How does Romer's endogenous growth theory explain sustained growth without relying on exogenous technology?

Paul Romer's endogenous growth theory argues that technological progress results from purposeful R&D investment by profit-seeking firms, not from an unexplained external force. The key insight is that knowledge is a non-rival good — one firm's use of an idea does not prevent others from using it — which creates increasing returns at the economy-wide level.\n\nWhy Knowledge Differs from Physical Capital:\n\n1. Non-rivalry: A machine can only be used by one firm at a time. An idea (software algorithm, production technique, chemical formula) can be used simultaneously by unlimited firms.\n2. Partial excludability: Patents and trade secrets provide temporary monopoly profits, incentivizing R&D, but knowledge eventually diffuses.\n3. No diminishing returns: The 1,000th idea is potentially just as valuable as the 10th. Unlike capital, there is no natural decay in the productivity of accumulated knowledge.\n\nRomer's Model Structure:\n\n`mermaid\ngraph TD\n A[\"R&D Sector
Researchers produce new ideas\"] --> B[\"Knowledge Stock A
Grows with R&D investment\"]\n B --> C[\"Intermediate Goods Sector
New designs become products\"]\n C --> D[\"Final Goods Sector
Y = A x K^alpha x L^(1-alpha)\"]\n D -->|\"Profits\"| E[\"Incentive for R&D
Patent rents\"]\n E --> A\n B -->|\"Spillovers\"| F[\"Other firms benefit
from knowledge diffusion\"]\n F --> D\n`\n\nSolow vs Romer Comparison:\n\n| Feature | Solow (Neoclassical) | Romer (Endogenous) |\n|---|---|---|\n| Source of growth | Exogenous technology | Deliberate R&D investment |\n| Returns to capital | Diminishing | Constant or increasing (with knowledge) |\n| Steady state | Yes (without tech progress) | No — perpetual growth possible |\n| Policy role | Limited (can affect level, not growth) | Critical (subsidies, IP, education) |\n| Convergence | Poor countries catch up | Not necessarily — knowledge gaps persist |\n\nWorked Example:\n\nConsider two economies: Novara (invests 4% of GDP in R&D) and Terrano (invests 0.5%).\n\nIn the Solow model, both converge to the same growth rate (determined by exogenous tech progress). In Romer's model:\n- Novara's growth rate: g = delta_A x fraction_researchers x A\n- Terrano's growth rate: significantly lower because fewer resources devoted to innovation\n- The growth rate gap persists indefinitely — no convergence\n\nPolicy Implications for CFA:\n\n1. R&D subsidies can permanently increase the growth rate (not just the level)\n2. Intellectual property protection creates the monopoly rents that incentivize innovation, but too-strong protection can block spillovers\n3. Education investment increases the stock of researchers, accelerating idea production\n4. International trade facilitates knowledge diffusion across borders\n5. Scale effects — larger economies have more researchers and potentially faster innovation\n\nCriticism:\nThe scale effect prediction (larger populations = faster growth) is not consistently supported by data. Later models by Jones and others modified this to semi-endogenous growth, where policy affects the growth rate only during transition.\n\nExplore growth models and their investment implications in our CFA Economics course.