EC - EconomicGrowth 13:50 TheFarmerGrowthmodel...

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Economic Growth 13:50 The “Farmer” Growth model General idea in the model o Some income is saved, the rest is consumed. o Saved income translates into capital investment Ex: Bank takes savings deposits, lends them out for construction projects or firm  capital investments o Capital investment grows the capital stock (accumulation) and hense raises future output  (income) Predicts: higher savings rage and faster accumulation Higher income growth, higher long-run consumption Income and consumption growth can go on forever at the same pace (not realistic) The Solow Growth Model Y=output per worker, k=capital per worker Each additional unit of capital for the average worker adds less production Two key curves o Actual investment curve: sy=sAf(k)=savings/working=investment/worker o Break-even investment line: (n+d)k o Actual investment curve-where does it come from o An actually investment curve-where does it come from? Income/worker(=output/worker) is y, where y=Af(k) A productivity
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f function with diminishing returns  workers save a fixed fraction of income, s, so savings/worker is sy all savings translates into investment in short o more capital/worker is more output/worker(=income/workers) leads to more  savings/worker and more investment/worker (but with diminishing returns to scale) capital accumulation k  investment/worker-sy-sAf(k)   o movement along actual investment curve productivity growth A   investment/worker=sy=sAf(k)   o rotation up of actual investment curve (production function) o increased savings rate= s  investment/worker=sy=sAf(k)   rotation up of actual investment curve  break-even investment line-where does it come from o tells us how much investment/worker is needed to maintain the current amount of capital/ worker (k) o two factors behind maintaining the amount of capital/worker: replacing depreciated capital d=capital depreciation rate supplying new workers with capital n=population growth rate hence (d+d)k=break-even investment/worker o Example: Imagine K=100 L=100 so k(=K/L)=1 Depreciation rate= d=20% Population growth rate= n=5% How much investment/worker needed to “break even”=keep k fixed? Since n=5% next year L=105. So, need next year’s K=105 Since d+20% units of K lost, leaving 80 for next year. To get K grom 80 to 105 you need invesement=25 Investment/worker=25/100 (n+d)k o In sum, positive investment is needed to maintain k at a fixed level: To replace depreciating capital To keep the capital stock growing along with the labor force (n) Capital accumulation= k   break even investment= (n+d)k   
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Solow Growth Model 13:50 How can/should we compare development levels?
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This note was uploaded on 04/21/2011 for the course EC 310 taught by Professor Ahlin during the Spring '11 term at University of Michigan.

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EC - EconomicGrowth 13:50 TheFarmerGrowthmodel...

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