Week 7

Week 7 – Deterministic Dynamics: The Neoclassical Growth Model

Learning Outcomes By the end of this week, students will be able to:

1. Formulate the deterministic neoclassical growth model in discrete time.
2. Set up the law of motion for capital and simulate it forward.
3. Identify and compute the steady state.
4. Visualise convergence paths to the steady state.
5. Interpret how parameter changes affect transition dynamics.

Suggested Readings

• Greenwood & Marto, Numerical Methods for Macroeconomists, Ch. 6 (Deterministic Dynamics).

In-Class Activities

• Write down the capital accumulation equation:
  [ k_{t+1} = s k_t^\alpha + (1-\delta)k_t ]
• Compute the steady state capital analytically and numerically.
• Simulate the model over 50 periods starting from ( k_0 < k^* ) and ( k_0 > k^* ).
• Plot convergence to the steady state for different initial conditions.
• Comparative statics:
  • Change savings rate ( s ) and observe new steady state and speed of convergence.

Homework / Practice

• Extend the simulation to include output and consumption over time.
• Create a function that takes alpha, s, delta, and k0 as inputs and returns the simulated paths.
• Run the function for three different parameter sets and plot results on the same figure.
• Write a short paragraph (in comments) interpreting how parameter changes affect dynamics.

Files

• Slides Week 7 – Slides from lecture.
• codes_week7 on Matlab online
  • week7.m – Example script from lecture.
  • fig_fixedpoint.m – File to reproduce figure for: “Difference Equations and Stability” slide.
  • fig_law_of_motion.m – File to reproduce figure for: “Graphical Representation” slide.
  • week7_challenge_solution.m – Solution file for the challenge.
  • week7_homework_solution.m – Solution file for the homework.

Homework submission

• Submit your homework here
• Please upload your homework as a single zip file. Access it’s now open with any email address! But remember to name your file with your full name and or student ID.
• The submission should include the .m file used to produce the results.
• You can modify you submission until the beginning of week 8 at 9am.