Consider the Solow-Swan model of growth. Imagine that the production function isY = AKªL²-a1. Use the production function to compute output per capita, y = Y /L, as a function of capitalper person, k = K/L.2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps.Furthermore, imagine that the savings, depreciation, and population growth rates take thevalues s = 0.3, 8= 0.1 and n =0.01. You do not know the value of A.3. Use the fundamental equation of the Solow-Swan model to compute the growth rate ofcapital per person as a function of k.4. In the steady-state, the growth rate of capital is zero. Using the parameters assumed above,find the steady-state level of the capital stock, k_.5. Calculate GDP per capita at the steady state.6. Imagine that this country is in its steady state so its capital stock is k_. Imagine that thecountry receives a gift of one unit of capital from the world bank (so, suddenly, the capitalstock is k_+1). Can you say what is going to happen to the growth rate immediately after thedonation? Why? What will the capital stock be in the long run? Explain.

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Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKa L¹-a 1. Use the production function to compute output per capita, y = Y/L, as a function of capital per person, k = K/L. 2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps. Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 8= 0.1 and n =0.01. You do not know the value of A. 3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k.

Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKa L¹-a 1. Use the production function to compute output per capita, y = Y/L, as a function of capital per person, k = K/L. 2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps. Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 8= 0.1 and n =0.01. You do not know the value of A. 3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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an economy is described by the Solow-Swan model with the following variables, E(t)=1 The saving rate is 0.41 per year. Labor's share of income is 0.44. The growth rate of labor efficiency is 0.03 per year. The growth rate of the labor force is 0.02 per year Depreciation is 0.09 per year. calculate the steady-state value of the capital-to-labor ratio, K/L Enter your answer to two places after the decimal.
Assume positive population growth ( n > 0) and technological progress ( g > 0 ). Derive analytically the steady-state growth rates of output and capital, and the steady-state levels of output and capital per efficiency unit of labour. Illustrate your answer graphically and briefly discuss the economic intuition.
9. Consider a numerical example using the Solow growth model. Suppose that F(K, N) KO.5N0.5, with d = z = 1, and take a period to be a year. (a) Determine capital per worker, income per capita, and consumption per capita in the steady state. 0.1, s = 0.2, n = 0.01, and
= 2. Consider a Solow growth model in which the production function is Yt AK²N₁¹/2, where A = 1. Moreover, assume that the depreciation rate is d = 0.02, the rate of population growth is n = 0.02, and the saving rate is s = = 0.2. a. Compute the value of the capital stock per worker in steady state. b. Draw a graph that represents the steady-state equilibrium of the model. c. Suppose that the capital-labor ration in year t is 90. What will the level of the capital- labor ratio be in year t+1? Will it increase or decrease in future periods? Explain. d. Compute the rate of change of the capital labor ratio between time t and t + 1. How does it compare to the rate of growth of the capital-labor ratio in steady state?
Question 27 Consider countries A and B, with A having a higher population growth rate than B. According to the Solow-Swan model, output per person in A and output per person in B are the same in steady state. Answer True or False. Remember to include your explanation.
Consider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.