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1 Growth Rates of...
3 Growth Model Suppose that output (Y) in an economy is given by the following aggregate...
3 Growth Model Suppose that output (Y) in an economy is given by the following aggregate production function: Y = K + NE where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate 8 and that savings is a constant proportion s of income. You may assume that 8 > S. 1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. 2. Now suppose that the population grows...
MALTHUS AND SOLOW GROWTH MODEL
Malthusian Model of Growth Notation: Yt Aggregate output; Nt Population size; L¯ Land (fixed); ct Per capita consumption Production: Aggregate production function is Yt = F(Nt , Lt) = zN2/3 t L 1/3 t Population Dynamics: Nt+1 = g(ct)Nt Population growth function: g(ct) = (3ct) 1/3 Parameter Values: Land: L¯ = 1000 for all t. Productivity parameter: z = 1 ...
A country has the following production function: Yt=Kt^0.5Lt^0.5 Assume that 5 percent of of capital depreciates...
A country has the following production function: Yt=Kt^0.5Lt^0.5 Assume that 5 percent of of capital depreciates each year and the country saves 20 percent of output each year. What is the per worker production function, What is the steady-state level of capital per worker? What is the steady-state level of output per worker? The steady-state level of consumption per worker is: The steady-state level of saving per person is: The growth rate of output per person in the steady-state is:
1. Solow growth model: a. Draw the steady-state equilibrium by drawing the savings line and the...
1. Solow growth model: a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
Solow growth model: 1. a. Draw the steady-state equilibrium by drawing the savings line and the...
Solow growth model: 1. a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yYt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
1. Let's review the setup of the Solow growth model with saving rate s, constant population...
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
1. Let's review the setup of the Solow growth model with saving rate s, constant population...
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
all but part a 2. (Population growth and technology growth) Consider an economy that is described...
all but part a
2. (Population growth and technology growth) Consider an economy that is described by the production function Y depreciation rate of capital is 6 n 0.05 and the technology growth rate is g = 0.1 K (LE). Moreover the 0.15, the population growth rate is (a) What is the per effective worker production function, that is y ? What is the marginal product of capital, that is ? (b) If the saving rate is s 0.3, find...
The following problem is based on the idea of a Malthusian trap. Thomas Malthus, an 18th...
The following problem is based on the idea of a Malthusian trap. Thomas Malthus, an 18th century British cleric and scholar, argued that as population increases, the limited amount of natural resources will lead societies into a trap of gradually decreasing standard of living, thus negating the effects of any technological progress. We can study this idea using the Solow model framework. Consider a modified version of the Solow growth model where the aggregate production function in period t is...
Consider the Solow growth model. Output at time t is given by the production function Yt...
Consider the Solow growth model. Output at time t is given by the production function Yt = AK 1 3 t L 2 3 where Kt is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation Kt+1 = (1 − d) ∗ Kt + It , where d is the depreciation rate. Every person saves...
3 Growth Model Suppose that output (Y) in an economy is given by the following aggregate production function: Y = K + NE where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate 8 and that savings is a constant proportion s of income. You may assume that 8 > S. 1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. 2. Now suppose that the population grows...
1. Solow growth model: a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
Solow growth model: 1. a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yYt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
all but part a
2. (Population growth and technology growth) Consider an economy that is described by the production function Y depreciation rate of capital is 6 n 0.05 and the technology growth rate is g = 0.1 K (LE). Moreover the 0.15, the population growth rate is (a) What is the per effective worker production function, that is y ? What is the marginal product of capital, that is ? (b) If the saving rate is s 0.3, find...
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