Final answer:
Developing new technology helps an economy overcome the obstacles of diminishing marginal returns of capital deepening by effectively shifting the production function upwards, leading to sustainable growth. Per capita output is a crucial measure that needs to outpace population growth to ensure economic welfare. Changes in savings, depreciation, and growth rates affect the economy's output and capital stock.
Step-by-step explanation:
Developing new technology can sidestep the diminishing marginal returns of capital deepening in an economy's production function, an insight that's crucial for understanding how increases in the amount of human and physical capital per worker (referred to as capital deepening) affect per capita output.
When considering an economy's aggregate production function with constant technology, more capital leads to higher output, but with diminishing returns. This is illustrated as a curve that begins steep and flattens out, signaling that additional capital increases output by smaller increments over time. However, the introduction of new technologies shifts this curve upwards, demonstrating how technology can maintain sustained economic growth despite diminishing marginal returns to capital.
Understanding the concept of GDP per capita is also crucial. It is derived by dividing each input by the population, leading to the per capita production function. Here, the influence of population growth on per capita income becomes evident, and for individuals' income growth to have true impact, it should outpace population growth.
To determine the effects of changes in the saving rate, depreciation, worker growth, and technological progress on the economy, one must consider how these factors interact within the production function and the resulting changes in output, capital stock, and economic welfare.