Exercise 3: Population growth and technological progress Consider a version of Solow's Model: Y₁ = AK L¹-a sYt = Kt+1 - Kt +6Kt Lt = Lo(1 + n)t 1 a) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of labor, i.e. k = K/L; y = Y/L b) What are the values of k and y in a steady state? What are the growth rates of aggregate output and aggregate consumption? Consider this different version of Solow's Model: Y₁ = AK₂ª (E₂L₁) ¹- 1-a sYt Kt+1 - Kt +6Kt Lt = Lo(1 + n)t Et = Eo(1+x)t Rewrite the production function and the equation of capital accummulation using variables normalized by the units of effective labor, i.e. k = K/(EL); y = Y/(EL) . d) What are the values of k and y along a balanced growth path? What is the growth rate of aggregate output and aggregate consumption along this BGP?

Exercise 3: Population growth and technological progress Consider a version of Solow's Model: Y₁ = AK L¹-a sYt = Kt+1 - Kt +6Kt Lt = Lo(1 + n)t 1 a) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of labor, i.e. k = K/L; y = Y/L b) What are the values of k and y in a steady state? What are the growth rates of aggregate output and aggregate consumption? Consider this different version of Solow's Model: Y₁ = AK₂ª (E₂L₁) ¹- 1-a sYt Kt+1 - Kt +6Kt Lt = Lo(1 + n)t Et = Eo(1+x)t Rewrite the production function and the equation of capital accummulation using variables normalized by the units of effective labor, i.e. k = K/(EL); y = Y/(EL) . d) What are the values of k and y along a balanced growth path? What is the growth rate of aggregate output and aggregate consumption along this BGP?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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In 1928, Charles Cobb and Paul Douglas published a study in which they modeled the growth of the US economy during the period 1899 to 1922. The function used to model production was of the form: (1) P(L, K) = 6LªK!-a where P is total production (monetary value of goods produced in the year); L, the amount of work (total number of person-hours worked in a year); and K, the amount of capital invested (monetary value of machinery, equipment and buildings). In these terms, the hypotheses made by Cobb and Douglas can be stated as follows: (i) If either labor or capital cancel each other out, so does production. (ii) The marginal productivity of labor is proportional to the amount of output per unit of work. (iii) The marginal productivity of capital is proportional to the amount of production per unit of сapital. 1. The output per unit of work is (a) Tick the alternative that, for some constant a, describes the hypothesis (ii) = aP·L. = a. P () aL L P = a. (b) If we keep K constant, K = K0,…
Consider now the two-period model in general equilibrium, so that prices, investment and labour supply are endogenous, i.e. the production economy. Analyse and carefully explain graphically and in words the general equilibrium effects of a decrease in TFP(total factor production) for a benchmark economy with no frictions.
Consider an economy in which the aggregate production function is given by the equation: Y = 3.6 K0.5 N0.5 where (Y) is aggregate production, (A) measures productivity, (K) is the stock of physical capital and (N) is the amount of labor, measured in millions of workers. Both Y and K are measured in billions of reais. K is given and is 10,000 (i.e., 10,000 billion reais), so K0.5 = 100. The aggregate labor supply is given by the following equation: NS = [(1-t).w]2 where (t) is the income tax rate on labor and (w) is the real wage, measured in reais per hour. t = 0.20 (20%). The equilibrium levels of the real wage (w) and employment (N) are, respectively, [ANSWER] and [ANSWER]. The full employment production level (Y) is [ANSWER]. Finally, the after-tax real wage that workers receive per hour in this economy i
Consider the model of a firm that produces final goods using R&D and components as inputs, with cost dataas follows:Assembly: Total cost of production = PAQA = 400Earnings of High-Skilled Labor = WHHA = 100Earnings of Low-Skilled Labor = WLLA = 200Earnings of Capital = RKA = 100R&D: Total cost of production = PRQR = 400Earnings of High-Skilled Labor = WHHR = 175Earnings of Low-Skilled Labor = WLLR = 125Earnings of Capital = RKR = 100A) Which factor is assembly intensive? In which factor(s) is R&D intensive?B) Suppose that due to the opening of trade, the price of assembly falls by ∆PA/PA = −20%, the price of R&D remains unchanged, ∆PR/PR = 0%, and capital’s share earnings remains constant.C) What has happened to the relative wage of high-skilled/low-skilled labor? Does this match the predictions of the offshoring model?
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Suppose that production in an economy is represented by the production function Y = K1/4. If the investment rate is equal to 0.25 and the depreciation rate is equal to 0.10, calculate the steady-state levels of capital and output.
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D A: F(LKHN) C A:F(L,KH N) 7- Suppose the U.S. economy is producing at point A on Production Function 1 (F). An increase in the labor force participation rate causes more labor to be used in production. The direct effect of this shift is to move the economy O A. Point A O B. Point B OC. Point C O D. Point D O E. Point E