We create a general and tractable theory of increasing sorting in pairwise matching models with monetary transfers. The positive quadrant dependence partial order subsumes Becker (1973) as the extreme cases with most and least sorting and implies increasing regression coefficients. Our theory turns on synergy—the cross-partial difference or derivative of match production. This reflects basic economic forces: diminishing returns, technological convexity, insurance, and learning dynamics. We prove sorting increases if match synergy globally increases, and is cross-sectionally monotone or single crossing. We use our results to derive sorting predictions in major economics sorting papers and in new applications.

Technological advance is often embodied in capital inputs, like computers, airplanes, and robots. This paper builds a framework where capital inputs advance through (i) increased automation and (ii) increased productivity. The interplay of these two innovation dimensions can produce balanced growth, satisfying the Uzawa Growth Theorem even though technological progress is capital-embodied. The framework can further address structural transformation, general-purpose technologies, the limited macroeconomic impact of computing, and declining productivity growth and labor shares. Overall, this tractable framework can help resolve puzzling tensions between micro-level observations of innovation and balanced growth while providing new perspectives on numerous macroeconomic phenomena.