Macroeconomics Solow model with technological progress
The Solow model with technological progress.
In the lecture, we talked about the Solow model with technological progress and population
growth. Now consider a simpler model with only technological progress. Denote the
technology level at time \(\mathrm{t}\) by \(\mathrm{A}_{\mathrm{t}}\), and the growth rate of technology by \(\mathrm{g}_{\mathrm{A}}\). The number of
worker is constant, \(\mathrm{N}\). The production function is given by
$$ Y_{t}=K_{t}^{\alpha}\left(A_{t} N\right)^{1-\alpha} $$
where \(\alpha\) is a constant.
(a) Define \(x_{t}=X_{t} / A_{t} N\), where \(X_{t}\) stands for all relevant aggregate variables in the model.
Write down the production function, investment equation, and the law of motion of
capital in terms of per effective worker variables, \(x_{t}\).
(b) Solve the steady-state capital, output, consumption, and investment per effective
worker.
(c) Solve the golden-rule saving rate. For a country with a capital share \(0.36\) in output,
what is its golden-rule saving rate?
(d) What are the growth rates of capital and output per effective worker, capital and output
per worker, capital and output in the steady state.
Homework Answers
![Yu= K (AUN) - & Yt ته ® Odpunt per effective worker, te = [Xce (Atw ]-a)/ QEN) (X+/AENDO where x = X+/A+N investment equation](http://img.homeworklib.com/questions/b9771660-aeff-11eb-99f6-c723e69531ae.jpg?x-oss-process=image/resize,w_560)
In the Solow model with a positive rate of population growth n and technological progress z,...
In the Solow model with a positive rate of population growth n and technological progress z, the steady state level of total real output Y grows at the rate: a. n. b. zero. c. z. d. n + z. In the Solow model with a positive rate of population growth n and technological progress z, the steady state level of per worker real output y grows at the rate: a. n. b. zero. c. z. d. n + z. In...
3) Consider the Solow model with population growth and labor-augmenting technological progress. Suppose that the aggregate...
3) Consider the Solow model with population growth and labor-augmenting technological progress. Suppose that the aggregate production function is Cobb- Douglas, i.e. Y = AK"(E · L)1-a, where A is a constant, while E denotes technological progress and grows at rate g. Labor grows at an exogenous rate n, and capital depreciates at rate d. As usual, people consume a fraction (1 – s) of their income. a. Use a graph similar to what we have seen in class to...
In the Solow growth model with technological progress (and diminishing marginal returns to capital), explain the...
In the Solow growth model with technological progress (and diminishing marginal returns to capital), explain the steady-state growth rates for: a. Capital per effective worker b. Output per effective worker c. Output per worker d. Total output
Question #3: Solow Model with Technological Progress Suppose than the economy's per effective worker production function...
Question #3: Solow Model with Technological Progress Suppose than the economy's per effective worker production function is given by y=Ros. Assume that the savings rate (8) is equal to 16 percent, the depreciation rate (8) is equal to 10 percent, the population growth rate (n) is equal to 2 percent and the rate of technological growth (g) is equal to 4 percent. (a) Find the steady-state value of capital per effective worker (K). (b) Find the steady-state value of output...
1. Assume that an economy described by a Solow model has a per-worker production function given...
1. Assume that an economy described by a Solow model has a per-worker production function given by y- k05, where y is output per worker and k is capital stock per worker (capital-labor ratio). Assume also that the depreciation rate δ is 5%. This economy has no technological progress and no population growth (n 0). Both capital and labor are paid for their marginal products and the economy has been in a steady state with capital stock per worker at...
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...
An economy is described by the standard Solow model without technological progress and without population growth....
An economy is described by the standard Solow model without technological progress and without population growth. You are given the information that the savings rate dropped to a lower level in this economy, but you don’t know by how much it did so. Suppose that prior to the drop in s the economy was in a steady-state with a capital stock per worker higher than the Golden Rule level. a. In a graph which should include the production function, the...
Answer the following questions using the basic Solow growth model, without population growth or technological progress....
Answer the following questions using the basic Solow growth model, without population growth or technological progress. (a) Draw a diagram with per worker output, y, consumption, c, saving, s and investment, i, on the vertical axis and capital per worker, k, on the horizontal condition. On this diagram, clearly indicate steady-state values for c, i, and y. Briefly outline the condition that holds in the steady state (i.e. what is the relationship between investment and the depreciation of capital?).
Consider the Solow model with population growth and technological progress. The population grows at rate of...
Consider the Solow model with population growth and technological progress. The population grows at rate of d and the technology grows at rate of g. The depreciation rate of capital is λ. The aggregate production function is given as Y=100 ?![(1-u) ?]" where Y, K, L, ?, ? and u refers to aggregate output, aggregate capital stock, aggregate labor, output elasticity with respect to capital, output elasticity with respect to labor, and natural rate of unemployment, respectively. Draw a well-labeled...
3) Consider the Solow model with population growth and labor-augmenting technological progress. Suppose that the aggregate production function is Cobb- Douglas, i.e. Y = AK"(E · L)1-a, where A is a constant, while E denotes technological progress and grows at rate g. Labor grows at an exogenous rate n, and capital depreciates at rate d. As usual, people consume a fraction (1 – s) of their income. a. Use a graph similar to what we have seen in class to...
Question #3: Solow Model with Technological Progress Suppose than the economy's per effective worker production function is given by y=Ros. Assume that the savings rate (8) is equal to 16 percent, the depreciation rate (8) is equal to 10 percent, the population growth rate (n) is equal to 2 percent and the rate of technological growth (g) is equal to 4 percent. (a) Find the steady-state value of capital per effective worker (K). (b) Find the steady-state value of output...
1. Assume that an economy described by a Solow model has a per-worker production function given by y- k05, where y is output per worker and k is capital stock per worker (capital-labor ratio). Assume also that the depreciation rate δ is 5%. This economy has no technological progress and no population growth (n 0). Both capital and labor are paid for their marginal products and the economy has been in a steady state with capital stock per worker at...
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...
Most questions answered within 3 hours.
-
An individual who has automobile insurance from a certain
company is randomly selected. Let Y be...
asked 4 minutes ago -
A 3330-kg spacecraft is in a circular orbit 2770 km above the
surface of Mars.
How...
asked 4 minutes ago -
Initial mean=6600 and median = 1500, after 2 data sets removed,
new mean = 1850 and...
asked 5 minutes ago -
The outcome X of an experiment has only two possible values, X=4
and X=5. Given that...
asked 5 minutes ago -
When UV light of wavelength 288 nm falls on a metal surface, the
maximum kinetic energy...
asked 16 minutes ago -
Your company has just brought in a new line of products... And
they are pieces of...
asked 19 minutes ago -
in three paragraphs or more discuss the role of the U.S.
Children’s Bureau in dealing with...
asked 18 minutes ago -
Place the following salts in order of increasing water
solubility:
i. Fe(OH)2 Ksp = 7.9 ×...
asked 21 minutes ago -
If inflation is increasing at 2.6 percent per year, and your
salary increases at the same...
asked 22 minutes ago -
An aspirin dose of 5.0mg per kg of body weight has been
prescribed to reduce the...
asked 28 minutes ago -
The AASB Conceptual Framework (2.12-2.19) refers to ‘faithful
representation’ as being necessary for financial information to...
asked 33 minutes ago -
A U.S. corporation with net receivables in euro could hedge by
_________________.
A. buying euro forward...
asked 35 minutes ago