3). Let's consider the Solow Model without technology advancement. Y(t)=2K(t)^(1/2)*L(t)^(1/2) The population growth rate=D0.02 Capital accumulation is s*Y(t)-d*K s=0.2, d=0.03 d is the capital depreciation rate. In the steady state, please calculate the following measurements. (a)Capital per capita 16

3). Let's consider the Solow Model without technology advancement. Y(t)=2K(t)^(1/2)L(t)^(1/2) The population growth rate=D0.02 Capital accumulation is sY(t)-d*K s=0.2, d=0.03 d is the capital depreciation rate. In the steady state, please calculate the following measurements. (a)Capital per capita 16

MACROECONOMICS

14th Edition

ISBN:9781337794985

Author:Baumol

Publisher:Baumol

Chapter7: Economic Growth: Theory And Policy

Section: Chapter Questions

Problem 3DQ

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Consider the Solow growth model. Suppose that F(K, N) = zK^a N^1-a,where a = 0.3. Also, assume that capital depreciation rate is 10% (that is d = 0.1), savings rateis 25% (that is s = 0.25), populations growth rate is 2% (that is n = 0.02), and z = 2.• First, determine capital per worker, income per capita, and consumption per capita in thesteady state.• Second, assume that the savings rate has increased to 40% but the total factor productivitydecreases to 1. Discuss the effect of savings and productivity on the steady state level ofconsumption per worker. PLEASE SHOW ALL HAND WRITEN STEPS!!
Consider the country of Solow, which is described by the Solow–Swan model. Let the saving rate θ =0.8; let the population growth rate n = 0.05; let the rate of depreciation d = 0.05. If per capita incomey = 100 and the per capita capital stock k = 1000, which of the following is true? a.Replacement investment is 100, saving is 80 and k will increase towards the steady state per capita capitalstock b.Replacement investment is 100, saving is 60 and k will decrease towards the steady state per capita capitalstock c.Replacement investment is 100, saving is 80 and k will decrease towards the steady state per capita capitalstock d.Replacement investment is 100, saving is 80 and k is at the steady state per capita capital stock
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 it
In a Solow growth model with population growth but no technological change, show graphically that an increase in the rate of depreciation will reduce the steady-state value of capital per worker and output per worker. It is reasonable to expect that depreciation rates differ across countries? Why or why not? Please be specific.
QUESTION 1 (10 marks) Consider the Solow growth model without population growth or technological change. The parameters of the model are given by s = 0.2 (savings rate) and δ = 0.05 (depreciation rate). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. a. Rewrite production function per-worker terms. b. Find the steady-state level of the capital stock, kss
Question 3 Consider the steady state of the Solow model with population growth and technological progress. (a) Use a graph to show what happens to steady-state capital per effective worker and output per effective worker in response to a decrease in the depreciation rate (?). Explain your answer. (b) Use a graph to show what happens to steady-state capital per effective worker and output per effective worker in response to a decrease in the population growth rate (?). Explain your answer. (c) Briefly explain any differences between the growth rate of output per worker (?⁄?) in the steady state when comparing your answers to parts (a) and (b). Define the steady state.
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?
4.The Solow growth model differs from the Harrod-Domar because: a.Assumes that depreciation rate and population growth are exogenous b.Assumes that the rate of technological progress varies from country to country. c.Predicts that permanent growth is achievable only through technological progress d.Predicts that poorer countries will grow faster than richer countries.
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.
Consider a Solow–Swan model with saving rate s = 0.4, labour force growth gL = 0.05, constant productivity A = 1, and depreciation ?δ = 0.05. If output per worker is y = Y/L = 200 and capital per worker is k = K/L = 1000, which of the following is true? Group of answer choices - Effective depreciation per worker is 80, saving per worker is 100 and k will increase towards the steady state - Effective depreciation per worker is 100, saving per worker is 80 and k will decrease towards the steady state - Effective depreciation per worker is 100, saving per worker is 80 and k is at the steady state - Effective depreciation per worker is 80, saving per worker is 100 and k will decrease towards the steady state
Suppose the economy of Poorland is described by the simple Solow model without technological progress or population growth. The economy starts at the steady state. Suppose another country concludes that income per worker is too low in Poorland and therefore sends them at one-time development aid package (in form of capital) at period t0. a. Show what happens as a result of this aid package in a graph showing the production function, investment function and depreciation function (all in per-worker terms). b. Show a time path of output per worker that shows the old steady state, the change due to the aid package and the transition to the long-run equilibrium over time. Briefly explain your graph. c. If Poorland would like to maintain the capital stock per worker that it had right after the aid package was received, what would it need to do?
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.