Assume a new invention greatly increases the productivity of the U.S. economy. In the Solow model, this can be viewed as an increase in the TFP parameter A. a. Draw a Solow Diagram with output showing the effects of this policy. You should clearly label the initial steady state (K, Y), the transition dynamics for output and capital, and the long run equilibrium (KIR, Y LR).
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- What is the principle of transition dynamics? Why does the Solow model leadto this principle, and why is it useful?Consider the Solow growth model with concave production function as studied in class. Supposethe economy is initially in the picture below, and currently has the level of capital stock of K0. What wouldhappen to the dynamics of capital accumulations when depreciation rate increases? Graphically denote thedirection and the speed of change/accumulation/decumulation of the capital stock, then verbally explain whythey move like so.(a) Consider an economy that is initially in a steady state equilibrium. Assume that in this equilibrium it has a saving rate of 50 per cent and a depreciation rate of 2 per cent. Further assume that the population growth rate is 3% and that the level of output produced can be represented by the following production function: = where A = 1 and = 0.5. Use the Solow-Swan model to determine the level of capital per worker and output per worker in this economy. (1 mark) (b) Now suppose the government introduces a set of policies to improve the institutional set up as well as better production technique which increases total factor productivity by double. What is the new steady state level of capital per worker and output per worker? (1 mark) (c) Use a Solow-Swan diagram to show the qualitative effects of this new government policy upon steady state output per worker and capital per worker. Briefly describe the intuition behind this result. (1 mark) (d) Now suppose, population growth rate…
- 4 Consider the context of the Solow model with technical progress in an excess saving scenario, that is,the savings rate is higher than the golden rule savings rate. Imagine that the economy started is in steady state, but at time t0 the saving rate increases suddenly. Elaborate graphs that show the evolution over time of the variables mentioned in the followingparagraphs as a result of the previous event .a) Growth rate of capital per effective workerb) Growth rate of capital per workerc) Capital growth rated) Natural logarithm of capital per effective workere) Natural logarithm of capital per workerf) Natural logarithm of capital2. Solow-Swan Model (a) You will demonstrate the importance of diminishing returns to capital in the Solow-Swanmodel. Draw a Solow-Swan diagram in which there are constant returns to capital. Thiswould happen if the production function were Yt= AKt, where A = 1. Furthermore,assume that the sum of population growth and the depreciation rate is greater than thesaving rate. Does the economy converge to a steady state in this case? To answer thisquestion, you should draw a Solow-Swan diagram in terms of output per person, as we didin class. Use this diagram to explain why the economy converges to a steady state or doesnot. (b) Assume, instead, that the sum of population growth and the depreciation rate is equal tothe saving rate. In this case, are there any steady states? If yes, describe the steady-statelevels of capital per person. If no, explain why not. (Note: Diagram is not needed for thispart.)4. Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows:kt+1 = sAkαt + (1 − δ)kt.Consumption per worker is given by:ct = (1 − s)Akαt.(a) Solve for an expression for the steady state capital stock per worker. Indoing so, assume that the level of productivity is fixed at some value A.(b) Use your answer on the previous part to solve for an expression forsteady state consumption per worker.(c) Use calculus to derive an expression for the s which maximizes steadystate consumption per worker.
- Draw the Solow model and fully label your graph. This should includeper-worker production, steady state investment per-worker, and some labelfor consumption. Where is the “golden rule” consumption level? Is it at themaximum sustainable capital level? Explain.Consider the Solow Model with no population or technological growth. Suppose that two countriesare identical except that in Country A the depreciation rate is greater than the depreciation rate inCountry B.a. How do you compare the steady state level of capital per worker in these countries? Illustrategraphically. Explain the economic intuition for the di erences in capital per worker in steadystate.b. Which country a higher output per worker in steady state? What about investment per workerin steady state? Explain carefully.Assume that a E (0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label properly.
- Consider a one time change in immigration policy that immediately and permanently increases the level of the labour force in an economy. Suppose it rises permanently from L to L 0 . Assuming 2 the economy starts in its initial steady state, use the Solow model to explain what happens to the economy over time (transition dynamics) and in the long run (steady state). In particular, discuss what happens to the levels of capital, capital per worker, GDP and GDP per worker both at the new steady state as well as during the transition to the new steady state. You are not required to discuss how growth rates change over time (this is tricky). To answer this question use both the Solow diagram with total output, and diagrams with time on the horizontal axis and each of these variables on the vertical axis. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Assume the economy can be described by the Solow model. Assume also that the economy is in its steady-state, defined in per-worker terms. Explain what happens in the event of a decrease in total factor productivity, both in the long-run and during the transition, in aggregate and per-worker variables. Is there a policy you could think of where the capital per worker in the new steady-states is the same as in the old steady-state? What would happen to consumption per-worker under this hypothetical policy?Question 2 If a natural disaster destroys a large portion of a country's capital stock but the saving and depreciation rates are unchanged, the Solow model predicts that the economy will grow and eventually reach:a. A lower steady-state level of output than it would have before the disasterb. None of these answers is correctC. The same steady-state level of output as it would have before the disasterd. A higher steady-state level of output than it would have before the disaster e. Not enough information is given now suppose you are given the data for Brazil and Portugal. In Brazil, the saving rate is 0.1 and the depreciation rate is 0.1, while in Portugal saving rate is 0.2 and the depreciation rate is 0.1. Using the Solow model, you conclude that in the steady-state: a. Brazil has a higher capital-output ratio than Portugal b. Portugal has a higher capital-output ratio than Brazil c. Brazil has a higher level of output than Portugal d. Portugal has a higher level of output than…