Equation 5 · How xAI's Infrastructure Build Compares to the Rest of the Field

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s

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the value the firm places on each unit of time saved reaching $P^*$ sooner. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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s

Symbol s

the value the firm places on each unit of time saved reaching $P^*$ sooner.

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Model the choice as a simple trade. A firm can reach a target power capacity $P^*$ either by waiting for grid interconnection, taking time $T_{\text{grid}}$ , or by generating on site in the shorter time $T_{\text{site}}$ , at an extra cost $\Delta$ C over grid power — fuel, turbine leasing, and the practical cost of operating ahead of a permit, including the risk of enforcement. Let s be the value the firm places on each unit of time saved reaching $P^*$ sooner. A firm behaves as though it believes

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