Economy R has a per-worker production function of 30√k (30 times the square root of k). Note that the MPK for this production function can be written a variety of ways, 15k among them. Capital depreciates at a steady rate, at a rate of 10% per year. Citizens consume 80% of their income, saving the rest. This economy has no population growth or increases in technology or human capital over time. Below is the table for Economy R: k 6400 Y a с b i C Sk d Ak e Enter the value for Cell d. Enter only numbers, a decimal point, and/or a negative sign in your answer. Round your answer to two decimal places as needed.

Economy R has a per-worker production function of 30√k (30 times the square root of k). Note that the MPK for this production function can be written a variety of ways, 15k among them. Capital depreciates at a steady rate, at a rate of 10% per year. Citizens consume 80% of their income, saving the rest. This economy has no population growth or increases in technology or human capital over time. Below is the table for Economy R: k 6400 Y a с b i C Sk d Ak e Enter the value for Cell d. Enter only numbers, a decimal point, and/or a negative sign in your answer. Round your answer to two decimal places as needed.

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Production And Growth

Section17.1: Economic Growth Around The World

Problem 1QQ

See similar textbooks

Similar questions

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.)
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?
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].
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 ??
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.
Given a saving rate of 5%, a depreciation rate of 1%, and a production function in which y = k0.5where y is output per worker and k is capital per worker, calculate the steady state values fori. capital per worker, ii. output per worker, iii. consumption per worker
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?
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 saving
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…
Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is yt = 2.2kt^0.5, where y is output per worker and k is capital per worker. The depreciation rate of capital is 10% per year a- Households initially consume 80% of income and save the remaining 20% of income. There is no government spending. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker? b-Suppose saving rate decreases to 10% permanently. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?
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)∗?
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: %