Question

Assume that f(k) = Akα , and that the saving rate is s. Solve for the...

Assume that f(k) = Akα , and that the saving rate is s. Solve for the steady state level of capital, and for the golden rule level of capital. What is the condition on s that would imply that they are the same?

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Savings rate = s

At the steady state, investment is just enough to cover depreciation i.e. capital per worker will remain constant, ∆k = 0

To find the golden rule level of capital, planner wants to maximize consumption

At the steady state, capital is k* and

To maximize consumption and find golden rule level of capital

Condition on s so that

Hence needs to be satisfied for .

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the production function Y = F (K, L) = Ka * L1-a, where 0 <...
Consider the production function Y = F (K, L) = Ka * L1-a, where 0 < α < 1. The national saving rate is s, the labor force grows at a rate n, and capital depreciates at rate δ. (a) Show that F has constant returns to scale. (b) What is the per-worker production function, y = f(k)? (c) Solve for the steady-state level of capital per worker (in terms of the parameters of the model). (d) Solve for the...
Let’s solve the two sector model from page 281 of your textbook. The economy has two...
Let’s solve the two sector model from page 281 of your textbook. The economy has two sectors, manufacturing firms and research universities. The two sectors are described by the production functions Y = K1/2[(1-u)LE]1/2 ?E = u E where u is the fraction of labour force in universities (assume u is exogenous). Write the equation of motion of capital, ?K = sY - ?K, in intensive form. Write down the steady state condition and find the steady state level of...
Assume that the production function in an economy is given by y=k1/2, where y and k...
Assume that the production function in an economy is given by y=k1/2, where y and k are the per-worker levels of output and capital, respectively. The savings rate is given by s=0.2 and the rate of depreciation is 0.05. What is the optimal savings rate to achieve the golden-rule steady state level of k?
Suppose Neverland is identical to Korea, except that it has a higher saving rate. Then for...
Suppose Neverland is identical to Korea, except that it has a higher saving rate. Then for Neverland, compared with Korea: 11. the steady state capital stock per person is: a) higher b) lower c) same d) uncertain 12. the steady state growth rate in capital is: a) higher b) lower c) same d ) uncertain 13. the golden rule capital per person is: a) higher b) lower c) same d) uncertain
Assume that an economy described by the Solow model has the production function Y = K...
Assume that an economy described by the Solow model has the production function Y = K 0.4 ( L E ) 0.6, where all the variables are defined as in class. The saving rate is 30%, the capital depreciation rate is 3%, the population growth rate is 2%, and the rate of change in labor effectiveness (E) is 1%. For this country, what is f(k)? How did you define lower case k? Write down the equation of motion for k....
Question 1 Production is given by: ? 1−? ?≡?(?,?)=?? ? where ??+1 = (1 + ?)??...
Question 1 Production is given by: ? 1−? ?≡?(?,?)=?? ? where ??+1 = (1 + ?)?? and ??(0,1) Show that F exhibits a constant return to scale technology. Express output as a function of the capital labor ratio ?? = ?? ∕ ??. Find the dynamical system (describing the evolution of ?? over time) under the assumption that the saving rate is ? ?(0,1) and the depreciation rate is ? ∈ (0,1]. What is the growth rate of ??, ???≡(??+1...
Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to...
Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y = Kα [(1 – u)L]1-α where K is capital, L is the labor force, and u is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate δ. a. Write a condition that describes the golden rule steady state of this economy. b. Express the golden rule...
Consider a numerical example using the Solow growth model: The production technology is Y=F(K,N)=K0.5N0.5 and people...
Consider a numerical example using the Solow growth model: The production technology is Y=F(K,N)=K0.5N0.5 and people consume after saving a proportion of income, C=(1-s)Y. The capital per worker, k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k. (a) Describe the steady state k* as a function of other variables. (b) Suppose that there are two countries with the same steady state capital per worker k* and zero growth rate of population(n=0), but differ by saving rate, s and depreciation rate, d. So we assume that...
2. Consider a numerical example using the Solow growth model: The production technology is Y=F(K,N)=K0.5N0.5 and...
2. Consider a numerical example using the Solow growth model: The production technology is Y=F(K,N)=K0.5N0.5 and people consume after saving a proportion of income, C=(1-s)Y. The capital per worker, k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k. (a) Describe the steady state k* as a function of other variables (b) Suppose that there are two countries with the same steady state capital per worker k* and zero growth rate of population(n=0), but differ by saving rate, s and depreciation rate, d. So we assume...
Consider an economy described by the production function: Y = F(K, L) = K0.3L0.7. Assume that...
Consider an economy described by the production function: Y = F(K, L) = K0.3L0.7. Assume that the depreciation rate is 5 percent per year. Make a table showing steady-state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent, and so on. Round your answers to two decimal places. (You might find it easiest to use a computer spreadsheet then transfer your answers to this table.) Steady State...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT