Abstract

We develop a quantitative task-based model of automation in which machines feature task-level fixed costs, e.g., application-specific training or fine-tuning costs in the case of AI models. Machine’s comparative advantage over workers across tasks reflects both the conventional marginal-productivity differences as well as a novel scale advantage (whether task scale justifies the fixed cost). We characterize the resulting production function given the firm’s task composition, deriving expressions for the degree of machine-labor elasticity of substitution, nonhomotheticity, and returns to scale. We illustrate the quantitative potential of the model in an application to computer vision AI automation. Using scaling laws that map computing requirements to task characteristics, estimated from a fine-tuning experiment and LLM-based task descriptions, we recover the patterns of AI comparative advantage for 1,920 vision tasks across the U.S. economy. Calibrated to 2023 firm-level adoption rates, the model projects the future path of automation under current trends in computing prices. Aggregate output rises by about 18% by 2075; substitutability is high early on but falls as automation deepens, real wages increase throughout, and the labor share follows a U-shape, declining initially before recovering as AI and labor gradually become complements.

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