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In the Solow model of economic growth, population growth plays a critical role in determining the steady-state level of capital per worker and output per worker. The model assumes a production function where output is produced using capital and labor, often represented as a Cobb-Douglas function, and where technological progress can be included to account for long-run growth. When the population grows, the labor force increases, which affects the accumulation of capital per worker. Specifically, higher population growth leads to a larger denominator in the capital-labor ratio, reducing the amount of capital available per worker unless savings and investment increase proportionally. This, in turn, lowers output per worker and slows down the growth of living standards in the long run. The Solow model shows that, in the absence of technological progress, economies with high population growth tend to have lower steady-state capital per worker, implying that rapid population growth can dilute the impact of capital accumulation and slow per capita economic growth. Population growth also interacts with savings and depreciation in the Solow framework. The steady-state level of capital per worker is determined by the point at which investment per worker equals the sum of depreciation and the amount of capital required to equip new workers due to population growth. If the population grows rapidly without a corresponding increase in savings and investment, the economy may settle at a lower steady-state level of capital per worker. Consequently, the economy could remain trapped at a low-income equilibrium, where output per worker is stagnant. Conversely, economies with lower population growth can achieve higher levels of capital per worker and higher output per capita, ceteris paribus. Thus, the Solow model provides a clear illustration of how demographic factors influence long-run economic outcomes and living standards, highlighting the tension between population growth and the accumulation of productive capital. The ______ _______ __________ _____ ____ ________ ____ _______ ___ _______ ___.
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