Macroeconomics

Exogenous growth model with capital accumulation, diminishing returns, and a steady state.

Optimal growth with a representative dynastic household. Endogenous savings, saddle-path dynamics, and the modified golden rule.

Agents live two periods. They work and save when young, consume their savings when old. Capital accumulation is driven entirely by the savings of the young cohort. Because each generation cares only about its own life-cycle utility — not the welfare of all future generations — the resulting equilibrium can over-accumulate capital relative to the golden rule, producing the famous *dynamic inefficiency* result and a Pareto-improving role for pay-as-you-go social security.