Brock–Mirman Growth Model

Lecture 2 · 2026-03-10 / 03-17

Using the Brock–Mirman (1972) optimal growth model as the running example, we develop value function iteration as a method for solving dynamic programming problems: constructing the state grid, building the return function with index packing, and verifying the contraction property of the Bellman operator together with the various convergence norms, before benchmarking the numerical solution against the closed-form solution under log utility. We treat the deterministic, iid-shock, and Markov-shock cases in turn; in the last, the Tauchen method discretizes the AR(1) productivity process into a Markov chain, and we close by simulating the model dynamics. A supplementary handout on the two-period model serves as an Euler-equation warm-up.

Materials

Readings

  • Brock & Mirman (1972), “Optimal Economic Growth and Uncertainty: The Discounted Case,” JET 4(3), 479–513.