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.)

“Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

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

See similar textbooks

Similar questions

Which of the following is NOT a determinant of the level of investment: A. Sales Outlook B. Capacity Utilization Rate C. Disposable Income D. Expected Rate of Proft
Do not type in dollar signs or round any of your answers. Suppose a country's production function is Y = K1/2L1/2. If capital depreciates at the rate of 5 percent each year and the population grows at the rate of 1 percent each year, calculate the savings rate that would lead to a steady-state equilibrium value for capital per worker of 100 machines: savings rate = percent In this steady-state equilibrium, output per worker is and consumption per worker is
answer questions a and b please
Assume the economy is initially in its balanced growth state. Suppose policymakers pursue policies that would increase the saving rate to s1=0.3. Draw a carefully-labelled diagram to illustrate the effect of the change in the saving rate on the economy in the long run. Explain the effect of the change in saving rate on steady-state capital per effective worker and steady-state consumption per effective worker?
6
Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Explain how the economy goes from one steady state to another.
5. Consider an economy that has been on steady state until period tw (see Figure 4 below). Thus, capital per worker has been constant until tw. The economy's capital per worker until period tw is equal to k. (i.e. steady-state value) and is indicated by the horizontal line. Assume that the economy experiences a significant decrease in productivity after year tw. That is, A decreases or jumps downward after year tw (due to, for example, a corrupt group of oligarchs taking over the government and the economy becoming less efficient as a result). Using the plot in Figure 3, show how this change affects the dynamics of capital per worker (kt) during the periods after tw. Explain (verbally) the economic intuition. Figure 5.1 k₂ y* kt. Yt tw tw Figure 5.2 t
1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function а. b. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.)
An economy consumes 1 million chickens each year. A new technology in raising chickens lowers the price of each chicken from $50 to $40. Suppose the economy still consumes 1 million chickens each year at the lower price. Do you agree that since the consumers pay $10 million less, the national saving due to the change in price equals $10 million?
Assume that the production function for a country is given by Y=√K and annual investment is given by the function I=γ×YI where γ=0.280, and that the yearly depreciation rate is 4.67%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking.
1.
41. Assume that a country's per-worker production is y=1.5k3/4, where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year and there is no population growth or technological change. a. If the saving rate (s) is 0.15, what are capital per worker, production per worker, and consumption per worker in the steady state? b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s-0.3. c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s-0.45. d. Is it possible to save too much? Why?