EXERCISE #1. In a Solowian economy with a constant saving rate s € (0,1) in which time is continuous, the production function and the growth rate of labour force are respectively given by Y (t) = (K (t))ª (L(t)) ¹-a L(₁) = (K6) L(t) where y(t) is produced output, K (t) is the stock of capital, L(t) is the employed labour force, whereas a € (0, 1) is the elasticity of output with respect to capital. Under the assumption that 8> 0 is the instantaneous depreciation rate of capital, find the possible balanced growth paths of the economy and discuss their main properties. -2

Exercise 4: Growth and capital over-accumulation = Suppose two countries, A and B, with the same production function Y KaL¹-a. The value of a is 0.30, the growth rate of population is 2% and the depreciation rate is 5%. a) Show that with price-taking firms the share of labor must be 1 a. b) Compute the stock of capital, output and consumption per unit of labor in the steady state if the savings rates were 25% for country A and 35% for country B. c) Compare both economies to the Golden Rule. d) Explain what would happen to both countries if suddenly their savings rate became the Golden Rule savings rate.

Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker?

Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker? Only D, other option answered

Suppose that the production function is Y = 10 ( K )^1/4 ( L )^3/4 and capital lasts for an average of 50 years . Assume that the rate of growth of population equals 0 and saving rate s = 0.128 . a. Calculate the steady - state level of capital per worker , output per worker , consumption per worker , saving and investment per worker , and depreciation per worker b. Suppose that initial level of capital per worker is 100 , explain the moving process to the steady state . c . Use relevant graph to demonstrate . Plsss provide detailed answers, thank you

An economy's production function as follows Y = 8 (K)¹/2 (EL)¹/2 If depreciation rate is 10%, population growth rate is 4%, tech progress grows 6%, and saving rate is 20%. a. b. C. d. e. f. Write production function in term of per effective worker variables. Find steady state capital per effective worker, output per effective worker, consumption per effective worker, investment per effective worker. Find growth rate of capital per worker and output per worker at steady state. Find growth rate of capital stock and total output at steady state. Propose policies to encourage long run growth of total output and living standard? Draw relevant graph for the above questions.

Population Growth and Technological Progress-Work It Out An economy has a Cobb-Douglas production function: Y = K (LE)¹- The economy has a capital share of 0.20, a saving rate of 49 percent, a depreciation rate of 4.00 percent, a rate of population growth of 1.50 percent, and a rate of labor-augmenting technological change of 4.0 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: Output per effective worker is constant in the steady state and does not change. increases in the steady state. declines in the steady state. % Output per worker growth rate: %

Please no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain.  (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k).  (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6.  (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…

Suppose that the production function for an economy is given by Y = K1/4L3/4.  The depreciation rate is 4%, the saving rate is 12%, Suppose that now there is labor augmenting technology, the rate of labor-augmenting technological is 2 percent. At what rate does total output, output per worker, and output per effective worker grow?

7. Suppose that the economy's production function is Y = √K√LA where K is capital, L is labor, and A is the state of technology. Suppose that the saving rate (s) is equal to 6%, the rate of depreciation of capital (8) is equal to 5%, the number of workers grow at 5% per year and the rate of technological progress is 4%. (a) Find the steady state values of: i. 11. iii. capital stock per effective worker output per effective worker growth rate of output per effective worker