RBC Simplified Model

The simplified RBC model strips the full Kydland-Prescott (1982) framework down to its bare essentials: one representative household, one production technology, one exogenous shock, and no government sector. This pedagogical version appears in Romer (2019, Ch. 5) and Williamson (2018, Ch. 11) as the entry point to dynamic stochastic general equilibrium modeling. The goal is to isolate the core propagation mechanism - technology shocks hitting an economy with capital accumulation and endogenous labor supply - before layering on fiscal shocks, nominal rigidities, or financial frictions.

The mechanism is straightforward. A positive technology shock raises the marginal product of both capital and labor. Households respond along two margins: they work more (intratemporal substitution toward labor, which is temporarily more productive) and they save more (intertemporal substitution toward future consumption, since the return to capital is temporarily high). Capital accumulation carries the shock forward, generating persistence in output even after the productivity innovation has died out. This is the entire propagation story - no multiplier-accelerator, no sticky prices, no financial amplification.

This simplified version is the standard first DSGE model in graduate macro sequences at most research universities. It is used as a building block: once students can solve the steady state, derive the Euler equation, log-linearize, and compute impulse responses on this model, they add government spending (full RBC), then sticky prices (New Keynesian), then heterogeneous agents (HANK). The stripping-down is the point - every equation present is load-bearing.

Three blocks: a representative household choosing consumption, labor, and saving; a representative firm operating Cobb-Douglas technology with stochastic TFP; and a resource constraint tying output to consumption and investment. No government, no transfers, no taxes. The household owns the capital stock and rents it to the firm.

Equilibrium is pinned by two optimality conditions (the Euler equation and the labor-leisure condition), one production function, one capital accumulation law, and one AR(1) technology process. That gives five equations in five unknowns per period: output, consumption, investment, hours, and the capital stock. Factor prices (wage and rental rate) are determined residually from the firm's marginal product conditions.

Solution proceeds by finding the deterministic steady state, log-linearizing around it, and solving the resulting linear rational expectations system. In the full augmented system, capital and technology are predetermined states and consumption is the jump variable; determinacy requires one unstable root associated with the jump variable and stable state dynamics for capital and technology. If technology is treated as an exogenous forcing process and the endogenous block is reduced to capital and consumption, the same saddle-path logic appears as one stable root and one unstable root.

Graduate macro courses at institutions like MIT, Chicago, and Minnesota use this model as the first complete DSGE students solve. It teaches steady-state computation, the Euler equation, log-linearization, Blanchard-Kahn conditions, and impulse response analysis in one compact package. Romer (2019) and Williamson (2018) build entire chapters around it.

The simplified RBC is the baseline when researchers add one friction at a time - sticky prices, habit formation, investment adjustment costs - to measure the marginal contribution of each friction. Starting from a stripped-down version makes the comparison clean because there is no second shock to confuse the attribution.

For policy analysis involving monetary policy, fiscal multipliers, financial crises, or distributional questions, use a fuller model that nests this one as a special case. The simplified RBC has no nominal variables, no government, and no heterogeneity.