Int Macro Econ popuation growth
Int Macro Econ popuation growth Economics 5570
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This 2 page Class Notes was uploaded by Ashish Kondoju on Saturday March 12, 2016. The Class Notes belongs to Economics 5570 at Wayne State University taught by Shuan Jung in Spring 2016. Since its upload, it has received 43 views. For similar materials see Intermediate Macroeconomics in Economcs at Wayne State University.
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Date Created: 03/12/16
Population Growth The equation of motion for k Δk = s f(k) – δk The Solow model’s central equation Determines behavior of capital over time… …which, in turn, determines behavior of all of the other endogenous variables because they all depend on k. E.g., income per person: y = f(k) consumption per person: c = (1 – s) f(k) The steady state Δk = s f(k) – δk If investment is just enough to cover depreciation [sf(k) = δk ], then capital per worker will remain constant: Δk = 0. * This occurs at one value of k, denoted k , called the steady state capital stock. Prediction: The Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run. Are the data consistent with this prediction? The Golden Rule: Introduction Different values of s lead to different steady states. How do we know which is the “best” steady state? The “best” steady state has the highest possible consumption per person: c* = (1–s) f(k*). An increase in s leads to higher k* and y*, which raises c* reduces consumption’s share of income (1–s), which lowers c*. So, how do we find the s and k* that maximize c*? the Golden Rule level of capital, the steady state value of k that maximizes consumption. To find it, first express c in terms of k : c* = y * − i * * * = f (k ) − i * * = f (k ) − δk The transition to the Golden Rule steady state The economy does NOT have a tendency to move toward the Golden Rule steady state. Achieving the Golden Rule requires that policymakers adjust s. This adjustment leads to a new steady state with higher consumption. But what happens to consumption during the transition to the Golden Rule? Break-even investment (δ + n)k = break-even investment, the amount of investment necessary to keep k constant. Break-even investment includes: δ k to replace capital as it wears out n k to equip new workers with capital (Otherwise, k would fall as the existing capital stock is spread more thinly over a larger population of workers.)