In Chapter 11 we found that the steady‐state level of capital‐per‐worker was therefore 11 Since 0 and 0. 11 Similarly, so 11 And since 11 then 11 Variable Steady‐State Growth Rate Capital 1 Output 1 Labor Capital/output ratio 0 Capital‐per‐worker 1 Output‐per‐worker 1 Equation 1 The change in capital always, in and out of the steady‐state, is ∆ so ∆ Since ∆ then the growth rate of capital is always • If there’s very little capital per unit of worker, capital will be fairly productive and it will accumulate faster. What happens to /? o A small capital‐output ratio / would make large, turning into a positive number, so the capital stock rises. As capital accumulates, / will rise. • If there’s too much capital per unit of worker, capital will be relatively unproductive and it will de‐accumulate. What happens to /? o A very large capital‐output ratio / would make low, turning into a negative number, so the capital stock falls. As capital de‐accumulates, / will contract. That is, • When does / stabilize? When . We know that, in the steady state, and . Then in the steady state, . Put together Equations 1 (the growth of K in the steady state) and 2 (the growth of K always): 11 11 11 1 Steady State capital‐output ratio Equation 2
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