What drives the patterns of AI automation: expanding capabilities or falling computing costs? We develop a quantitative task-based theory of production in which firms choose among various vintages of an automation technology (in this case, AI models) for each task, subject to adoption frictions. Larger models are more capable but require more computing, so automation of some tasks relies on models smaller than the frontier. An expanding frontier lowers costs only in tasks that may rely on new models, while cheaper computing lowers automation costs for all tasks that AI can perform. We measure the capabilities and costs of AI models across different tasks using a new survey: workers grade the output of 41 language models on samples of 7,400 production tasks in over 800 occupations. The token costs for producing each task/model combination offer measures of the corresponding computing costs. Using this data, along with additional moments of AI spending and occupational adoption, we quantify our model and use it to project the future path of AI automation given trends in capabilities and computing costs. The model predicts that by 2050 AI will perform 54 percent of all work in the US economy. Halving the rate at which computing prices fall lowers this share to 39 percent, while halving the growth rate of frontier models leaves it almost unchanged.