, making them a valuable product we should all consider adopting.

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