Question

I have been given a production function which states Yt= Kt^0.25N^0.75 Im told the number of...

I have been given a production function which states Yt= Kt^0.25N^0.75

Im told the number of workers is N constant, the saving rate is s and the deprecation of physical capital is δ .

How do I go about explaining the evolution of physical stock over time?

How do I show the the steady state levels of capital per worker and output per worker in terms of the saving rate and depreciation rate?

Thank you

Homework Answers

Answer #1

to find output per capita divide output by number of worker

The steady state is the level of capital per person at which the increase in capital per capita from investment equals its decrease from depreciation and population growth

population growth is 0 because number of workers is constant

this is steady level of capital per worker

this is steady level of output per worker

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
If the production function is given by Yt=A(KtLt) 0.5 where Y is the output, A is...
If the production function is given by Yt=A(KtLt) 0.5 where Y is the output, A is the technology, L refers to the labor stock, and K is the capital stock. Suppose that the saving rate (s) equals 0.6 and the depreciation rate (δ) is 0.3 a. Write the output and capital accumulation equations in terms of the capital per worker? b. Find the steady state capital, output, investment, and consumption? c. What would happen to the steady state capital if...
Suppose that output (Y ) in an economy is given by the following aggregate production function:...
Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate δ and that savings is a constant proportion s of income. You may assume that δ > s. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. Now suppose that the population grows at rate n. Solve...
Assuming the following Cobb-Douglas production function is given for a closed economy without government. i. Where...
Assuming the following Cobb-Douglas production function is given for a closed economy without government. i. Where returns to capital = 0.5; and rate of depreciation of physical capital Determine the steady-state level of capital per worker. What is the savings rate at which the steady-state level of capital is achieved?             [6marks] ii Prove that the steady-state level of output is the ratio of the saving rate to the rate of depreciation                                                                       [6 marks] iii. Assuming that , what will be...
Suppose that the economy’s production function is given by Y = K1/3N2/3 and that both, the...
Suppose that the economy’s production function is given by Y = K1/3N2/3 and that both, the savings rate s and the depreciation rate δ are equal to 0.10. a. What is the steady-state level of capital per worker? b. What is the steady-state level of output per worker? Suppose that the economy is in steady state and that, in period t the depreciation rate increases permanently from 0.10 to 0.20. c. What will be the new steady-state levels of capital...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by: Y = 1.6K1/2L1/2 In this economy, workers consume 75% of income and save the rest.  The labour force is growing at 3% per year while the annual rate of capital depreciation is 5%. Initially, the economy is endowed with 4500 units of capital and 200 workers. Is the economy in its steady state?  Yes/no, explain.  If the economy is not in its steady state, explain what...
17. Solow growth The production function in your country is: Y = K^0.5(LE)^0.5. Your economy saves...
17. Solow growth The production function in your country is: Y = K^0.5(LE)^0.5. Your economy saves 24% of output each period, and 5% of the capital stock depreciates each period. The population grows 2% annually. Technology grows 1% annually. You begin with 1000 workers and 1 unit of capital, and a tech- nology level equal to 1. a) Write the production function in per-eective-worker terms, so that per-effective-worker output (y = Y/LE ) is a function of per-effective-worker capital (k=...
1. Suppose that the economy’s production function is Y = K.2 (eL).8 , that the saving...
1. Suppose that the economy’s production function is Y = K.2 (eL).8 , that the saving rate, s, is equal to 10 percent, and the depreciation rate, δ, is equal to 3 percent. Suppose further that the number of workers, L, grows at 1 percent a year and that the rate of technological progress, g, is 1 percent per year. Find the steady-state values of the following: a. The capital stock per efficiency units of labor 2 b. Output per...
A closed economy (NX = 0) without government (G = T = 0) has a production...
A closed economy (NX = 0) without government (G = T = 0) has a production function Y = K^1/4 ^L 3/4 . Capital depreciates at a rate of 3 percent per year. Workers spend 76 percent of their income each year. Investment adds up to the capital stock which is available for production next year. Assume that capital per worker is 5.0625 at the beginning of 2017 and the number of workers stays the same each year. (a) Find...
4. Golden Rule. Suppose that we have a standard Solow Model. There is no population or...
4. Golden Rule. Suppose that we have a standard Solow Model. There is no population or technology growth. (a) The rm problem is to maximize prots, t. The rm's problem can be written as: max KtC0;NtC0 t = AK t N1− t − wtNt − rtKt: The rm takes the factor prices as given. Find the rst order conditions characterizing the optimal rm behavior. (b) Use the FONCs from 4a to show that wtNt~Yt = 1 − , where Yt...
An economy has the following Cobb-Douglas production function: Y = Ka(LE)1-a The economy has a capital...
An economy has the following Cobb-Douglas production function: Y = Ka(LE)1-a The economy has a capital share of 1/3, a saving rate of 24 percent, a depreciation rate of 3 percent, a rate of population growth of 2 percent, and a rate of labor-augmenting technological change of 1 percent. It is in steady state. a. Does the economy have more or less capital than at the Golden Rule steady state? How do you know? To achieve the Golden Rule steady...