Answer First
Technology shocks propagate in the RBC model through intertemporal substitution in labor and consumption, capital accumulation, and productivity‑driven changes in marginal products. A positive shock raises output, increases labor supply, boosts investment, and generates persistent effects through capital deepening.
Problem Setup
Production function: \[ Y_t = A_t K_t^\alpha L_t^{1-\alpha}. \] Technology shock: \[ \ln A_t = \rho \ln A_{t-1} + \varepsilon_t. \] Household Euler equation: \[ u'(c_t) = \beta (1+r_{t+1}) u'(c_{t+1}). \] Labor supply condition: \[ \frac{w_t}{c_t} = v'(1-L_t). \]
Step-by-Step Explanation
1. A positive technology shock raises productivity
Higher A_t increases marginal products of labor and capital.
2. Labor supply rises through intertemporal substitution
Higher wages induce households to work more today because the return to working is temporarily high.
3. Output rises immediately
Higher productivity + higher labor → higher output.
4. Investment rises sharply
Higher MPK increases the return to capital, causing households to shift consumption toward the future.
5. Capital accumulation creates persistence
Even after the shock fades, the higher capital stock keeps output elevated.
6. Consumption rises gradually
Households smooth consumption, so consumption responds less than investment.
Intuition
A technology shock is like giving the economy better tools. Workers become more productive, firms invest more, and the higher capital stock keeps output elevated even after the shock dissipates.
Common Exam Mistakes
- Thinking consumption jumps as much as output (it does not).
- Ignoring the role of intertemporal substitution in labor supply.
- Forgetting that persistence comes from capital accumulation, not the shock itself.
- Confusing RBC propagation with New Keynesian propagation.
Final Summary
Technology shocks propagate in the RBC model through labor supply, investment, and capital accumulation. The shock raises productivity, increases labor and output, boosts investment, and generates persistence through capital deepening.
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