Goodwin Growth Cycle Model (1967)

This repository provides a lightweight, interactive Julia implementation of Richard M. Goodwin’s “growth cycle” model (1967): a two-dimensional predator–prey dynamic system in which the employment rate (𝑣) and the wage-share (𝑢) orbit an interior steady state, generating endogenous cycles without exogenous shocks. The formulation adapts the Lotka–Volterra mechanics from biology —originally developed by Lotka (1925) and Volterra (1928)—to macroeconomics, assuming that wage dynamics respond to labor-market tightness while capital accumulation and GDP growth are profit-led.

App Features

• Backend: Julia HTTP server with JSON API
• Frontend: Static HTML with Plotly.js
• Solver: Custom Runge-Kutta 4th order integrator
• Memory footprint: ~50-100 MB (vs 500-700 MB with full stack)
• Parameter adjustment: Real-time through sliders
• Plots: Time series and phase diagram
• Additional output: Equilibrium point calculation for main endogenous variables

🌐 Online Demo

Try it now: https://goodwin-growth-cycle.onrender.com

Note: First load may take 30-60 seconds as the free-tier server wakes up from sleep mode.

App Preview

The animation shows:

1. Initial state - Default parameters loaded
2. First simulation - Running with default parameters (σ=4.0, α=β=0.02, γ=0.03, ρ=0.07)
3. Parameter adjustment - Changing σ to 4.5 and v₀ to 0.80 using interactive sliders
4. Second simulation - Observing how different parameters affect the cycle dynamics

Model details

Equations

The Goodwin model describes economic cycles through a predator-prey system:

dv/dt = v * [(1/σ - (α + β)) - u/σ]
du/dt = u * [ρ*v - (α + γ)]

Where:

• v = employment rate
• u = workers' share of output
• σ = capital-output ratio
• α = labor productivity growth rate
• β = labor force growth rate
• γ = constant in wage adjustment function
• ρ = sensitivity of wages to employment level

Parameter ranges (you can modify them locally)

• σ (0.5-2.0): Capital-output ratio
• α (0.001-0.1): Labor productivity growth rate
• β (0.001-0.1): Labor force growth rate
• γ (0.001-0.1): Wage adjustment constant
• ρ (0.001-0.2): Wage sensitivity to employment

Alternatives for running locally

Option 1: Run with Julia (Direct)

Prerequisites:

• Install Julia 1.10 or newer from julialang.org/downloads

Steps:

1. Download the code from GitHub (green "Code" button → Download ZIP, then extract)

2. Open terminal/command prompt and navigate to the project folder (where you unzip the repo):

   cd path/to/GoodwinApp

   Example (Windows): cd C:\Users\YourName\Downloads\GoodwinApp

   Example (Mac/Linux): cd ~/Downloads/GoodwinApp

3. Install required Julia packages (only needed first time):

   julia -e "using Pkg; Pkg.add([\"HTTP\", \"JSON3\"])"

   This will download and install the necessary packages (~2-3 minutes).

4. Start the server:

   julia server.jl

   You should see:

   🚀 Starting Goodwin Model Server...
   🌐 Server listening on: http://0.0.0.0:7860
   ✅ Access in browser: http://localhost:7860
   

5. Open your browser and go to:

   http://localhost:7860
   

   Note: The server binds to 0.0.0.0 but you must access it via localhost in your browser.

6. Stop the server when done: Press Ctrl+C in the terminal

---

Option 2: Run with Docker (Containerized)

Prerequisites:

• Install Docker Desktop from docker.com

Steps:

1. Download the code (same as Option 1)

2. Open terminal/command prompt and navigate to the project folder:

   cd path/to/GoodwinApp

3. Build the Docker image (only needed first time or after updates):

   docker build -t goodwin-app .

   This will take ~2-3 minutes to build.

4. Run the container:

   docker run -p 7860:7860 goodwin-app

   You should see the server starting message.

5. Open your browser and go to:

   http://localhost:7860
   

6. Stop the container: Press Ctrl+C in the terminal

Troubleshooting:

• If port 7860 is already in use, try: docker run -p 8080:7860 goodwin-app and open http://localhost:8080
• Make sure Docker Desktop is running before executing docker commands

References

Goodwin, R. M. (1967). "A Growth Cycle". In C. H. Feinstein (Ed.), Socialism, Capitalism and Economic Growth. Cambridge University Press.

License

MIT License

Author

Demian Panigo (UNLP) - Educational use in macroeconomics courses