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Explain the absolute convergence and conditional convergence hypotheses in the Solow-Swan model (provide country examples as well).
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- Which of the graphs (if any) show a surprising or seemingly incorrect relationship based on what you know about conditional convergence and the Solow model?Derive the expression for the speed of convergence for k in the Solow model. Show this is also the speed of convergence for output y. Interpret.In the Solow model in which y=Akα (where y is GDP per worker and k is capital per worker), compare the poverty trap model to the incentives model. Discuss whether the following statements are true or false in each model, using graphs and equations to explain and prove your conclusions:a. There exists some level of aid sufficient to get any poor country out of povertyb. There exists some threshold above which aid can be discontinued.c. A country’s long-run per capita income depends on where its per capita income is now.d. When the country is open to capital flows in or out, the main determinant of development is government policies and institutions e. Two pieces of evidence support the existence of poverty traps: (1) Growth of poor countries is slower than that of richer countries, and (2) Growth accelerates when a poor country exits poverty (explain why the poverty trap model predicts (1) and (2) and whether these predictions are confirmed by the data).
- Consider a numerical example of the Solow model: Assume that n=0.2 s=0.3 d=0.1 F(K,N)=K12N12 Initially, in period t=0, that z=3 N=1 and the economy is in a steady state: Suppose that at t=1, total factor productivity falls to z=1 and then returns to z=3 for periods t=2,3,4.... What is the value of per person aggregate output at period t=1?Consider the basic Solow model with no population growth and no technological progress and a production function of the form F (K, H ), where H denotes the efficiency units of labor (human capital) given by where N is the set of all individuals in the population, and hi is the human capital of individual i. Assume that H is fixed. Suppose there are no human capital externalities and factor markets are competitive. (a) Calculate the steady-state equilibrium of this economy. (b) Prove that if 10% higher h at the individual level is associated with a% higher earnings, then a 10% increase in the country’s stock of human capital H will lead to a% increase in steadystate output. Compare this result to the immediate impact of an unanticipated 10% increase in H (i.e., consider the impact of a 10% increase in H with the stock of capital unchanged).With the help of the Solow growth model diagram, explain the effects of shocks on steady state per worker capital and output.
- Consider the Solow model. Draw the paths over time for the log of y, c and k for an economy that starts below its balanced-growth path.1. In the Solow model, if investment (I=sY) is lower than depreciation (dK), then…. A. Depreciation (dK) in the following period will be higher than in the current period. B. Capital stock (K) in the following period will be lower than in the current period. C. Per-capita GDP (y) in the following period will be the same as in the current period. D. Overall GDP (Y) in the following period will be higher than in the current period. The answer is B - - Can you show work for it, graph the representation for itThe Solow growth model is characterised by both successes and failures. Explain the main problems with the Solow growth model that led to the emergence of endogenous growth models.
- Consider a Solow economy that begins with capital stock equal to $200 billion, and suppose itssteady-state level of capital is $400 billion. Now suppose this economy receives a gift of foreign aidin the form of $100 billion worth of capital.(a) Use the Solow model to explain what happens to capital per worker, output per worker, andconsumption per worker, both immediately and over time in this economy. (b) Suppose instead of starting below its steady state, the economy begins in steady state withcapital equal to $400 billion. Answer part (a) for this case. (c) In this example, does foreign aid have a long-run effect on the welfare of poor countries?Consider the endogenous growth model AK, in which the production function is given by Y = AK. Suppose s denotes the saving rate; that δ represents the depreciation rate; and that the variable that represents the population and that grows at the rate n. Calculate the growth rate of capital per capita in the same way as for the Solow model and, from there, solve the differential equation to obtain the capital per capita (denoted by k) as a function of time.. Using the Solow growth model suppose that there is a hurricane coming toward a city. Because it is fully anticipated a lot of the people can leave and come back safely, but a lot of physical capital (K) is destroyed (buildings cannot move). Show graphically what the Solow model predicts will happen to the steady state. Does the poverty trap model have any different predication? Compare this graphically.