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].
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Question 2
Assume 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].
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- 4. If the production function is given by Y=K2L'3 and the saving rate saving rate (s) equals the depreciation rate (8). Find the numerical values of the steady state capital and output?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…Solve for the steady state of K with: An Investment (I) function with a rate of growth of 0.4 times the square root of K and a depreciation (D) function of 0.03 * K. Now graph what this looks like. Hint: you need to set the production function equal to the depreciation function and solve for k.
- Consider an economy with a Cobb-Douglas production function Y= K1/3 2/3, the rate is 15% Calculate the golden rule steady state capital per worker (koR). Round the numbers up to two decimals 3.18 b.5.18 02.18 od 4.18 growth rate of population is 2%, the rate of capital depreciation is 5%, and the saving1. Consider an economy where the production function is Y = K0.5 (LE)0.5 The depreciation rate is = 0.04, the savings rate is s = 0.2, the popula- tion growth rate is n = 0.03 and technology growth rate is g = 0.03. (a) What is the 'per effective worker' production function? (b) Find the steady state levels of capital per effective worker (k*), in- come per effective worker (y*), investment per effective worker (¿*) and consumption per effective worker (c"). (c) Find the golden rule levels of capital per effective worker (kg), income per effective worker (y), investment per effective worker (it) and consumption per effective worker (c2). Also find sg, that is the level of the savings rate that would lead the economy to the golden rule steady state. (d) Suppose the government pursues policies that change the savings rate from s = 0.2 to sg. What is the immediate effect on income per effective worker and consumption per effective worker? What is the long run effect on income per…Country A and country B both have the production function Y = F(K, L) = K^0,5L^0,5 A. Does this production function have constant returns to scale? Explain. B. What is the per-worker production function, y = f(k)? C. 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 your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Theen find the steady-state levels of income per worker and consumption per worker. D. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator or a computer spreadsheet…
- An economy has the per-worker production function yt=f(kt)=4kt)0.4, where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04. Saving is St=0.5Yt, where St is total national saving and Yt is total output. The slope of the per worker production function is given by f' (kt)=1.6kt-0.6 . What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.Question 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…7 Assume a Cobb-Douglas production function, where © =0.5 and A = 1. If AN/N = 0.06, d = 0.04, and s = 0.2, what is the steady state value of capital per capita ??
- Production function is given by Y = 45K (AN)-a, where a=1/3. The rate of depreciation of capital is equal to 10 percent, and the rate of population growth is equal to 2 percent. The saving rate at time t was equal to 12 percent and the level of technology A, was equal to 5. The economy was in the steady state at time t and the rate of growth of aggregate capital stock was equal to 5 percent. Use the Solow growth model to answer the following questions. (Please fill in numbers, percentage values should be provided as numbers greater than 1. For example if inflation is 10 percent, you should write "10" in the blank space provided) 1. The rate of technological progress at time t was equal to 2. The level of per capita consumption at time t was equal to 3. Assume that at time t+1 the saving rate increased to the optimal (golden rule) saving rate. The difference between the new steady state level of percent consumption per unit of effective labor and the level of consumption per unit of…da qaoudon Suppose that the production function is given by Y=05/K √N, where Y is output, K is capital, and N is the number of workers. The steady-state level of capital per worker in terms of the saving rate, s, and the depreciation rate, 6, is KIN= (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g. a superscript can be created with the character.) The steady-state level of output per worker in terms of the saving rate, s, and the depreciation rate, 6, is VIN= (Property format your expression using the tools in the palette.) The equation for steady-state consumption per worker in terms of the saving rate, s, and the depreciation rate, 6, is CIN=(Property format your expression using the tools in the palette.)The aggregate production function is Y = 5KL. If there are 18 units of capital and 50 units of labor, the capital productivity is ___________.
