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as a beginner in macro, I'm trying to understand the Brock-Mirman model for one of my assignments and I am told (in the assignment) that there is a $k^*$ such that k is bounded.

From the production function I see that $\ k_{t+1} = k_t^\alpha $ will go to a $k^*$ as $t\to\infty$, and we already know that marginal product of capital will go to zero. But what is the intuition behind this? How does $ k^* = k^*{^\alpha} $ work as a bound?

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