2. Recall that general form of fundamental equation of growth in Solow model is described as follows: k = s f(k) – (gs + 5)ka Noting that at steady-s tate k s = 0 and hence %3D a Using the fact ksg= 0, show the steady-state graphically and provide econ omic interpretation of the steady-state condition s: f(k ss) = (gs + 6)k s b. Using the same graph you draw in part (a) explain the transitional dynamics of
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- Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.Forecasts for Sa’s economic growth rate have been droppingconsistently in 2023, from 1.2% year on year at the start of thefirst quarter to 0.7% in March, 0.6% in April and now 0.4% inthe outcome of the May survey (all Bloomberg).A more recent survey from Reuters in May places the outlookfor economic growth even lower, at 0.2% for 2023.Market perceptions of the global outlook have also dimmed, withChina’s economic recovery proving weaker than anticipatedafter its 2022 lockdowns, as recent production data disappoints,including that on household spending, investment and tradeactivity.Global trade defragmentation is also weakening sentiment, withrisks of limitations on trade competitiveness growing. Theseconcerns, along with US recession fears and disappointment overChina’s ability to lead the global economy stronger in 2023, haveweakened sentiment, reflecting in the recent fall in oil prices.Markets had expected a ramp-up in economic activity in Chinain the second quarter, but has also…Forecasts for Sa’s economic growth rate have been droppingconsistently in 2023, from 1.2% year on year at the start of thefirst quarter to 0.7% in March, 0.6% in April and now 0.4% inthe outcome of the May survey (all Bloomberg).A more recent survey from Reuters in May places the outlookfor economic growth even lower, at 0.2% for 2023.Market perceptions of the global outlook have also dimmed, withChina’s economic recovery proving weaker than anticipatedafter its 2022 lockdowns, as recent production data disappoints,including that on household spending, investment and tradeactivity.Global trade defragmentation is also weakening sentiment, withrisks of limitations on trade competitiveness growing. Theseconcerns, along with US recession fears and disappointment overChina’s ability to lead the global economy stronger in 2023, haveweakened sentiment, reflecting in the recent fall in oil prices.Markets had expected a ramp-up in economic activity in Chinain the second quarter, but has also…
- 2. 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.)7. Explain how the Solow growth model differs from models of endogenous growth with respect to the sources of technological progress. Give at least one policy implication of the Endogenous growth models.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 capital
- 11) The relationship between the growth rate of an economic variable, gt, and its level, yt, can be approximated by A) gt = yt - yt - 1. B) gt = logt - log yt - 1. C) yt = log gt - log gt - 1. D) log gt = yt - yt - 1. 12) The business cycle component of the log of real per-capita GNP is equal to A) log of actual real GNP - log of trend GNP. B) log of trend GNP ÷ log of actual real GNP. C) log of trend GNP - log of actual real GNP. D) log of actual real GNP ÷ log of trend GNP. 13) For the study of economic growth, it is most helpful to examine movements in ________; for the study of business cycles, it is most helpful to examine movements in ________. A) trend GNP; trend GNP B) trend GNP; deviations from trend in GNP C) deviations from trend in GNP; trend GNP D) deviations from trend in GNP; deviations from trend in GNP 14) Over the twentieth century, growth in per-capita GNP was highest A) immediately prior to the Great…Consider an economy for which y = Ake with the parameter values as listed: A=19, s=0.4, n=0.3, d=0.2 ,0 =0.5. Compute the steady state value for k. As a first step, graphically depict an economy in steady state. Be sure to label the axes, all lines, and steady state for k, y, c, and i . Suppose that productivity A decreases. Include on your graph the impact this will have on the economy. Be sure the direction of change is clear. The graph should depict the original and new steady states and clearly indicate which is which.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.
- 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.which statement \s are true. use graphs to exlain a. In the Solow growth model, the saving rate is a crucial determinant of the economy's long-run growth rate of output per worker. b. In the endogenous growth model , the representative firm sets the wage so that the demand and supply of efficiency units of labour are equal. c. In the endogenous growth model , there is no steady state of the economy as human capital will always continue to grow forever. d. The assumption of Constant Returns to Scale technology implies that the marginal product of factor imput is always decreasing.a.Assume that α(0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. also Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , b.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. c.Discuss the key difference(s) between the scenario in a and b as much as you want.