econonimcs.... the following are given questions

Consider the following standard Homer Model and a variation that includes human capital. Goods Production Flmction Ideas Production Function Human Capital Production Function Resource Constraint Allocation of Labour Human Capital Y. = as... 15AM] : EAthLGJ H: 2 L511; Lyt+La3g +LM = L La; : TE Assume parameters take the following values in each specication. Standard Human lCapital E 1000 1000 Ly; 750 700 LG; 250 200 La; r 100 :2 0.0005 0.0005 A5 10 1 l] 1. Explain what using labour to produce human capital implies for the economy? 2. Solve for the balanced growth path of output per capita in both models, showing all working. 3. Does the inclusion of human capital increase the rate of growth compared to the standard model? What is the impact on output in the short and long run? Human lCapital Model: Fieinterpretthe human capital growth model as follows: Suppose there are two groups of people in a country, the lowskilled and the highskilled, where the lowskilled have less human capital per person initially than the highskilled. Each type of worker produces output independently from the other, using efficiency units of labor and total factor productivity, 2, which is assumed to be common across groups. Each individual in this economy accumulates human capital on their own,1 and each has one unit of time to split between human capital accumulation and work. Assume that the high skilled have initially higher efficiency of learning: bh :> bl , and that uh 6: ul . {a} In all developed countries, there has been an increase in the socailed skill premium, the gap between the wages of highskilled workers and lowskilled workers, over the last 3G years. Determine how this model can explain this observation. Human lCapital Model: Fieinterpretthe human capital growth model as follows: Suppose there are two groups of people in a country, the lowskilled and the highskilled, where the lowskilled have less human capital per person initially than the highskilled. Each type of worker produces output independently from the other, using efficiency units of labor and total factor productivity, 2, which is assumed to be common across groups. Each individual in this economy accumulates human capital on their own,1 and each has one unit of time to split between human capital accumulation and work. Assume that the high skilled have initially higher efficiency of learning: bh :> bl , and that uh 6: ul . {a} In all developed countries, there has been an increase in the socailed skill premium, the gap between the wages of highskilled workers and lowskilled workers, over the last 3G years. Determine how this model can explain this observation. Consider an economy where production uses labor (N), physical capital K and human capital H. Total output is given by Y = =K"/ N1-@-8. In this economy a fraction s of total output is saved each period and invested in physical capital, while a fraction s, is saved to be invested in human capital. The output that remains after investment is consumed. Population grows at a constant rate a so that N = (1+ n) N. The current stock of physical and human capital depreciates at a constant rate o every period. The capital accumulation equations are: K =(1 -5 ) K + SKY H = (1 -6) H + SAY 1. Find the output per-worker. 2. Find the steady state value of kas, has; yes. You should get to the following expressions: 1-a-A 1-0- 1-a -8 k.= = nto nto (n + 6) 3. Compare the effect of an increase in the capital saving rate on output in this model and in the model without human capital. For which model is the effect greater? Explain why introducing human capital changes the effect of savings in the way it does. We measure the effect with the elasticity of steady state output to 8%. Remember that in the model without human capital we have: yas = 2 ( 28%9.1 Explain the Solow Growth model. Include the following: a. Write the per-capita production function and the per-capita capital accumulation equations. Define the variables that you use. b. Graph the production, savings, and capital maintenance functions. Show what happens when savings increases. Show what happens when population increases. Explain your graph. c. Graph the output, capital, consumption, rate of change in capital, and the growth rate. Explain your graph.Question 2: Capital formation in growth models 10 points each sub-part equally weighted 1.Derive the growth equation for Harrod Domar model. 2. Derive the capital formation equation for Solow model with and without labor augmenting technological progress. 3.Derive the human capital formation equation for the following production function Y = HOK'(TL)1-a-B where Y is output, H is human capital in the production function, K is physical capital used in the production function and L is labor. The saving rate in human capital is given by s.Exercises Exercise 10.1 (Moderate) Answer: True, False, or Uncertain, and explain. 1. "Did you know that America's 22 million small businesses are the principal source of new jobs?" (Source: Web page of the Small Business Administration.) 2. "In the next century, 20% of the population will suffice to keep the world economy Exercises 93 going.... A fifth of all job-seekers will be enough to produce all the commodities and to furnish the high-value services that world society will be able to afford" the remaining 80% will be kept pacified by a diet of "Tittytainment". (Source: Martin, Hans-Peter and Harald Schumann. The Global Trap. New York: St Martin's Press. 1996.) Exercise 10.2 (Easy) The plant-level rate of employment growth is defined as: Zest where: A.Nest = Nest - Nes,i-1. That is, A Nest is the change in employment at plant e in sector s from t -1 to t. Show that fest = 2 for all plants that are born between t - 1 and t, and show that gest = -2 for all plants that die between t - 1 and t. Exercise 10.3 (Easy) Show the following: Ca = > (- ) gest, and: net = = > (2 ) Best. Here cat is the average rate of job creation of all plants in sector s. What does the term Zest / Zat mean? Exercise 10.4 (Moderate) For the purposes of this exercise, assume that you have data on annual national job creation G and job destruction D: for N years, so t = 1. .. N. Show that if annual national job reallocation R, and net job creation NET, have a negative covariance, then the variance of job destruction must be greater than the variance of job creation. Recall the definition of variance of a random variable X for which you have / observations, (2)M: var(X) = ~ _(x; -2), where z is the mean of X. Similarly, recall the definition of the covariance of two variables X and Y . If there are N observations each, {z;, y:}My, then: cov(X, Y) = = )( -2)(: -D). These definitions and the definitions of NET, and R, provide all the information necessary to answer this exercise.Exercises Exercise 11.1 (Easy) Suppose the aggregate production technology is Y = 34 . and that [ = 150. Both the labor force and productivity are constant. Assume that the depreciation rate is 10% and that Exercises 109 20% of output is saved and invested each year. What is the steady-state level of output? Exercise 11.2 (Moderate) Assume that the Solow model accurately describes the growth experience of Kuwait. As a result of the Gulf war, much of the capital in Kuwait (oil extracting equipment, vehi- cles, structures etc.) was destroyed. Answer the following questions, and provide brief explanations. . What will be the effect of this event on per capita income in Kuwait in the next five years? . What will be the effect of this event on per capita income in Kuwait in the long run? What will be the effect of this event on the annual growth rate of per capita income in Kuwait in the next five years? What will be the effect of this event on the growth rate of per capita income in Kuwait in the long run? . Will recovery in Kuwait occur faster if investment by foreigners is permitted, or if it is prohibited? . Would Kuwaiti workers gain or lose by a prohibition of foreign investment? Would Kuwaiti capitalists gain or lose? Exercise 11.3 (Moderate) In this and the following two exercises, you will apply growth accounting to measure the determinants of growth in output per worker in a country of your choice. To start, you need to pick a country and retrieve data on real GDP per worker and capital per worker. You can get the time series you need from the Penn World Tables. See Exercise 9.1 for information about how to access this data set. You should use data for all years that are available. In Section 11.3, we introduced growth accounting for output growth, while in this exercise we want to explain growth in output per worker. We therefore have to redo the analysis of Section 11.3 in terms of output per worker. The first step is to divide the production function in equation (11.11) by the number of workers Ly, which yields: (11.20) Equation (11.20) relates output per worker 1,/L, to capital per worker K-1/L. If we use lower case letters to denote per-worker values (1: = Y:/Lt, ke-1 = Ki-1/L:), we can write equation (11.20) as: (11.21) 1 = APRET