Economic Growth Akila and her family are the only inhabitants of a small oasis in the...
Suppose that the aggregate production is given by
, where Y is real GDP, K is the total capital stock and L is the
(constant) labour force. Assume that aggregate investment is equal
to aggregate savings and that the depreciation rate is 0.05, hence
the total capital stock evolves according to K=sY − 0.05K, where s
is the savings rate.
1) Under the stated assumptions for this question, what is the
steady-state level of capital per worker when the saving...
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 and B only
Consider the Solow growth model with the following production function where y is output. K is capital, s is the productivity and is labor. Assume that 0 < α < 1 Further, suppose that labor grows at a constant rate n. That is. 1 + n. Also, assume that capital depreciates at rate d and that gross investment in capital is fraction s of output. a Letting k-N, obtain the law of motion for capital accumulation...
Consider an economy in a steady state with population growth rate η, a rate of capital depreciation δ , and a rate of technological progress g. a) At the steady state Δk = 0, where k equals capital per effective worker. What condition must be met for this to hold? Describe the condition in words as well as mathematical expressions. b) Describe in words what is maximized at the Golden Rule level of k. c) What mathematical condition must be...
1. Country A and country B both have the production function Y = F(K,L)= VKL. (5 Points) Does this production function have constant returns to scale? Explain. (5 Points) What is the per-worker production function, y=f(k)? (10 Points) Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using...
Section B (LONG QUESTIONS): Answer any THREE (3) of the following four ques tions. Each question is worth 25 marks for a total of 75 marks. B1. Solow (neoclassical) growth model: Consider the Solow (neoclassical) growth model seen in class where y denotes output per worker, k physical capital per worker, and A total factor productivity. Suppose that at any point in time the production function in per-worker terms is represented by where f(k) is increasing in k and there...
mm LCIUTOT 9.U6 PM 3. The land of Grim can be described by the following production fune! tion Y = K L Moreover, there is no population growth nor is there technological progress. (a) Find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate. (b) Research shows that the depreciation rate in the Land of Grim is 10% per year. Make a table showing steady-state...
everything but part a
Problem Set 8 1. (Population growth but no technology growth) Consider an economy that is described by the production function Y = K L. Moreover the de preciation rate of capital is 8 = 0.05 and the population growth rate is n=0.05 (there is no technology growth) (a) What is the per-worker production function, that is y = ¥? What is the marginal product of capital, that is 8X? (b) If the saving rate is 8...
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...
Consider the Solow growth model with depreciation rate and population growth rate n. The equation of motion for the capital stock and the per worker production function in this economy are given by: Ak= s(f(k) - (8 + n) k y= f(k) = k1/4 a). Suppose adoption of modern birth control methods in a developing country causes the population growth rate to decrease. What happens in the main Solow diagram: what curve(s) shin, what happens to the steady- state level...