Answer :
Final answer:
The per-worker production function [tex]y = k^1/3[/tex]. Savings per worker is 0.20 times per-worker output. Capital depreciation per worker is 0.10 times per-worker capital. The steady-state level of capital is reached when net change in capital is zero. The graph shows the relationship between savings per worker, capital depreciation per worker, and per-worker capital.
Explanation:
a. To find the per-worker production function, we substitute the given aggregate production function Y = K1/3 L2/3 into the equation for per-worker output y = LY. Therefore, y = k1/3.
b. To find savings per worker, we multiply the saving rate (s = 0.20) with per-worker output. Therefore, savings per worker is 0.20 times y.
c. To find capital depreciation per worker, we multiply the depreciation rate (δ = 0.10) with per-worker capital. Therefore, capital depreciation per worker is 0.10 times k.
d. The net change in capital is equal to savings per worker minus capital depreciation per worker. If per-worker capital today is 2, we can use the per-worker production function to find per-worker output (y) and then calculate savings per worker and capital depreciation per worker. The steady-state level of capital is reached when net change in capital is zero.
e. To draw the graph, we plot the savings per worker and capital depreciation per worker against per-worker capital (k) on the x-axis. The steady-state level of capital per worker is where the savings per worker curve intersects with the capital depreciation per worker curve.
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