2. Consider the Solow growth model without population growth or technological change. The savings rate is 20% (s = 0.2) and depreciation rate is 5% (8 = 0.05). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. (a) Rewrite production function Y = K1/3 L2/3 in per-worker term. (b) Find the steady-state level of the capital stock, k*.
2. Consider the Solow growth model without population growth or technological change. The savings rate is 20% (s = 0.2) and depreciation rate is 5% (8 = 0.05). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. (a) Rewrite production function Y = K1/3 L2/3 in per-worker term. (b) Find the steady-state level of the capital stock, k*.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![2. Consider the Solow growth model without population growth or technological change. The
savings rate is 20% (s = 0.2) and depreciation rate is 5% (8 = 0.05). Let k denote capital per
worker; y output per worker; c consumption per worker; i investment per worker.
(a) Rewrite production function Y = K1/3 L²/3 in per-worker term.
(b) Find the steady-state level of the capital stock, k*.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd920f800-7cb4-4708-a86f-fdc64006663e%2Fc6af45ff-605e-4896-91bf-19ccd19aee5b%2F320tfki_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the Solow growth model without population growth or technological change. The
savings rate is 20% (s = 0.2) and depreciation rate is 5% (8 = 0.05). Let k denote capital per
worker; y output per worker; c consumption per worker; i investment per worker.
(a) Rewrite production function Y = K1/3 L²/3 in per-worker term.
(b) Find the steady-state level of the capital stock, k*.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Part a.
Y = K1/3L2/3
Dividing both sides by L,
Y/L = (K1/3L2/3) / L
Y/L = (K/L)1/3
y = k1/3 where y = Y/L and k = K/L
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