### Replace Your Bulbs: An Economic Analysis

Suppose you want to be environmentally conscious and replace the incandescent bulbs in your home with fluorescent ones. Should you replace them immediately, or wait until the current incandescent bulbs have burned out and then replace them? Let’s look at it from a purely economic standpoint (that is, only looking at the microeconomics of bulb purchases and electricity usage).

First, we need a definite period over which to measure the economics which is on the order of (but probably larger than) the lifetime of light bulbs in general, so that the results are significant and applicable to a relatively short-term analysis. We’ll call this T. This time isn’t expressed in wall clock time, but rather in the hours during which a given light socket is operated – for example, if we talk about a socket that’s run 8 hours a day for 6 years, T is only considered 2 years.

We’ll simplify things by assuming that the cost of electricity is some constant k \$/Wh over time period T. It may be possible to model the cost in terms of time t, but I currently don’t have the necessary figures, and my guess is that the effect would be negligible anyway.

So, let’s say Pf and Pi are the respective consumer prices of fluorescent and incandescent bulbs of equal brightness, that Wf and Wi are their respective watt ratings, and that Lf and Li are their respective projected lifetimes.

Further, let’s suppose a given incandescent bulb i has been in operation in its socket for some time, and its remaining lifetime is Ri. For the purposes of this analysis, I assume that the value of a bulb to a consumer starts at its price P and decreases linearly, intersecting zero at the end of its lifetime L, so that at any given time, the current value of the bulb can be computed as P/R.

Assuming we choose T > Li, the cost over T of running the incandescent bulb to its end and then replacing it with the fluorescent bulb, and continuing to use fluorescent bulbs thereafter (case 1) is:

C1 = ((TRi)/Lf)Pf + kRiWi + k(TRi)Wf

And the cost over T of immediately replacing the incandescent bulb with the fluorescent bulb, and continuing to use fluorescent bulbs thereafter (case 2) is:

C2 = (T/Lf)Pf + kTWf + (Ri/Li)Pi

Note that in case 2 I explicitly include the “cost” of tossing an incandescent bulb which hasn’t yet burned out, even though technically by the time we finish this analysis it may turn out that such a bulb is actually worthless.

Here’s what I’ve found for bulbs of equivalent brightness (feel free to substitute your own findings):

NOMA Mini Spiral Soft White Bulbs (Fluorescent)
Pf = \$3.33, Wf = 26W, Lf = 8000h

GE Standard 100 Watt (Incandescent)
Pi = \$1.69, Wi = 100W, Li = 1000h

Enwin Utilities
k = 0.000053 \$/Wh (\$0.053/kWh)

Let’s assume, as exampled above, that we have 2 years, or T = 17532h, of constant running for the socket. The equations then become:

C1 = ((17532 – Ri)/8000)(3.33) + (0.000053)(100)Ri + (0.000053)(17532 – Ri)(26)
C1 = 7.2977 – 0.0004163Ri + 0.0053Ri + 24.1591 – 0.001378Ri
C1 = 0.0035057Ri + 31.4568

C2 = (17532/8000)3.33 + (0.000053)(17532)(26) + (Ri/1000)1.69
C2 = 7.2977 + 24.1591 + 0.00169Ri
C2 = 0.00169Ri + 31.4568

Clearly, regardless of Ri (since Ri > 0), case 2, which prescribes immediately replacing the incandescent bulb with the fluorescent bulb, has a lower associated economic cost. This, of course, holds for brand new incandescent bulbs as well, in which case (using the numbers above) one can save \$1.82 over that period by simply getting rid of the already-purchased incandescent bulb and buying a fluorescent replacement. Longer analyzed time periods (T) and longer remaining lifetime on the incandescent bulbs (Ri) only reinforce the result. Finally, I have little doubt that almost any brightness or format of bulb could be put to the same test and case 2 would still come out cheaper.

The only thing left to consider is whether disposing of the incandescent bulbs early has a net negative environmental impact. I can’t prove it, but I highly doubt this is the case: the bulb is simply being disposed of early, and would probably end up in the landfill within a year or so anyway, whereas the same time period in energy savings substantially reduces the use of non-renewable energy per light socket.

My recommendation, now backed up with an economic rationale: replace your damn bulbs!

Jun 13th, 2007
1. Jun 14th, 2007 at 14:18 | #1

Actually, I just recently watched an episode of How It’s Made about CFLs, and the manufacturing process looks at least as simple as incandescent bulbs. Fluorescent lights are a very simple and elegant design. Also, the mercury thing is mostly FUD from people who want to poke holes in the environmental movement for other reasons — there’s a tiny, tiny drop in each bulb. The latest David Suzuki newsletter talks about this.

Anyway, I suggest picking up some CFLs with a warranty. The NOMA lights from Canadian Tire have one. I’m not 100% sure what the terms are, but they’re rated to last 8 times longer than the average 100W bulb, so…

Of course, turning your lights off and such (reducing resource consumption) is the best solution, but accepting that some interior lighting is going to be used, pound for pound, better to use a more efficient and cost-effective method.

Finally, I’ll leave you with this — the future of lighting is probably LED. They’re easy to build en masse with our current semiconductor manufacturing capabilities, are dropping in price hugely, are getting brighter, essentially never burn out, and are orders of magnitude more energy efficient than incandescent or fluorescent lights.