Pricing Electricity Markets

Basic models of peak-load pricing

For no reason whatsoever, there’s nothing in the news or anything, let’s talk about electricity markets and pricing. What does price theory have to tell us about how electricity markets should be priced?

Well, I have no idea about electricity markets. But I do know a bit about pricing more generally. Let’s talk about that.

Within economics, marginal cost pricing is almost gospel. When price equals marginal cost, life is good. When price doesn’t equal marginal cost (like with all those dang markups everyone is finding everywhere), life is bad.

In Econ 101, we go through an important exception to marginal pricing: a natural monopoly. If marginal costs are declining everywhere, as in a natural monopoly, marginal costs are below average costs. If the firm sets price equal to marginal cost, the firm will lose money and go out of business. That’s not good.

Now someone like Abba Lerner may say that the proper thing to do is to have the government run these enterprises and cover the loss for the natural monopoly. Sure. Possible.

The other solution is to loosen our commitment to P=MC, such as through two-part tariffs or allowing price to be above marginal cost and closer to average cost, as Coase recommended in “The Marginal Cost Controversy,” published back in 1946.

Returning explicitly to the topic of electricity, it looks like we will have to go beyond marginal cost to understand viable pricing systems. Luckily, we have almost a century of economic research on the topic this topic, sometimes called “peak-load pricing",” including related work by basically all my favorites: Hirshleifer, Williamson, Alchian, Coase, Spulber, Buchanan, etc.

Fluctuating Demand

There are two main issues when thinking about electricity markets and the peak-load pricing problem, one on the demand side and one on the supply side. First, demand varies widely from hour to hour, day to day, month to month. That wouldn’t be a huge complication, except for the supply side problem: electricity cannot really be stored in any meaningful sense. Therefore any electricity that is produced needs to be used immediately.

Peak-load pricing refers to any attempt to price “non-storable” commodities, whose demand varies. If price were uniform over time, the quantity demanded would rise and fall periodically. I’ve seen numbers that the difference between peak and trough over a year is a factor of three or more. Even over a day, the quantity demanded may double between nighttime and the hottest part of the day.

At this point, the idea of peak-load pricing is just that the electricity provided should be charging a high price during demand peaks and a lower price during off-peak time periods.

There is nothing too complicated; this type of peak-load pricing is just supply and demand and fits perfectly with marginal pricing. If we recall the readings from the Book of Alchian, the quantity axis of supply and demand is a rate. That is, the costs are always defined as costs per time period. That’s always true; not just for the peak-load pricing problem. If we think of there being two different time periods, moderate days and cold days, the demand curve shifts out for cold days, while the MC curve is per day. This type of peak-load pricing tells us that prices should fluctuate, so that price is higher on cold days.

Most electricity prices are regulated, so this sort of dynamic pricing isn’t allowed. But maybe electricity prices should be more dynamic.

The Real Peak-Load Problem

But shifting demand alone does not make something a peak-load pricing problem. The second feature of a peak-load pricing problem is that to meet demand at the peak would then require the costly installation of additional capacity. Because electricity cannot be stored, the network needs to have a physical capacity to meet “peak” demand, even if most of the time, demand is well below peak. Otherwise, the system fails.

However, because demand is fluctuating, that capacity will be under-utilized over the remainder of the cycle.

So how do you trade off meeting peak demand against underutilization at other points? That is there is some cost to increase capacity. How should it be borne? It’s not enough to yell P=MC and claim victory.

There are lots of ways to incorporate these capacity costs. What traditionally goes under the name of “peak-load pricing” is the following from (and solution) from Peter Steiner in 1957, although I take my exposition from Jack Hirshleifer’s comment on Steiner. Steiner considered the following problem.

Suppose there are two periods (day and night) and demand is different (but independent) across the two periods. There is some capacity quantity q per period. Up to quantity q there is a per-unit cost of b. Above quantity q, the cost if b + c, which incorporates the per-unit cost of the new capacity, say investing in new capital. Notice the capacity cost is not a fixed cost, but a discontinuity in the marginal costs.

One intuitive answer is that off-peak customers should be charged only for the original per unit cost b, which does not include the capacity costs. The intuition is that they are not responsible for the excess capacity. If there were only the off-peak hours, there would be no need for the new capacity, so they shouldn’t pay.

And that is the solution some of the time. Nightime (off-peak) users pay b and daytime (peak) users pay b+c. Don’t worry. This analysis makes it clear that such a policy is not “price discrimination” since the marginal cost is different in these two time periods, even if the marginal cost curve is the same in the two periods. Hirshleifer makes this point in his paper. Instead, it’s just supply and demand. In each period, users pay their marginal cost, in the appropriate sense. Steiner calls this the “firm-peak case”.

But some of the time is not all of the time.

The problem with the naive solution is it can lead to a so-called “shifting peak.” If demand is sufficiently elastic, the quantity demanded during peak hours at the higher price b+c can actually be less than the quantity demanded at the off-peak hours at the lower price of b. So even though the demand curve during the peak hours is shifted to the right, the quantity demanded switches. If the naive solution was right (as many economists thought), the period with a lower quantity would have a higher price. Something’s wrong.

Instead, what Steiner and Hirshleifer show is that in the case of a shifting peak, it is optimal (in the sense of maximizing welfare) for people in both periods to pay for the capacity, although the peak price should still be higher. The exact optimal solution is an okay exam question, but not particularly relevant for a newsletter.

For a newsletter, the general idea is that to cover capacity costs, everyone should share the costs. And that’s more general than Steiner’s specific example.

In 1976, John Panzar extended the problem to a more traditional “neoclassical” production function, compared to the discontinuous costs above. He considers a production function, F(q_1,…,q_T, K) that uses a general capital investment, K, that must be the same for every time period (which is like choosing capacity above) with variable inputs for each period, q_t.

Panzar proves two important results. First, there should always be excess capacity. The idea is that with a neoclassical production function, more capital doesn’t just provide capacity but is also a substitute for the variable costs. At the optimum solution, the marginal cost of capital should equal the marginal cost of other inputs and you shouldn’t be “at capacity”. This is an analog of the more traditional result that firms should never drive the marginal product of any costly input to zero. The firm should have “excess’ production capabilities.

The second result is the generalization of Steiner. The cost of capital investments (capacity costs) should be split across all time periods, not just paid by the peak hour users.

Finally, I like to point out that, in the Panzar model, capacity is explicitly a fixed cost of capital. Everyone sharing the capacity costs in the optimal solution means that everyone is paying a price above marginal cost. Call in the markup police 🚨🚨🚨 Oh wait, this markup is efficient… I’ll write more on this later.

Snarky comments aside, let’s circle back to real electricity grids. I see three basic takeaways from these models, which were explicitly grappling with real electricity pricing problems, especially in the U.S. and France. First, there should basically always be excess capacity. Of course, there is always a truly unexpected event, but on the margin, we should probably increase capacity. Second, prices need to be higher to cover the capacity costs. We should not be afraid of P>MC when there are fixed costs. Third, we should find ways to allow more dynamic pricing. I’m a big fan of dynamic prices, even if they are for price discrimination, but especially if they are not for price discrimination.

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