Solow Growth Model Explained with India’s Economic Growth Trajectory

Over half the size of the U.S. economy, the recent statement by NITI Aayog Vice-Chairman Suman Bery on India’s economy at $15 trillion in purchasing power parity (PPP) terms presents a fascinating starting point for study of important economic models and ideas. This article explores SOLOW GROWTH MODEL using real-world India economic data.

Before diving into the model, lets understand the difference between NOMINAL GDP and GDP at PPP across two countries.  Gross Domestic Product (GDP) measures the total value of goods and services produced over a specific time period.GDP across nations can be mostly compared in two ways:
1. Nominal GDP: Calculated using current market exchange rates.
2. GDP at Purchasing Power Parity (PPP): Adjusts for price level differences across countries, providing a more accurate reflection of living standards and real output.

The fifth-largest economy by market exchange rates, India's nominal GDP in 2024 was roughly $3.94 trillion, according to the International Monetary Fund (IMF). With PPP taken into account, India's GDP came out to be about $15.0 trillion, third in the world. 

The Solow Growth Model

According to Solow Growth Model the long term economic growth is driven by the following:

• Capital accumulation: Investment in physical capital like machinery and infrastructure.
• Labor force growth: An expanding workforce contributes to higher output.
• Technological progress: Innovations that improve productivity.

India’s reported $15 trillion economy (in PPP terms), over half the size of the U.S. economy, can be better understood through this lens—not just as a reflection of size, but of deeper economic forces driving that output.

Let us understand the analysis by diving deeper into how the Solow Growth Model explains India’s $15 trillion economy (in PPP terms), especially through Total Factor Productivity (TFP) improvements and capital accumulation.

In the graph above:

1. Blue Line (Output with A = 1)¹:
   This is India’s initial production function:
   • y=Ak^α with A=1, α=0.33
2. Green Dashed Line (Investment with A = 1):
   • Investment =s² ⋅ y = s ⋅ Ak^α
   • Reflects savings invested back into capital.
3. Black Dotted Line (Depreciation):
   • δk
   • The capital that wears out each period.
4. Steady State (Intersection):
   • Where investment = depreciation, the economy stabilizes.
   • Vertical gray line (k₁): India’s initial steady-state capital per worker.

Now the question is what happens when there is growth, that is the TFP increases ?

In the recent past, India has made significant productivity gains via:

• Digitization (e.g., UPI, Aadhaar)
• Infrastructure development
• Foreign direct investment
• Economic reforms (GST, Insolvency Code, etc.)
• and many more..

Let’s say:

• India’s capital per worker improves through new factories, highways, or rural electrification
• At the same time, education and technology boost worker efficiency (TFP ↑)

→ This allows India to move along the capital axis from k₁​ to k₂​, and also enjoy a shift up in output, from blue to orange.

Outcomes:

• Red Dashed Line: New investment curve (higher for every k)
• Purple Vertical Line (k₂): New, higher steady-state capital per worker
• Result: Higher income per worker, i.e., GDP per capita increases

Concept	India-Specific Interpretation
Capital Accumulation (k ↑)	Infrastructure, industrial growth, energy expansion
TFP Improvement (A ↑)	Digital economy, skilled labor, tech innovation
Savings Rate (s)	Moderately high savings fuels investment
Depreciation (δk)	Natural wear and aging of capital—ongoing challenge

My Thoughts:

Real structural and productivity changes are reflected in India’s $15 trillion PPP GDP, which is not merely a statistical anomaly. We can see through the Solow Growth Model how productivity reforms, a growing labor force, and wise investment work together to drive the economy toward a new, higher steady-state.

Related Articles:

Viksit Bharat 2047: Boosting Labour Productivity Is Key

Related links:

Indian economy size $15 tn in PPP term, more than half of US economy: NITI VC Bery – The Economic Times

India must increase labour productivity to become a developed nation, says Niti Aayog’s Suman Bery | Mint

(39) Suman K. Bery | LinkedIn

Resources:

Robert Solow’s Original Paper (1956)

N. Gregory Mankiw’s Macroeconomics Textbook

• Widely used for undergraduate economics courses; contains intuitive explanations of the Solow model.

To understand the basic concept you can watch the video titled, "The Solow Model Explained" by Khan Academy.
Khan Academy – Solow Model

Python Codes for the Graph

import matplotlib.pyplot as plt
import numpy as np

# Parameters
A1 = 1        # Initial total factor productivity
A2 = 1.5      # Improved TFP (e.g., through reforms or technology)
alpha = 0.33  # Capital share
s = 0.3       # Savings rate
delta = 0.05  # Depreciation rate

k = np.linspace(0.1, 12, 200)  # Capital per worker

# Production functions
y1 = A1 * k ** alpha
y2 = A2 * k ** alpha

# Investment functions
investment1 = s * y1
investment2 = s * y2

# Depreciation line
depreciation = delta * k

# Plotting
plt.figure(figsize=(12, 7))

# Original production function
plt.plot(k, y1, label='Output (A=1)', color='blue')
plt.plot(k, investment1, '--', label='Investment (A=1)', color='green')

# Improved productivity scenario
plt.plot(k, y2, label='Output (A=1.5)', color='orange')
plt.plot(k, investment2, '--', label='Investment (A=1.5)', color='red')

# Depreciation line
plt.plot(k, depreciation, ':', label='Depreciation (δk)', color='black')

# Annotations
plt.axvline(x=3.5, color='gray', linestyle='--', label='Initial Steady State (k₁)')
plt.axvline(x=6.2, color='purple', linestyle='--', label='New Steady State (k₂)')

plt.title('Solow Growth Model – India’s Growth Explained via TFP Improvement')
plt.xlabel('Capital per Worker (k)')
plt.ylabel('Output / Investment / Depreciation')
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

End Notes

1. In the Solow Growth Model, the variables A and α (alpha) play crucial roles in determining output and explaining how economies grow over time.
   
   A – Total Factor Productivity (TFP)
   What it represents:
   A captures technology, efficiency, or the overall productivity of labor and capital.
   Interpretation:
   It tells us how efficiently capital (K) and labor (L) are being used to produce output.
   Example:
   Two countries with the same capital and labor can have different outputs if one has better infrastructure, institutions, or innovation. That difference is captured by A.
   Real-world analogy (India):
   India’s rising digital infrastructure (e.g., UPI, Aadhaar) or policy reforms improve A, allowing more output from the same inputs.
   
   α (alpha) – Capital’s Share of Output
   What it represents:
   α is the elasticity of output with respect to capital. It shows how much output increases when capital increases, holding everything else constant.
   Typical Value:
   In many models: α ≈ 1/3 (or 0.33), meaning about one-third of output is attributed to capital and two-thirds to labor.
   
   Mathematical Role (in Cobb-Douglas Production Function):
   Y=A⋅Kα⋅L1−αY
   
   K: capital
   L: labor
   A: productivity
   α: capital’s contribution to output
   
   If α = 0.33:
   33% of output comes from capital
   67% comes from labor
   ↩︎
2. In the Solow Growth Model, the symbol s stands for the savings rate.
   
   📌 s – Savings Rate
   Definition:
   s is the fraction of total output (Y) that a country saves and reinvests as capital (K), rather than consuming (C).
   In Formula:
   s=S/Y
   where:
   S = total savings
   Y = total output (GDP)
   Role in the Solow Model:
   Savings → Investment → Capital Accumulation → Economic Growth
   More savings means more capital accumulation, which leads to higher output in the short and medium run.
   
   💡 Key Equation with s:
   Δk=sf(k)−(δ+n)k f(k) =
   where,
   Δk = change in capital per workeroutput per worker (production function)
   δ = depreciation rate
   n = population growth
   s affects how much of the output is turned into investment
   
   Real-World Example (India):
   Suppose India saves 30% of its GDP → s = 0.3
   That 30% becomes investment in infrastructure, factories, education, etc.
   Over time, this raises capital per worker, leading to higher productivity and output.
   ↩︎