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# Auto Draft

Earlier this week, we wrote about embodied energy of buildings, and the concerns it poses when we think about legislating building efficiency measures.  Today we take a broader view, examining economic limitations of any technology replacement effort, from rebuilding houses to replacing lightbulbs.

Suppose that high-efficiency washing machines are a necessary part of a low-carbon economy (as we believe they must be).  Government tax write-offs are an effective way to encourage consumers to spend the extra money on these energy-saving machines.  If the U.S. started an incentive program so effective that every consumer chose a high-efficiency machine over a conventional one, however, it would still take quite some time to replace all the energy-hogging washers in the country.  Because they are such a large purchase, the vast majority of consumers replace their washing machine only when forced to do so by problems with the old machine’s operation.  If you assume the average washing machine has a lifetime of around 10 years, it will take roughly that long (10 years) until every consumer has had an opportunity to buy a high-efficiency machine.

In the graph below, we show the diffusion curves for technologies of varying lifetimes.  If we assume the government incentive is so strong that every consumer chooses the efficient version when they buy a replacement — We say the adoption rate is 100%.  We can see the curve for washing machines (and other goods with a 10 year lifetime) above the tan strip.   Starting from 0% of the technology stock, high-efficiency machines take roughly 10 years to replace conventional ones.  So even with the ideal incentive program, there is still a considerable lag time during which inefficient washers are wasting energy and water.

In this simple model, there are two technologies with the same given lifespan, and each consumer has a chance to upgrade from the inefficient version to efficient only when their existing unit stops working.  Once a consumer buys the efficient version, he or she never goes back (For those interested, the math is a simple Monte Carlo model).  As we can see below, no matter at what percentage we start when the incentive is implemented, the time until every old unit has been replaced is bounded by the lifespan of the good.  Think about the consumer who bought an inefficient machine the day before the incentive started:  They won’t have a chance to take advantage of it for another 10 years!

In reality, no incentive will bring the adoption rate to 100%.  In the graphs below, we show the 100% adoption rate scenario alongside three others which assume 50%, 25%, and 12.5% adoption rates, respectively.  A 50% adoption rate means that 50% of consumers make the `efficient’ choice at their next opportunity, and 50% buy something similar to what they currently have.  We can see that replacement actually happens more slowly than the upper bound dictated by technology lifespan.  With washing machines, for example, a 50% adoption rate means that the stock of high-efficiency machines only reaches 90% of the total after roughly 30 years.

Let’s explore what these graphs say about power consumption of washing machines.  Assuming a 10 year lifetime, we can do a very rough calculation of the average power consumed by washing machines in the U.S.  A conventional washing machine uses roughly .35 kWh per day if we assume one load every three days.  There are roughly 100,000,000 households in the U.S., so let’s assume there is one washing machine per household.  Thus, if every washing machine in the U.S were conventional, the power consumed by them would be roughly:

$$\frac{ .35 \text{ kWh per day per machine} \times 100,000,000 \text{ households in U.S.} }{ 24 \text{ hours per day} \times 1,000 \text{ kW per MW}}= 1458 \text{ MW}.$$

This is on the order of the total electricity consumption of a major city!  Energy Star washing machines are advertised to cut energy costs by roughly one third.  Using these estimates, we can make a simple estimation of power consumed by washing machines in the U.S. for various constant adoption rates, shown in the graph below:

While these models are extremely simple, almost any technology, not just washing machines, will follow this rough characterization.  In any case, consumers, utilities, governments, and other players in the climate game are likely to require extreme motivation before they would discard their appliances, facilities, and infrastructure while they could still extract earnings from their up-front investment.  For technologies with longer lifespans like power-plants and houses, this restriction seriously slows the effectiveness of a policy to cut energy use.  This is why in-the-know climate leaders like James Hanson of NASA say we should build zero new coal-fired power plants.  Today’s decisions will likely dictate the electricity grid makeup for the next 50 or 60 years!

The take-away message from this entry is that no matter how aggressively we push policy incentives to replace infrastructure, the effect will likely be delayed by the constraints of economics.  The policies with greatest effect are those that take this into account in one of two ways.  First, our graphs show that targeting technologies with short lifetimes is inherently a better way to quickly replace technology stock.  For two technologies with similar energy use profiles, the better incentive is the one supporting that with the shorter lifetime.  Unfortunately, the majority of our energy use is accounted for by long-term infrastructure: our houses, cars, electricity grid, transportation needs, etc.  For these items, however, we can try to sidestep the bounds on diffusion curves through targeting parts of the infrastructure that can be replaced without significant loss of investment.  Very few people will rebuild their entire house while it still functions, but many could be convinced to invest in additional insulation for it.

Second, since the barrier to these diffusion curves is economic, the most effective policies will target the technologies where significant monetary gains are possible by replacing old infrastructure.  If the payback periods for new technologies are favorable and publicized, policies might just motivate consumers to make purchasing decisions which exceed the diffusion curves.  We should approach this with caution, however, as there are energy trade-offs that come with replacing useful infrastructure.  If you read our entry on Embodied Energy of Buildings, you know that construction and manufacturing takes energy which for some technologies is comparable to the savings from high-efficiency replacements.  Just another reason why vigilant accounting is essential to making good decisions!