Starting from steady state, a permanent decrease in the rate of depreciation in the Solow model causes output per capita to rise in the short run. In the long run, the growth rate of the economy remains unchanged .

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In this question, we’re evaluating the effects of a permanent decrease in the depreciation rate δ within the Solow growth model and distinguishing between short-run and long-run implications.
Option 1: rise
- A permanent drop in δ means capital stock wears out more slowly. With depreciation lower, for a given investment flow, the economy can accumulate more capital over time, raising the steady-state capital per worker and, correspondingly, output per worker in the steady state. In the immediate or short run after the shock, the higher net investment (since depreciation is smaller) pushes up capital accumulation and hence increases output per capita before the economy fully adjusts.
- Intuitively, with less depreciation, the economy can sustain a higher level of capital stock without changing the investment rate, so y per worker increases as the capital stock grows toward a new, higher steady state.
Option 2: remains unchanged
- The long-run growth rate in the (one-sector) Solow model is driven by exogenous technological progress (if present) and is unaffected by changes in the saving rate, population growth, or depreciation rate in the classic setup. A permanent change in δ shifts the level of output per capita and the steady-state, but it does not alter the long-run growth rate unless technology itself changes.
- Therefore, once the economy has fully adjusted to the lower depreciation rate, the growth rate per capita remains governed by the exogenous growth process (e.g., g of technology), not by δ, so the long-run growth rate stays unchanged.
- In other words, you observe a higher steady-state level of output per capita, but the trajectory toward that level occurs, and the eventual long-run growth rate does not accelerate or decelerate due to this depreciation shock alone.
Overall, the statement that output per capita rises in the short run is correct due to faster capital accumulation, while the long-run growth rate remains unchanged because the Solow model’s long-run growth is determined by exogenous technological progress, not by depreciation adjustments. The reasoning above explains why the two dropdown choices align with the standard Solow framework.

SP25 ECON 312 001 Homework #3 - Part 1 (Solow Growth Model)

Starting from steady state, a permanent decrease in the rate of depreciation in the Solow model causes output per capita to rise in the short run. In the long run, the growth rate of the economy remains unchanged .

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