The proposed research builds upon a well-defined intellectual progression in economic growth theory, which has moved from early models treating technology as an exogenous residual to modern frameworks where innovation is an endogenous, profit-driven activity. This evolution provides the necessary theoretical architecture for investigating not just the rate of technological progress but also its direction. This section synthesizes the core theoretical constructs from the source material to establish the foundation upon which the new research questions are built, charting a course from the neoclassical benchmark to the frontier of directed innovation.

2.1 The Neoclassical Benchmark

The Solow and Ramsey-Cass-Koopmans models (Chapter 2 and Chapter 8, respectively) form the bedrock of modern growth theory. They provide a powerful framework for understanding how capital accumulation and exogenous productivity gains drive long-run economic growth. However, for the research question at hand, their primary limitation is their inability to explain the origin and bias of technology. Technological progress is assumed to arrive from outside the model. While Uzawa’s theorem (Proposition 2.11) demonstrates that a balanced growth path requires technology to be purely labor-augmenting (Harrod-neutral), the neoclassical framework offers no economic mechanism to explain why innovation should endogenously take this specific form, nor why it might deviate to become skill-biased.

2.2 Innovation as an Endogenous Process

The endogenous growth models pioneered in the late 1980s and early 1990s provided the critical next step. The expanding variety models (Chapter 13) and models of competitive, quality-improving innovations (Chapter 14) established the micro-foundations of innovation as a purposeful economic activity. In these frameworks, firms invest in research and development (R&D) in pursuit of monopoly rents that can be captured from new products, processes, or ideas. This conceptual leap—from exogenous technological “manna from heaven” to an endogenous, profit-seeking process—is a necessary precondition for any theory of directed innovation. By establishing that innovation responds to profit incentives (monopoly rents), these models create a channel through which economic forces—such as changing factor supplies—can influence not just the rate of R&D, but also the type of R&D that firms choose to pursue.

2.3 The Core Framework of Directed Technological Change

The baseline model of directed technological change (Chapter 15) provides the central theoretical apparatus for this proposal. It builds on the endogenous growth framework by allowing firms to choose not only how much to invest in R&D, but also what type of R&D to pursue. In a canonical model with two factors, such as skilled (H) and unskilled (L) labor, firms can invest in creating either L-complementary or H-complementary technologies. The relative profitability of these two types of innovation is determined by the interplay of two fundamental economic forces.

The crucial parameter governing the balance between these two effects is the elasticity of substitution (σ) between the factors of production (L and H).

• When the market size effect dominates the price effect, an increase in the relative supply of a factor induces a technological bias in its favor. This result, termed the weak equilibrium bias, holds under general conditions. It provides a direct mechanism to explain the skill premium puzzle: an increase in the supply of skilled labor (H) makes the market for H-complementary technologies larger, inducing profit-seeking firms to innovate in a skill-biased direction.
• This induced innovation shifts the relative demand curve for skilled labor outward. If the elasticity of substitution (σ) is sufficiently large, this induced shift can be so strong that the long-run relative demand curve for skilled labor becomes upward-sloping. This strong equilibrium bias provides a powerful explanation for how the skill premium can rise in tandem with the supply of skills.

This theoretical foundation provides a robust and internally consistent framework for understanding the puzzle of the rising skill premium. The next step is to extend this framework to articulate and test specific hypotheses about the more complex interactions involving capital.