Consider an economy with a Cobb‑Douglas production function per worker $y = k^{0.5}$, where $k$ is capital per worker. The savings rate is $s = 0.20$, the labour force grows at $n = 0.02$ per year and the depreciation rate is $\delta = 0.05$ per year.\n\n(a) Find the steady‑state level of capital per worker $k^*$ and output per worker $y^*$.\n\n(b) If the savings rate rises to $s' = 0.25$, determine the new steady‑state output per worker $y'^*$ and the percentage change in output per worker relative to the initial steady state.

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Initial steady‑state: $k^* \approx 8.16$, $y^* \approx 2.86$. After increase: $y'^* \approx 3.57$, a 25 % rise in output per worker.

Gce Model Questions Vol1 2025 Economics Question 33

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