Macroeconomics (Fourth Edition)
4th Edition
ISBN: 9780393603767
Author: Charles I. Jones
Publisher: W. W. Norton & Company
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Chapter 5, Problem 4E
To determine
The impact of the government policy that permanently increases the level of the labor force.
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In this question, you will explore how changes in the saving rate and the rate of technological progress affect an economy’s growth. In addition, you will examine how the golden rule saving rate depends on the production function. Consider the Solow (neoclassical) growth model with aggregate production function Y = K^alpha(AN)^(1-alpha). Each period lasts a year.
Consider the Solow Model. Suppose a country enacts a tax policy that discourages investment, and the policy reduces the investment rate immediately and permanently from sbar to sbarprime . Assuming the economy (and hence the initial capital stock) is in its initial steady state, use the Solow Model to explain what happens to the economy over time and in the long run. Draw a graph showing how output evolves over time (put Y_t on the vertical axis with a ratio scale and time on the horizontal axis), and explain what happens to economic growth over time.
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?
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Macroeconomics (Fourth Edition)
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- The Solow Growth Model is an exogenous model of economic growth that analyzes changes in the level of output in an economy over time as a result of changes in the population growth rate, the savings rate, and the rate of technological progress. Consider the Solow model. a) Explain using a graph why there is a poverty trap in this model b)Describe how an economy such as one characterized by this model may break out of a poverty trap.arrow_forwardPlease aid in answering the underlined questions in BOLD Question 4:a. Identify two assumptions of the basic Solow Growth Model. b. Why are these assumptions important in supporting the Solow Model? c. You are given the following information about an economy.Y = C + IY = F(K, L)The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns.s = saving rate (assume this is constant) per yearδ= depreciation rate (assume this is a constant) per yeary = Y/Lk = K/Lk* = steady state of capital per worker (K/L) and sf(k) < δk.i. What is sf(k)? ii. What is δk?iii. Interpret the meaning of sf(k) < δk? iv. Graphically illustrate sf(k), δk, and k*. Indicate on your graph where sf(k) < δk.v. Explain what happens in this economy when sf(k) < δk.arrow_forwardConsider Solow's model of economic growth, for a closed economy, without population growth or technical progress. In this case, indicate for each of the following statements whether it is correct by checking the appropriate box: a) Because of diminishing factor returns, the slower an economy grows, the closer its capital stock is to its stationary value; b) The model implies a negative relationship between the growth rate and initial income; c) In the long run, all economies converge unconditionally, in terms of income, to the same stationary state; d) In the long run, all economies converge unconditionally, in terms of growth rate, to the same steady state; e) None of the above statements is correct. ***WE COULD HAVE MULTIPLE ANSWER***arrow_forward
- Solow model is important because it implies that An economy that uses the neoclassical production function cannot grow at a positive rate forever. All the answers are implications of Solow model. An increase in savings results in a higher long-run economic growth. Heterogeneous economies will absolutely converge so that poor countries can catch-up rich countries in long-run.arrow_forwardConsider the Solow Model. Suppose a country enacts a tax policy that discourages investment, and the policy reduces the investment rate immediately and permanently from sbar to sbarprime . Assuming the economy (and hence the initial capital stock) is ABOVE its initial steady state (note: this is different from the standard case where we start at the intial steady state), use the Solow diagram to explain what happens to the economy over time and in the long run. Draw a graph showing how output evolves over time (put Y_t on the vertical axis with a ratio scale and time on the horizontal axis), and explain what happens to economic growth over time.arrow_forwardSuppose in a Solow model, we have the following parameter values: n = 0, s = 0.2, a = 0.33. There is no growth in the total factor productivity so that A, = A = 1. Moreover, we know that at time 0, the economy is at a steady state so that k = k, =1. Now imagine that a deadly pandemic hits the economy at time t=1. As a result, the population at time t =1 is 10% lower than the population at time t=0. The pandemic is a one-time shock so that population growth rate remains the same, i.e., from t-2 onward, the population remains the same as the population at time t=1. The total capital stock, however, is unchanged so that K, Ko. What is the growth rate of per-capita capital in percentage (rounded to the 2 decimal places, e.g., answer 1.08 if your calculation shows the growth rate is 0.01079) at time t=3 from time t=2? %3!arrow_forward
- Consider a Solow economy that begins with capital stock equal to $200 billion, and suppose its steady-state level of capital is $400 billion. Now suppose this economy receives a gift of foreign aid in the form of $100 billion worth of capital. (a) Use the Solow model to explain what happens to capital per worker, output per worker, and consumption per worker, both immediately and over time in this economy. a) (b) Suppose instead of starting below its steady state, the economy begins in steady state with capital equal to $400 billion. Answer part (a) for this case. point) (c) In this example, does foreign aid have a long-run effect on the welfare of poor countries? (1 pol)arrow_forwardConsider the Swan-Solow model of economic growth. [Hint: Question (e) below goes beyond the subject matter discussed in the lecture and requires you to think independently.] a) Draw a suitable diagram with a typical Aggregate Production Function in it. b) Draw a typical Investment curve into the diagram. Briefly explain how you came up with the curve and what you need to know to exactly pin it down. c) Draw a typical Depreciation curve into the diagram. Briefly explain how you came up with the curve and what you need to know to exactly pin it down. d) Briefly define the steady state and show it in your diagram. e) It has been argued that corruption affects economic growth (e.g. Mankiw/Taylor, 5th ed., pp. 479-480). Explain which of the curves in your diagram is most plausibly affected by a reduction in corruption in an economy, and what this effect would be. f) Use your diagram to show how the effect that you have identified in part (e) affects the steady state in the model.arrow_forwardIn the Solow model, population growth leads to steadystate growth in total output, but not in output per worker. Do you think this would still be true if the production function exhibited increasin g or decreasing returns to scale? Explain.arrow_forward
- Production function is given by Y = Ka(AN)'¯ª, where a=2/3. Initially, the saving rate was equal to s and the economy was in the steady state. Use the Solow growth model to answer the following questions. (Please fill in numbers; use a yomma as a decimal separator: 10,5) 1. In order to increase capital per unit of effective labor in the steady state by a factor of 27 (i.e. to make it 27 times larger), the rate of saving needs to increase by a factor of 2. In order to increase output per unit of effective labor in the steady state by a factor of 4 (i.e. to make it 4 times larger), the rate of saving needs to increase by a factor of 3. Suppose that s=25 percent, the rate of depreciation of capital is equal to 5 percent, the rate of technological progress is equal to 1 percent, and the rate of population growth is equal to 0,25 percent, a=2/3. The steady state level of investment per unit of effective labor is equal toarrow_forwardQuestion 4:a. Identify two assumptions of the basic Solow Growth Model. b. Why are these assumptions important in supporting the Solow Model? c. You are given the following information about an economy.Y = C + IY = F(K, L)The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns.s = saving rate (assume this is constant) per yearδ= depreciation rate (assume this is a constant) per yeary = Y/Lk = K/Lk* = steady state of capital per worker (K/L) and sf(k) < δk.i. What is sf(k)? ii. What is δk?iii. Interpret the meaning of sf(k) < δk? iv. Graphically illustrate sf(k), δk, and k*. Indicate on your graph where sf(k) < δk.v. Explain what happens in this economy when sf(k) < δk.arrow_forwardConsider 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?arrow_forward
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