Section 14 - Beyond the baseline

Applications, Critiques & Extensions

RCK is the canonical *normative* benchmark of modern macroeconomics: competitive equilibrium with infinitely-lived agents is Pareto efficient, so deviations require some friction or distortion. Most applications either characterise the friction or compute the welfare cost of policy.

Applications

Application	What RCK delivers
Optimal growth policy	Because the competitive equilibrium is first-best, no tax or transfer can raise welfare. Useful as a benchmark: any policy proposal must justify itself against a friction.
Welfare cost of business cycles	Embed RCK into a stochastic version and compute $\mathbb{E}[U]$ with and without aggregate shocks. Lucas (1987): the welfare cost of cycles is tiny, partly because RCK households smooth so heavily.
Capital-income taxation	Chamley (1986), Judd (1985): in steady state, the optimal tax on capital income is zero. Distorting the Euler equation is a first-order welfare loss; taxing labour is second-best.
Optimal monetary policy in NK models	Sticky-price models replace the RCK production sector but preserve the household problem. The Euler equation becomes the dynamic IS curve.
Calibration	$\rho$ from observed real interest rates; $\theta$ from consumption-growth/asset-return covariation; $\alpha$ from factor shares. The combination of these pins down most of modern macroeconomic models.

Critiques

Critique	Bite
Representative agent	A single dynasty cannot capture heterogeneity in wealth, skill, or longevity. Distributional effects of policy are invisible. Modern HANK (Heterogeneous Agent New Keynesian) models relax this.
Infinite horizon	Real households die. Diamond OLG (Section 2.1.3) takes the opposite extreme - two-period agents - and produces qualitatively different dynamics including dynamic inefficiency.
Perfect foresight	The household knows the entire future path of prices. In practice, expectations matter, and may be rational, adaptive, or heterogeneous. The RCK structure is preserved in stochastic models with rational expectations.
No financial frictions	No collateral constraints, no liquidity premia, no incomplete markets. Households can borrow and lend at $r$ frictionlessly. Bewley-Huggett-Aiyagari models add idiosyncratic risk and borrowing limits.
Exogenous technology	Long-run growth is whatever $g$ is. Why $g > 0$ ? Endogenous growth (Romer, Lucas, Aghion-Howitt) makes $g$ a function of innovation, human capital, or R&D.
No money	RCK is a real model. Adding money requires a friction (cash-in-advance, money in the utility function, sticky prices) since otherwise households are indifferent to holding it.

Extensions

Extension	Core modification
Stochastic growth (RBC, DSGE)	Replace the deterministic Euler equation with a stochastic Euler equation: $u'(c_t) = \beta \mathbb{E}_t[(1 + r_{t+1}) u'(c_{t+1})]$ . The backbone of modern quantitative macro.
Endogenous growth	Make $A$ a function of $K$ (Romer 1986, AK model), human capital (Lucas 1988), or R&D (Romer 1990). Sustained growth without an exogenous $g$ .
Open economy RCK	Allow international borrowing. Small open economy faces exogenous world rate $r^*$ ; saddle path becomes two-dimensional in $(k, b)$ where $b$ is net foreign assets.
RCK with heterogeneous agents	Continuum of households differing in $\rho$ , $\theta$ , or initial wealth. Aggregation requires care; long-run wealth concentration emerges if $\rho$ differs across agents.
Government in RCK	Add lump-sum taxes, distortionary taxes, or government spending. Ricardian equivalence holds for lump-sum taxes but fails for distortionary ones.