What to explore
Change parameters and watch the model adjust.
- Capital share, discount factor, risk aversion, depreciation, and TFP
- Initial capital and horizon for the optimal transition path
Optimal growth with endogenous saving
Ramsey-Cass-Koopmans Model
An optimal growth model where households choose consumption and saving over time, replacing the fixed savings rule from Solow with the Euler equation.
Focus
Euler equation, steady state, and optimal paths
Explore how preferences, technology, and depreciation alter the steady state and the planner's optimal transition path using a shooting algorithm.Core ideas
Interpret the mechanics before you chase the graphs.
- The Euler equation governs consumption growth across time.
- The steady state balances impatience against the marginal product of capital.
- The shooting algorithm finds an initial consumption level that satisfies the model's terminal condition.
Learning goals
What this model should help students internalize.
- Link the Euler equation to optimal consumption growth and steady-state capital.
- Interpret shooting methods for saddle-path stable dynamics.
- Compare endogenous saving to the fixed-savings Solow benchmark.
Prerequisites
Concepts to review before diving in.
- Solow model intuition
- Basic familiarity with optimization and intertemporal choice
Next models to study
Keep moving through the track.
Deterministic business-cycle dynamics
Basic Real Business Cycle Model
Change preferences, technology, depreciation, and shock size to see how a one-period TFP disturbance propagates through a closed economy with endogenous saving.
Advanced macroeconomics
Diamond Overlapping-Generations Model
Study the steady state, compare it with the golden-rule benchmark, and see when an economy may overaccumulate capital and become dynamically inefficient.