7. What is the half-life of the output gap, i.e. how many periods does it take until outputadjusts half way from its original level to the new steady-state level?8. How long does it take until the family actually benefits from the higher saving rateand has a higher consumption level than in the original steady state?9. Is it possible to reach the steady state associated with the 50% saving rate whileensuring that consumption never drops belowa. its original level of 7.5 orb. level of 7?Explain briefly. Economic GrowthAkila and her family are the only inhabitants of a small oasis in the middle of the desert.They grow various kinds of trees, which provide them with everything they need. Akilahas built an irrigation system that improves the productivity of the land.Production makes use of three factors: capital K (the irrigation system), labour N (thework done by Akila and her family) and land L (the oasis and the desert around it). Theproduction function is given by F(K,N,L)= K*N*L*. Labour supply is fixed at N=1 andthe family owns 64 units of land, L=64. The irrigation system is in constant need ofrepair; about 10% needs to be rebuilt every year to keep it in a good condition, i.e.K' = K – K +1, where I is investment in the capital stock.1. Show that for a saving rate s, the law of motion for the capital stock can be written inper-capita terms as k'=k-k+s2vk .2. Find the steady-state level of the capital stock k, output y and consumption e asfunctions of s.3. Currently, Akila is saving 25% of the output to re-invest it in the irigation system.What are the resulting steady-state levels of k, y, and c?4. The family considers adjusting the saving rate to 50% or 75%. What would be thesteady state levels of k, y, and e in these cases?5. If the family cares about consumption in the long run, what saving rate will it prefer:25%, 50% or 75%?6. Now suppose that Akila decides to increase the saving rate to 50%, starting today.The capital stock is still at its old steady state level, which you determined in part 3above. Use the law of motion from part 1 to calculate how k evolves for the first 20years after raising the saving rate. Also calculate output and consumption for these 20years. (If you use a spreadsheet program like Excel, which I recommend, calculate thevalues for 100 years and plot them.)

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1. Show that for a saving rate s, the law of motion for the capital stock can be written in per-capita terms as k' =k-k+s2√k. 2. Find the steady-state level of the capital stock k, output y and consumption c as functions of s. 3. Currently, Akila is saving 25% of the output to re-invest it in the irrigation system. What are the resulting steady-state levels of k, y, and c?

1. Show that for a saving rate s, the law of motion for the capital stock can be written in per-capita terms as k' =k-k+s2√k. 2. Find the steady-state level of the capital stock k, output y and consumption c as functions of s. 3. Currently, Akila is saving 25% of the output to re-invest it in the irrigation system. What are the resulting steady-state levels of k, y, and c?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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