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- 2) Consider an economy with depreciation 6=.2, saving rate s = .1. Worker productivity grows at rate g = .1. The economy starts with 5 units of capital per worker. The productivity function is given by: 2tnioq S) m6x9 grit no bazzim 23 0 2 2 19 0 f(k) = 3* k1/3 (1916978 zi 19verlɔirlw how to two lapiolandotdwong noitsluqoq TUOHTIW lebom wolo2011 ( The Marginal Product of capital is therefore 100037950 1 ritwong ytivitoub 1910 190 stign .6 MPK = 3* know 19q gniv brs (19) a. Using the above parameters, what is the golden rule steady state capital per (effective) worker? Please show your work below.Hello I need help to find the answer for my econ 101 hw for a question as follows: Assume that the production function for a country is given by ?=√K and annual investment is given by the function ?=?×? where γ=0.270, and that the yearly depreciation rate is 4.50%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking. I will be also attaching the original problem for your reference as I just need to find the time that it would take the country's output to catch up with its neighbor's output. Thank You and please refer to the image to further assist with the question that I want answered.A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
- 1. Suppose that the aggregate production function in the Solow-Swan model has the Cobb- Douglas form, y = ka. Also, assume a = 0.35, saving rate s = 15%, population growth n = 5%, technology growth g = 10%, and no depreciation ổ = 0%. (a) Show that f'(k) > 0, f"(k) < 0, and the Inada conditions limp-of"(k) = o and limz f'(k) = 0 are satisfied. (b) What are the numerical steady-state values of y* and e*? Show your workings. (c) Why is the steady state unique? (d) Assume labour and capital are paid their marginal products and the economy is on a balanced growth path at time t = 0: i) What is the real wage w(0) if A(0) = 1? ii) What is the growth rate of wages w/w along the balanced growth path? iii) What is the return to "working" capital r? iv) What are the shares of income going to capital and to labour? v) If the depreciation rate were positive (e.g., 6 = 10%), explain what would hap- pen to the return to "working" capital r and the shares of income going to (both "working" and…Let the production function be Q = K0.®L0.2 Solow's assumptions are K = sQ – 6K The symbols s represents a (constant) marginal propensity to save, n, a (constant) rate of growth of labor and 8 constant depreciation rate. (a) Derive the fundamental equation of Solow growth model for given production function. (b) Sketch graph of with k on the vertical axis and k on the horizontal take n = 0.01, s = 0.3, 8 = 0.1.Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].
- In Wonderland production per worker (y) depends on capital per worker() such the y=10vk. Every year 15% of the capital stock depreciates, while workers in Wonderland save 10% of their income. Every year the population grows ratas te of 3% (c) The country of Neverland is identical to Wonderland in terms of output per worker, the savings rate, the depreciation rate and population growth. They differ in one respect: Wonderland has capital per worker of 10, whereas Neverland has capital per worker of 20. Which country experiences a higher growth rate of output per worker and how will their growth rates evolve over time?In any Econorry the production function | 1-x is y=Ka L!-xnfinity Derive ss level of output per and capital per worker. vyorkerQuestion 1 Consider the following economy with production function: Y = AK"L-a where Y is total output; K is capital; L is labour force; A is the level of technology (exogenous); s is the saving rate; n is the population growth rate; 0 < a < 1. Assume the rate of capital depreciation (5) to be zero. Hence, capital accumulation equation is: K = sY (a) Does this production function exhibitconstantreturns to scale to capital and labour? Explain. Derive production function per worker. (b) Derive an equation showing how the growth rate of capital per worker depends on s, n, and A. Explain its growth implications and use a graph to support your answer. (c) Find out the expression for the steady state capital per worker andoutputper worker. How do they depend on s, n, and A? Explain. (d) Instead of assuming saving rate (s) to be a constant, suppose we assume that "s" depends on y,y =(equivalently on k, k = . In particular, s = e is constant. Find the expression for the growth rate of capital…
- suppose the production formula is given by yt= kt ^1/3 where y is the output per worker and k is the capital per worker. futhermore assume that the saving rate is exogenous and the capital deprecitates at delta rate. if the sum of both deprectiation rate and saving rate equals 1, answer the questions below 1. find the steady state values of capital, output, investments and consumption as functions of the saving rate only? 2. in a diagram show the steady state value values in a part (a)?Assume the rate of technological progress is constant in a SSGM with Cobb- Douglas production function. Show that a steady-state cannot be identifiede if the technological progress is capital augmented, i.e. F(K, L) = [A(t)K(t)]*L(t)'_ª, where A(t) is the efficiency term growinge with a constant rate g.tEconomics, physical capital represents the uildings or machines used by a business to produce product. The marginal product of physical capital presents the rate of change of output product with spect to physical capital (informally, if you increase e size of your factory a little, how much more Foduct can you create?). articular model tells us that the output product Y is given, a function of capital K, by Y = AKªL'-a ere A is a constant, L is units of labor (assumed to be stant), and a is a constant between 0 and 1. Determine marginal product of physical capital predicted by this del. ned with CamScanner