Article by Samuel Adeyemo, COO at Aurora Solar

A well-established concept in economic theory is the idea that profits are maximized when the marginal revenue earned from selling a good equals the marginal cost of producing that good. Marginal revenue means the amount of money you get for selling just one more unit of the product, and marginal cost is how much it costs you to make one more unit of the product. Profit is the difference between revenue and cost.

If marginal revenue is greater than marginal cost, then the producers of the good would make more profits by producing more units of it, because they could sell their produce for more than it costs to make it. This seems fairly simple: If you can sell a good for more than it costs you to make it, just keep making more of it and rake in the profits.

Unfortunately it is not that simple: With most goods, the more you produce, the lower the selling price of the good. To make matters worse, at some point when you produce a lot of a product, your marginal cost starts to rise. This is because at some point to produce more goods you have to incur significant fixed costs. For example, you may need to build a new factory or hire more people.

Putting these facts together, it means that at some point if you produce too much of the good, you will start to lose money, since the cost of producing it will be higher than the price you can sell it for.

The point at which you are not leaving money on the table by not producing enough goods, but are not losing money because you are producing too much, is called the profit maximization point and is represented by Q* on the chart below.

So what does this lesson in basic economic theory have to do with solar design? Well, you can think of the “producer” as being the homeowner, the good we are selling as electricity, the marginal cost of making that good as being your Levelized Cost of Energy (LCOE)[1], and the price (marginal revenue) for that good as being the effective utility rate.

Recall that economic theory states profits are maximized when marginal revenue equals marginal cost. Applied to solar, this means that the optimal amount of energy (Q* ) a solar installation should generate is achieved when the effective utility rate is equal to its LCOE. If the effective utility rate is higher than the LCOE, then the homeowner is leaving money on the table by not generating more energy—they should get a bigger (or higher-producing) system. If the effective utility rate is lower than the LCOE, then the homeowner is losing money on each unit of energy they generate—they should produce less energy (or none at all).

Let’s consider two examples to demonstrate this principle. In our first example, we look at a homeowner that is installing solar on their house in Pacific Gas & Electric’s E-1 Baseline Region S. This is a region that has tiered electricity rates. That means that the cost of electricity increases the more the home owner consumes, and the table below reflects those rates as of August 30, 2015.

For this example, let us assume that the homeowner is consuming about 33 kWh a day, or 12,045 kWh a year [2]. Since this is a net energy metering regime, any electricity above the homeowners consumption amount gets exported to the grid at a rate of $.05/kWh

If we draw a chart plotting the LCOE against the effective utility rate, we find the profit maximizing solar production amount is approximately 10,000 kWh, an offset of approximately 80% of the homeowner’s energy consumption.

Let’s consider another example, where we will use a flat utility rate of $.18/kWh, that has a sharp drop off to $.05/kWh at amounts above 12,045 kWh, since at that point the homeowner would be net exporting to the utility grid. In this case the profit maximizing level of production is to offset 12,045 kWh, 100% of the homeowners consumption. If we produce any less than that, we are leaving money on the table, and any more than that, we are losing money on every kWh we export to the grid.

These two solar designs should seem logical to you—with no economics background you would likely have offset only the most expensive energy in a tiered electricity price regime, and all of the bill in a flat-rate regime. So why go through the trouble of reframing the problem in economic terms?

This framework makes it easy to quickly determine optimal system production under different utility rate regimes. You can always double check your manual design by comparing its LCOE to the prevailing utility rate—good design software, such as Aurora (www.aurorasolar.com), allows you to do this. Designing a system that produces Q* kWh maximizes the benefit to your customer. If you ever come across an economist or any other similarly financially literate customer, you are a shoe-in to win the deal!

The examples above were stylized, but any good software should allow you to perform this type of analysis quickly. Aurora Solar, where I work, provides a one-stop solution that allows you to design a full solar installation from as little as an address, and a utility bill. We have a fully developed financial analysis suite, including a utility rate database, that allows you to calculate LCOE and numerous other financial return metrics. Visit www.aurorasolar.com to learn more.

Notes:

[1] For the purist, you could argue that LCOE corresponds to the Average Cost of producing energy as opposed to the Marginal Cost. Since at Qthe AC = MC, the model leads to the same analysis and I have chosen to call it Marginal Cost for simplicity. [2] This is about average for the typical American household.