SR Growth [Macro Economics]

Macro Economics 

- Chapter 5. Short-run Economic Growth

What is the Solow Growth Model?

The Solow Growth Model, developed by economist Robert Solow, builds on the basic production model by adding something crucial: capital accumulation over time.

Instead of treating capital like a fixed input, the model shows how investment in capital—factories, machines, roads—builds up over time, driving growth in output. This makes it a dynamic model, unlike the static models that look at one point in time.

Core Idea: Capital Accumulation Drives Growth—But Not Forever

In the short run, investment increases capital, and more capital means more output.

But here’s the twist: capital faces diminishing returns. The more capital you add, the less extra output you get from each new unit. Eventually, investment just replaces worn-out capital, and the economy settles into a steady state.

In this steady state:

• Capital per person is constant
• Output per person is constant
• Consumption per person is constant

So, long-run growth stops—unless something else changes.

Key Components of the Solow Model

1. Production Function

• Output depends on capital, labor, and productivity (TFP). • Typically modeled as a Cobb-Douglas function:

2. Capital Accumulation

• New capital = Investment – Depreciation
• Investment is a portion of output; depreciation wears capital down.

3. Savings and Investment

• A fixed portion of output is saved and invested.
• More saving means more capital in the future.

4. Steady State

• Where investment = depreciation
• No further growth in output per person

The Solow Growth Model

The Solow Growth model augments the production model with capital accumulation.
• Capital stock is no longer exogenous.
• Capital stock is now endogenized.
The accumulation of capital is a possible engine of long-run economic growth.

(Production model)

Y = F(K,L) = A・K∝L1-∝

(Resources model)

C + I =Y

**C: consumption

**I: investment

(Capital model)

Kt+1 = Kt + It -d・Kt

**Kt+1: next year’s capital
**Kt: this year’s capital
**It: this year’s investment
**d: depreciation rate (0≤d≤1) ex. d=0.07 or 0.10

(Labor)

Lt = L

(Investment)

I = s・Y

as same as, C = (1-s)Y

*s: fraction of total output invested
++Consumption is the share of output not invested.

Understanding the Solow Diagram

The Solow diagram visually shows how investment and depreciation interact.

• If investment > depreciation, capital grows.

• If investment < depreciation, capital shrinks.

• When they’re equal, the capital stock stays steady—this is the steady state.

As capital adjusts, so does output. This movement is called transition dynamics.

Investment - Depreciation = Net investment

Net investment: ΔK t → ΔK t+1 → ΔK t+2

Net Investment는 순투자를 의미하며, 기업 또는 개인이 자산(건물, 장비 등)에 투자한 금액에서 감가상각(자산 가치의 감소분)을 뺀 순수 투자 금액을 나타냅니다

그래프에서 K*점의 상태를 Steady state라고 한다. 

Equilibrium, as the state we call it “steady state”

Transition Dynamics: Why Growth Slows Over Time

The further a country is from its steady state, the faster it grows. But as it catches up, growth slows.

This explains why:

• Poor countries (far below steady state) grow fast if they have good policies.
• Rich countries grow slowly—they’re already near or at their steady state.

It’s not just about being poor or rich. It’s about how far you are from your potential.

What the Solow Model Gets Right (and Wrong)

✅ Strengths:

• Explains income differences across countries
• Shows how investment leads to growth—up to a point
• Offers a simple but powerful framework to predict growth trends

❌ Limitations:

• No long-run growth in output per person—once steady state is reached, growth stops
• Doesn’t explain why some countries have better productivity (TFP)
• Ignores factors like innovation, education, and institutions (which influence TFP)

So, while useful, the Solow model is only part of the story.

Real-World Lessons from the Solow Model

📈 Investment Increases Output—Temporarily

If a country increases its investment rate, capital rises, and so does output—but only until the new steady state is reached.

🔧 Higher Depreciation Reduces Output

A rise in depreciation means capital wears out faster. The result? A lower steady state and lower long-run output.

👥 Population Growth Doesn’t Boost Output per Person

More workers may grow total output, but due to diminishing returns, output per person doesn’t increase in the long run.

Case Study: South Korea vs. The Philippines

Between 1960 and 2017:

• South Korea grew rapidly—from 10% to 75% of U.S. income.
• The Philippines remained around 10%.

Why? South Korea had higher investment and productivity, and it started far below its steady state. Transition dynamics predicted fast catch-up growth.

The Philippines, closer to its steady state and with weaker fundamentals, saw slower growth.

Final Word: A Powerful but Incomplete Framework

The Solow Growth Model is a brilliant way to think about how capital and investment affect the economy. It shows that capital alone can’t fuel endless growth—and that productivity (TFP) is the real engine in the long run.

For deeper insights into innovation, human capital, and sustained growth, economists use more advanced models. But Solow remains a must-know foundation for anyone curious about growth economics.

[Reference]

[1] Charles I. Jones, Macroeconomics, 5th Edition, Norton.