The Valve

1Introduction: transformer prices have broken away

Between January 2015 and August 2026 the producer price index for power transformers rose about 100%, against about 50% for producer prices across all commodities. The ratio of the two averaged 0.99 over 2015 to 2019, never leaving a range of 0.96 to 1.04. It broke upward in 2020, peaked at 1.42 in October 2025 and stood at 1.34 in August 2026 (Exhibit 2). Power construction spending grew about 6% a year both before and after 2020 (Table 1). A faster pace of spending therefore does not by itself account for the break.

The idea we examine is narrow. Output of a chain is set by its smallest stage, so spending at stages that are not scarce leaves output unchanged, and demand that cannot be met is rationed by price, by waiting time, or by both. Price is the only one of the three with a long public history. This paper reads that history, together with utilization, spending and company filings, and then states where the evidence stops.

Picture a four lane highway that narrows to one lane for half a mile. The cars that get through each minute are set by the one lane. Widen the open stretches and nothing changes. Add cars and the line behind the one lane gets longer. When people size the market for data centers or count the capital going into the grid, they count the cars entering. They do not ask how wide the narrowest lane is.

We use one chain throughout, the equipment that connects new demand to the U.S. power grid, because it has long public data and a recent surge in demand. Every number comes from a named public series under its exhibit, and Appendix A lists them all. Where we have no public series, we say so.

2Measuring the lane: a barrel, a minimum and a delay

Output is set by the scarcest input, not by the average of all inputs. In 1840 the German chemist Justus von Liebig showed this for crops. A field can hold plenty of nitrogen and potassium. If phosphorus is short, the plant stops at the height phosphorus allows, and adding nitrogen does nothing. The picture that came to stand for it is a barrel of unequal staves. Water rises to the shortest one.

Monod (1949) put the same idea into growth equations for populations. Goldratt and Cox (1984) carried it to factories and called the slowest step the constraint. A power transformer is such a system. It needs a steel core, copper windings, a tank, insulation and cooling. If one is short, output is short, and spending on the rest buys nothing.

The model has two lines of math. A chain of stages with capacities c₁ to c_n delivers

It is the minimum, not the average. Demand in a real buildout grows at a roughly steady rate, D(t) = D₀e^gt. Capacity at the scarce stage arrives in steps and with a delay τ, because a dollar spent today becomes output only after permits, construction and qualification. When demand grows faster than capacity can be added over τ years, a gap opens and output stays flat. The extra demand is then rationed by price, by waiting time, or by a queue.

Equation 1 has a precise consequence. Raising the capacity of any stage other than the smallest leaves output unchanged. Raising the smallest by an amount Δ raises output by Δ until the next smallest stage becomes the limit. The delay has a second consequence. Capacity that starts at time t − τ is sized to the demand visible then. If demand compounds at rate g, demand at t is e^gτ times larger. As arithmetic only, and not an estimate for any industry, a rate of 10% a year and a delay of three years leave demand about 35% above that capacity on arrival.

The framework says a delay exists. It does not say how long it is. In real cases the gap seen several years earlier is what sets capacity today, and the length differs by industry. We did not find a way to read τ from public totals (Section 4).

3Evidence from one chain: prices, backlog, utilization and spending

We take four public readings of one chain in turn: price relative to producer prices overall, the turbine price and backlog, factory utilization, and spending after removing price changes. Each reading is a sign consistent with a tight stage, and none is proof alone. The ratio below is the transformer index divided by the all-commodities index, both set to 1.00 in January 2015.

Table 1 splits the period at January 2020. Transformer prices grew 1.5% a year before the break and 9.9% a year after. Producer prices overall grew 0.7% and 5.7%. Power construction spending grew about 6% a year in both periods.

Transformer prices grew 8.4 points a year faster after 2020 than before, producer prices overall 5.0 points faster, and spending growth did not change. The transformer index therefore accelerated by about 3.4 points more than the general price level. These series do not tell us what caused that difference.

Price alone is a partial signal. The same test for turbines gives a different answer. The turbine price index has risen 31.6% since 2015, less than producer prices overall.

The index records the price on shipments in a given month. If orders come long before shipment, scarcity could show in a queue before it shows in the price index. Exhibit 4 shows the contracted backlog at GE Vernova, a large turbine builder, which rose in each of the last six quarters in its public filings. It covers the whole company, including wind and electrical equipment, and it measures contracted revenue and not delivery time. It fits a queue and does not prove one. We have no public series for delivery times and we do not chart one.

Utilization and spending

Capacity utilization for electrical equipment manufacturing has averaged between 84% and 86% over the last twelve months. That is seven points above its 2000 to 2019 average of 78.8%. Its highest reading since 2000 was 89.8%, in January 2008.

A plant that is already full can add output only by building more plant. High utilization is consistent with a scarce stage. It is not proof of one, because utilization is measured for the whole industry, which includes many products.

Money has flowed in, but less than the headline suggests. Power construction spending is up 95% in dollars since January 2015. Deflated by producer prices it is up 30%.

Roughly two thirds of the dollar growth is price. We do not claim the physical amount built rose by 95%. Producer prices overall are an imperfect deflator for construction, and we have no better public series here, so 30% is a rough figure and not a precise one.

4Where the idea stops: two tests

The idea says a buildout is limited by its narrowest stage, and that the narrow lane has to be found case by case. We tested two extensions beyond that. Neither held in public data, and both results fit the case-by-case conclusion.

4.1 A measurable delay

The framework says capacity responds to the gap with a multi-year delay. It does not say that the delay can be read from public totals. We tried anyway. If spending drives capacity and capacity limits output, a rise in spending should be followed by a rise in transformer prices after about τ months. We correlated the 12-month change in power construction spending, lagged by 0 to 24 months, with the 12-month change in the transformer price index, using 128 monthly observations. The correlation is −0.07 at zero lag and stays negative at every lag up to 18 months. The readings at 21 and 24 months are positive and small, 0.02 and 0.11.

The most negative reading is −0.23, at nine months. A peak in the positive direction would have located τ. There is none. Spending totals for the whole power sector do not isolate one scarce stage, and prices after 2020 moved with many other forces. We do not draw a lag from this.

4.2 A screen across industries

If the idea worked as a screen, industries running tighter than usual should have seen bigger price increases. The framework says it does not: knowing that constraints exist in general does not tell you where one sits in a given industry. For each of 14 manufacturing industries we compared recent utilization relative to its own 2000 to 2019 average with the change in its producer price index since January 2020. The correlation across all 14 is −0.05 and the rank correlation is 0.07. Removing petroleum and coal and primary metals, the two largest price changes, gives 0.07 and 0.16 across the remaining 12, which is still weak. Electrical equipment, which contains transformers, sits high on both axes. Petroleum and coal, where utilization was near normal, saw prices more than double. Primary metals, with utilization 6.8 points below its average, saw prices rise 91.5%.

4.3 What this shows

Tightness measured across industries does not find the scarce stage. Industry groups combine many products, and one scarce part inside a group is not visible at that level. This is the reason the work is done one chain at a time: trace the chain back to its physical minimum, then check lead times, utilization and margins for that chain. The transformer chain is one such case. These tests give no evidence of how many others there are.

5A case study: a real scarcity that did not last

A real shortage does not guarantee a lasting payoff. The clearest case in the public record is a rare earth producer.

In September 2010 a dispute led to a de facto halt in Chinese rare earth shipments to Japan, which China denied imposing, and which lasted about two months. China then produced the large majority of the world’s supply. Prices of rare earth materials rose sharply. Molycorp owned the largest rare earth mine outside China. Its revenue went from $35 million in 2010 to $397 million in 2011, about eleven times higher, and it reported its first annual profit as a public company. It then reported a loss in each of 2012, 2013 and 2014. The scarcity rested on a government’s export decision. When shipments resumed and buyers found other sources, the price that supported those revenues did not last.

6Three questions to ask of any lane

Finding the lane is one job. Being paid for it is another. We do not test in this paper whether the questions below pick profitable investments. They are a checklist for organizing the evidence, and the Molycorp case in Section 5 is the only case we examine.

• Where is the physical minimum? Trace the chain back to the piece that cannot be bought quickly.
• Who owns it, and can they raise the price? Imagine a 25% price increase. Can the customer walk away, would redesign take a year or two, or is there no alternative?
• Does the scarcity last? A scarcity can end when someone builds around it, which takes time, or when a policy changes. In the one case we examine, a scarcity that rested on a government’s export decision did not last.

The second question separates the owner of the shortage from the one who earns on it. The third separates a physical scarcity from a policy one, as the case in Section 5 shows, though one case does not make a rule. A fourth force sits outside the chain. You can find the right lane and still lose money for a year or more, because interest rates and the mood of financial markets sit on top of the physical constraint. The real yield on ten-year Treasuries was below zero in 2020 and 2021. It has ranged between 1.6% and 2.9% since October 2023 and stood at 2.9% in October 2026.

We show the yield as context. We do not test its link to any outcome in this paper. A backlog can grow and margins can hold while a price does nothing, because the market has not yet agreed that the shortage will last. A full account needs the physical constraint and the financial one.

7Concluding thoughts

In the power equipment chain the public record shows a clear break: transformer prices sit 34% above producer prices overall, factories run seven points above their long-run average, and spending after removing price changes is up 30%. The idea behind this paper is simple. Output is set by the narrowest stage, and the profit from a shortage often sits somewhere other than the shortage. The data fit that picture in this chain. Public totals do not give a measurable delay, and industry-level tightness does not find the lane, so the work has to be done one chain at a time.

Notes

1. Data are as published at the retrieval date, October 15, 2026, and reflect the latest revision then available. We did not use real-time vintages, so figures may differ from what was visible in the past. Producer price indexes are revised for a limited period after first publication, and later revisions to older data are possible.
2. Two periods end in different months. PPI for transformers runs to September 2026, PPI for all commodities and power construction spending to August 2026. Rebased ratios use the latest month available for both, August 2026, except where the text says September.
3. The producer price index for transformers covers electric power and specialty transformer manufacturing. It includes small and specialty units as well as large power transformers.
4. Correlations in Exhibits 7 and 8 are of log changes. Overlapping 12-month changes make successive observations dependent, so we do not report significance levels. The cross-industry correlation uses 14 points and is descriptive.
5. The halt in 2010 rare earth shipments to Japan is reported by the BBC (November 24, 2010) and Reuters (January 31, 2011). The export quota cuts are described in the Molycorp prospectus filed with the SEC in June 2011. Company revenue and net income come from Form 10-K filings. We do not chart rare earth prices because we have no series we can source here. Molycorp net income was positive in 2011 and was a loss in each other year from 2010 to 2014.

Appendix A. Data series

Transformations: rebasing to January 2015 = 100 or 1.00; ratios of rebased indexes; deflating by rebased PPIACO; log 12-month changes; compound annual growth between end months; correlations across lags and across industries. FRED: Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org. EDGAR: https://data.sec.gov/api/xbrl/companyfacts/.

References

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2. Goldratt, E. and J. Cox. The Goal: A Process of Ongoing Improvement. North River Press, 1984.
3. Monod, J. “The Growth of Bacterial Cultures.” Annual Review of Microbiology, Vol. 3 (1949), pp. 371-394.
4. Sterman, J. Business Dynamics: Systems Thinking and Modeling for a Complex World. McGraw-Hill, 2000.
5. von Liebig, J. Die organische Chemie in ihrer Anwendung auf Agricultur und Physiologie. Vieweg, 1840.