Diamond Overlapping Generations Model

Section 4 of 16

Section 4

Assumptions

A. Demographic structure

Label	Assumption
D1	Time is discrete: $t = 0, 1, 2, \ldots$ .
D2	Agents live exactly two periods (young at $t$ , old at $t+1$ ).
D3	The young cohort at $t$ has size $L_t = (1+n) L_{t-1}$ with $n \ge 0$ .
D4	Each young agent supplies inelastically one unit of labour. The old supply zero.
D5	No bequests, no within-cohort heterogeneity, no death uncertainty.

Demographics drive the supply side of the model.

B. Preferences

Label	Assumption
P1	Utility is time-separable across the two periods of life.
P2	Felicity is CRRA: $u(c) = c^{1-\theta}/(1-\theta)$ if $\theta \ne 1$ , else $\ln c$ .
P3	Pure subjective discount factor $\beta = 1/(1+\rho) \in (0,1)$ .
P4	No labour–leisure choice; labour supply is exogenous and inelastic.
P5	No within-life borrowing constraints (the young can save freely).

Each agent maximises a CRRA two-period utility.

C. Technology

Label	Assumption
T1	Single homogeneous good, used for both consumption and capital.
T2	Aggregate production $Y_t = F(K_t, L_t)$ with constant returns to scale.
T3	$F$ is twice continuously differentiable with $F_K > 0, F_L > 0, F_{KK} < 0, F_{LL} < 0$ .
T4	Inada conditions: $\lim_{k \to 0} f'(k) = \infty$ , $\lim_{k \to \infty} f'(k) = 0$ .
T5	We will use Cobb–Douglas $F(K, L) = A K^{\alpha} L^{1-\alpha}$ for closed-form results.
T6	Capital fully depreciates each period ( $\delta = 1$ ) in the canonical formulation.
T7	No technological progress in the baseline ( $g = 0$ ).

The production side mirrors Solow / RCK.

D. Markets

Label	Assumption
M1	Firms and households are price takers.
M2	Labour market clears each period: wage $w_t = F_L(K_t, L_t)$ .
M3	Capital market clears each period: gross return $1 + r_{t+1} = F_K(K_{t+1}, L_{t+1}) + (1-\delta)$ .
M4	No aggregate uncertainty; perfect foresight.
M5	Government, if present, has access to lump-sum taxes/transfers across cohorts.

Standard competitive market structure.