# Anyone remember this economics research?

Looking at the blue LED Nobel I’m reminded of something that I think I remember (go figure!). Which is that spending on lumens has remained steady as a percentage of income over the centuries (0.7% of income maybe?).

Google’s not much help when searching for likely phrases to such research (lumen, light, income etc all seem to throw up other things). Does anyone recall more of this research so that I can track it down?

## 16 thoughts on “Anyone remember this economics research?”

1. Matt Ridley has section on Cheap Light in Chapter 1 of “The Rational Optimist” with references to Nordhaus, Don Boudreaux and others

2. You did this years ago, and I thought that spending on lighting remained constant over time, but with the amount of light bought going up as it got more efficient.

3. Surely there must come a saturation point where this relationship no longer holds. Most of us in affluent societies light our living and working spaces to the brightness we desire, and we’re getting to a point where luminous efficacy is running into fundamental physical constraints (100 lm/W is achievable right now and the limit for LEDs is about 300 lm/W, which is 44% of the absolute physical maximum of 683 lm/W from an ideal radiator under photopic conditions). Assuming the market-clearing price of these things continues to drop then sooner or later the cost per lumen curve must start to flatten out. At 300 lm/W a 100W incandescent is replaced by a 5.3W LED.

4. Also, a note on units. Candela (Cd) is the unit of luminous intensity i.e. how bright a light source is in a given direction. Lumen (lm) is the unit of luminous flux i.e. the luminous intensity integrated over area, equal to one candela steradian (Cd•sr). In lighting terms it measures the total output of the bulb. Lux (lx) is the unit of illuminance i.e. how much light falls on a given area. It is equal to one lumen per square meter. It’s lux that’s really the useful figure for how brightly lit is a room. One klx is a very bright room, or an overcast day. Normal lighting is 50-500 lx.

5. Bloke in Costa Rica,

There are two ways in which light output can grow: more lights in more places, or brighter lights in existing places. The former might already be saturated, but for the latter the sky’s the limit.

No doubt there’s a paper or two kicking around that shows a correlation between street lighting intensity and lower levels of crime. Cue calls for brighter street lights from the usual busybodies. At first it’ll just be city centres, but before long your local drab parade of shops will be lit up like daylight, even at 2am.

6. I’m sure there’s still room for growth, but overly-bright lighting is a quality of life issue all of its own. We’ll never banish night entirely (a bright sunny day has about 2500 times the illuminance of a well-lit office). I wouldn’t underestimate the efforts of the Green miserablists to put the kibosh on things, either.

Really, all I’m saying is that there has to be some Steinian sense that if spending on lighting cannot track increasing income forever, then it will cease to do so.

7. Why not ask the world’s greatest economist? He’s bound to know (or if he doesn’t he’s certainly bound to pretend he knows)

8. “Surely there must come a saturation point where this relationship no longer holds.”

There’s a law for that.

9. Runcie, that’s very interesting (and new to me), but I was referring more to the point where trying to keep lm/\$ (with d (lm/\$)/dt -ve) × \$ (with d\$/dt +ve) at that constant proportion of income will become impossible not out of technical constraints on how much light you can get out of an LED for a given chunk of dough, but out of a desire to not live as if someone were pointing an arc lamp at you. This is really rather interesting the more I think about it.

Some jottings: assume 200 lm/W. Then a 100W incandescent replacement (1.6 klm) uses 8W. With a 1/3 duty cycle consumption is ~23.4 kWh/year or about £2.50 a year in the UK. At a 5% discount rate that’s an NPV of 50 quid or so, given that quoted lifetimes for LED bulbs basically makes this a perpetuity. We are a way off from this in terms of commercially-available bulbs, but Philips say they’ve got a device that yields 1klm/\$, and Cree claim a 300 lm/W unit in the lab. Eventually, if Haitz’s Law holds, spending on illumination hits a floor almost entirely dominated by energy costs. If the Greens don’t throw their sustainably-produced clogs in the works then this number will fall as well.