Introduction
In Solow–Swan, savings was a fixed fraction of output — no theory of where the rate came from. In Ramsey–Cass–Koopmans, savings emerged from the optimal choice of a single representative household with an infinite horizon. Both models share a feature that is striking once you notice it: **every agent in the economy is the same**, and that agent lives forever.
Diamond's model breaks both assumptions in the simplest possible way. Time is discrete. Every period a new cohort is born; the old cohort dies. At any instant the economy contains exactly two generations: the *young*, who work and save, and the *old*, who consume their accumulated savings and then exit the stage. The young of today are the old of tomorrow — and they care about nothing else.
Why the change matters
- Capital comes from the young
- Aggregate savings at time equals the savings of the young cohort. There are no infinitely-lived households smoothing consumption across all of history.
- No intertemporal welfare aggregation
- Each cohort optimises *its own* two-period utility. Nobody internalises the welfare of unborn generations. The decentralised allocation need not maximise any social objective spanning generations.
- Steady state can be inefficient
- If agents save 'too much' from a social standpoint, the economy can converge to a steady state with capital *above* the golden rule. Reducing would raise consumption for all current and future cohorts. This is *dynamic inefficiency*.
- Policy has real bite
- Pay-as-you-go social security, public debt, and similar intergenerational transfers are *not* neutral. They alter the savings decision of the young and hence the path of capital. In dynamically inefficient economies they can be Pareto-improving.
The three big questions
| Question | Answered in |
|---|---|
| How do agents decide how much to save? | §6 Household Problem · §8 Derivations |
| Does the economy converge, and to what? | §9 Capital Accumulation · §10 Steady State |
| Is the equilibrium efficient? If not, can policy help? | §11 Dynamic Inefficiency · §13 Applications |