Economic Growth II: Technology & Policy – Macroeconomic Theory I Study Notes

Economic Growth II: Technology & Policy

Introduction to Technological Progress in Macroeconomics

Technological progress is a key driver of long-term economic growth, as observed in real-world data where income per capita increases over time. The Solow-Swan model, a foundational framework in macroeconomics, originally assumes constant production technology and a steady-state income per capita, but empirical evidence contradicts these assumptions.

• Key Point: U.S. real GDP per person grew by a factor of 8.3 from 1908 to 2013, averaging 1.9% per year.

• Examples: Farm sector productivity tripled (1950–2012); computer power prices fell 30% per year; internet and cell phone usage expanded rapidly; digital storage and media capabilities increased dramatically.

Technological Progress in the Solow Model

To account for technological progress, the Solow model introduces labor efficiency (E), which augments the labor force and is assumed to grow at an exogenous rate g. This modification allows the model to reflect increases in output due to improvements in technology.

• Labor-Augmenting Technological Progress: Technological progress increases labor efficiency at rate g.

• Formula: $g = \frac{\Delta E}{E}$

• Production Function: $Y = F(K, L \times E)$ where $L \times E$ is the number of effective workers.

• Interpretation: Increases in labor efficiency have the same effect on output as increases in the labor force.

Effective Workers and Capital Requirements

As labor efficiency rises, the economy effectively has more workers, each requiring capital to be productive. This necessitates additional investment to equip these new effective workers.

• Key Point: Each increase in effective workers requires proportional capital investment ($gk$).

Solow Model Notation and Per Effective Worker Analysis

To analyze growth with technological progress, variables are expressed per effective worker:

• Output per effective worker: $y = \frac{Y}{LE}$

• Capital per effective worker: $k = \frac{K}{LE}$

• Production function per effective worker: $y = f(k)$

• Saving and investment per effective worker: $sy = sf(k)$

Break-Even Investment in the Solow Model

To maintain a constant capital per effective worker, investment must cover three components: depreciation, new workers, and new effective workers from technological progress.

• Break-even investment formula: $(\delta + n + g)k$

• Components:

  • $\delta k$ – replaces depreciating capital

  • $nk$ – provides capital for new workers

  • $gk$ – provides capital for new effective workers

Capital Accumulation Equation with Technological Progress

The change in capital per effective worker is determined by the difference between investment and break-even investment.

• Equation: $\Delta k = s f(k) - (\delta + n + g)k$

• Steady State: Occurs when $\Delta k = 0$.

Steady-State Growth Rates in the Solow Model with Technological Progress

In the steady state, different variables grow at different rates depending on the presence of technological progress and population growth.

Variable	Symbol	Steady-state growth rate
Capital per effective worker	$k = K/(L \times E)$	0
Output per effective worker	$y = Y/(L \times E)$	0
Output per worker	$(Y/L) = y \times E$	$g$
Total output	$Y = y \times E \times L$	$n + g$

• Key Point: Output per worker grows at the rate of technological progress ($g$), while total output grows at the sum of population and technological growth rates ($n + g$).

Additional info: These notes cover the first part of the lecture, focusing on the integration of technological progress into the Solow model, its implications for growth rates, and the mathematical formulation of these concepts. Further topics in the full lecture include growth empirics, policy issues, and endogenous growth theory, which would be covered in subsequent sections.