$$s \cdot (T_{\text{grid}} - T_{\text{site}}) > \Delta C$$

Equation 7 · AI Industry

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

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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 $s \cdot (T_{\text{grid}} - T_{\text{site}}) > \Delta C$. whenever it takes the faster, costlier, more legally exposed route over the slower, cheaper, better-permitted one. The model does not say what s should be; it says xAI’s revealed…

Meanings in this article

• $s$: the value the firm places on each unit of time saved reaching $P^*$ sooner.
• $T_{\text{grid}}$: the taking time.

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