None Wonka Land has an aggregate production function given by the equation: Y=K^(1/5)(L)^(4/5). Examining the economy, we find the current savings rate is 45%, capitaldepreciates at a rate of 5%, and the current population growth rate is 10%.a) (2 points) What is the per-worker production function?b) (6 points) Find the steady-state levels of capital per-worker, output per-worker, andconsumption per-worker. (round answers to two decimals, if necessary)c) (6 points) Calculate the Golden Rule level of capital per-worker. What optimal savingsrate is necessary to achieve the Golden Rule equilibrium? Lastly, find the maximizedconsumption per-work. (round answers to two decimals, if necessary)d) (4 points) To achieve the optimum Golden Rule consumption level, policy makers(recalling training in their undergraduate economics course) argue that they can insteadmodify the population growth rate. Explain how this can be achieved using a diagram tojustify your thoughts. Afterwards, find the necessary population growth rate to achievethe Golden Rule consumption level.Upload Choose a File

Detailed explanation: Certainly! The Solow growth model is used to study the long-run economic…

Answered: Wonka Land has an aggregate production…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Assume that the per-worker production function is yt = 2kt^(0.3). The saving, depreciation and population growth rates are estimated at 0.3, 0.05 and 0.02, respectively. (a) Calculate the capital-labour ratio steady state for this economy. (b) Calculate consumption per worker at the steady state.
Suppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.
1. 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…
Consider an economy that exhibits both population growth (L grows at rate n) and technological progress (A grows at rate a) described by the production function, Y = F(K,AL) = Kª(AL)¹-α| Here K is capital and Y is output. (a) Show that this production function exhibits constant returns to scale. What is the per-effective-worker production function? (c) Find expressions for the steady-state capital-output ratio, capital stock per effective worker, and output per effective worker, as a function of the saving rate (s), the depreciation rate (8), the population growth rate (n), the rate of technological progress (a), and the coefficient a. (You may assume the condition that capital per effective worker evolves according to Ak = sf (k) − (a +n+8)k.) (d) Show that at the Golden Rule steady state the saving rate for this economy is equal to the parameter a.
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].
Suppose that there is a constant technological progress (A) and population growth (n) in a sample economy. Production function is given as Y, = F(Kt, N¿) = A/KN; a) What is the output per capita at the steady state?
Suppose that there is a constant technological growth (g) and population growth (n) in a sample economy. Production function is given as Y; = F(Kt, A¿N¿) = /KEJA;N: b) Write the output per effective worker as a function of capital per effective worker.
Why Capital does not Flow from Rich to Emerging Countries? We assume that the production function in country i is 1 1 2 Yi = A ² k², (1) where y, and ki are output and capital per capita, respectively, in country i, and A is a measure of technology in country i. (a) Calculate the marginal product of capital (MPK) denoted by Ri in country i. (b) Express the MPK in terms of output per capita, yi, i.e., eliminate ki from Ri by using the production function (1). (c) We consider two countries, indexed by i 1 and i 2, whose production function is described by (1). Both are assumed to have the same level of productivity, i.e., A₁ A2. We assume y2 50y₁. Calculate the ratio R₁/R₂. (d) We keep assuming that y2 50y1, but now we assume that A2 educational attainment is higher in country 2. Calculate the ratio R₁/R₂ under 10A₁ because these assumptions. FX = - (e) We keep assuming y2 50y₁ but now we consider that technology in country 1 is a function of technology of the more advanced country 2,…
Assume the per-worker production function is y = k1/2, depreciation is 4 percent of %3D capital, the labor force grows at 2 percent, and the savings rate is 30 percent. Then, the steady-state equilibrium is achieved when capital per worker is equal to: 2.5. 5. 6.25. 25.
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…
The production function for an economy is Y; = 1.5 Kª L(1«), where Y; is total output, K; is total capital, and L; is total labor. Total savings for the economy is given by S; = 0.2 Y. The rate of population growth, n, is 5% and the rate of depreciation, 8, is 10%. Write down the per capita production function. (a) (b) Write down the fundamental equation of Solow-Swan. (c) Imagine that a=0.7. In the long run, what is the growth rate of per capita output, y?? In the long run, what is the growth rate of total output, Y;? (d) In the long run, is there a constant level of capital per person, output per person and consumption per person? If so what are they? If not, why not? (e) Imagine that the depreciation rate increases from 10% to 12%. If the economy is initially in steady state, what are the effects on the levels and growth rates of k, y, and c? () Imagine that a=1. In the long run, what is the growth rate of per capita output, y.? In the long run, what is the growth rate of total…
Consider an economy described by the production function Y=F(K, L)=?^0.4?^0.6 A) What is the per-worker production function?B) Assuming no population growth or technological progress, 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.

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