Empirical evidence from the past seems to support

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Unformatted text preview: When the saving rate increases, sf(k) = i shifts upwards. Investment now exceeds depreciation, therefore the capital stock will gradually rise until the economy reaches the new steady state which has a higher capital stock and a higher level of output than the old steady state. The Solow model shows that the saving rate is a key determinant of the steady- state capital stock. Policies that alter the steady- state growth rate of income per person are said to have a growth effect, while a higher saving rate is said to have a level effect, because only the level of income per person - not its growth rate - is influenced by the saving rate in the steady state. When choosing a steady state, the policymaker’s goal is to maximize the country’s economic well- being, and people care about how much they can consume. The steady- state value of k that maximizes consumption is called the Golden Rule level of capital and is k*gold. We can write steady- state consumption per worker as: c* = f(k*) – δk*, which represents total output after paying for depreciation (which is equal to investment in the steady- state). This equation shows that an increase in steady- state capital has opposing effects on steady- state consumption. More capital means more output, but it also means more output must be used to replace capital that is wearing out. If the capital stock is below the Golden Rule level, an increase in capital stock raises output more than depreciation, so that consumption rises. In this case, the production function is steeper than the δk* line, so the gap between the two curves, which equals consumption, grows as k* rises. The opposite is also true: if capital stock is above the Golden Rule level, an increase in capital stock reduces consumption since the increase in output is smaller than the increase in depreciation, causing the gap between the f(k*) curve and the δk* curve (consumption) to shrink. The slope of the production function is the MPK, and the slope of the δk* line is δ. Therefore, since the slopes are equal at k*gold, the Golden Rule is described by the equation: MPK = δ If MPK – δ > 0, then increases in capital increase consumption, so k* must be below the Golden Rule level. If MPK – δ < 0, then increase...
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