1. Assume individual's utility flow function takes form: u(c) = log(c), and the production function takes form: Y(t) = AK(t) + BL(t). Describe the physical capital accumnlation equation and obtain the GDP growth rate in the following economy: (a) RCK economy (b) OLG economy
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- 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)∗?A. Investment in "infrastructure" represents spending on: O roads, bridges, canals, etc. O human capital (education) O government institutions O innovation to physical capital B. Which of the following was not one of Thomas Malthus' assumptions regarding population and economic growth? O Per-capita income would increase. O The economy was agriculturally based O The supply of land was fixed O The population would continue to increase6.5 Exercises Exercise 6.1 (Technological Progress and Long-Run Growth). Consider a Solow economy with population growth and technological progress. The evolution of the capital stock per efficiency unit of labor, denoted k1, is given by the law of motion (1+n)(1+ g)kt+1 = (1 – 8)kt +of(kt). Capital per efficiency unit of labor is defined as k, = Kt/(LEt), where Kt denotes the stock of physical capital, L, denotes population, and E is a tech- nological factor. Population grows at the rate n and the technological factor grows at the rate g. The subscript t denotes time, measured in years. The parameters d E (0, 1) and o > 0 denote, respectively, the depreciation rate of capital and the savings rate. The function f(k;) represents the produc- tion technology. Specifically, let Y, denote output and yt = Yt/(LEt) denote output per efficiency unit of labor. Then yt = f(kt). Assume that f(kt) = /k. 1. Find the steady-state stock of capital per efficiency unit of labor, de- noted k*, as a…
- The real GDP in 2010 was $1,800 billion and $1,944 billion in 2011.What is the growth rate in real GDP measured in percentage change? Question 9Answer a. 6% b. 7% c. 5% d. 8%Why is a Cobb-Douglas production function useful for analyzing economic growth?2. If the production function is given by YFA(KL.)0.5 where Y is the output, A is the technology, L refers to the labor stock, and K is the capital stock. Suppose that the saving rate (s) equals 0.6 and the depreciation rate (d) is 0.3 a. Write the output and capital accumulation equations in terms of the capital per worker? b. Find the steady state capital, output, investment, and consumption? c. What would happen to the steady state capital if the saving rate increased to 0.8 and the depreciation rate increases to 0.4?
- Over many years, small differences in growth rates can have large effects on the level of income. This question will help you understand this important point. Consider an initial value of real GDP equal to Yo. If real GDP grows at a rate of g percent annually, after N years real GDP will equal Yo(1+g). Now consider the following table. Let the initial level of GDP in all cases be 100. a. By using the formula provided above, compute the level of real GDP in column 1 for each year. For example, in Year 1, real GDP will equal 100x (1.01)¹=101. For each year, compute the GDP. Complete the rest of the columns. (Round your responses to two decimal places.) b. In year 20, how much larger (in percentage terms) is real GDP in the 2.0-percent growth case compared with the 1.5-percent growth case? Real GDP in the 2.0-percent growth case is% larger. (Round your response to the nearest whole number.) c. In year 50, how much larger is real GDP in the 2.0-percent growth case compared to the…5.2 Consider the following economy: FYI: for this production function.() = A Parameter Value Investment rate (0) 3% Depreciation rate (8) 5% Population growth (9₁) 2% Productivity level (A) 25 Productivity Growth (ga) 4% Currently, the economy has a labour force of 5,000 and a capital stock equal to 15,000. 5.2.1 Calculate this country's current rate of economic growth. 5.2.2 How fast will country grow annually once its steady state is reached? 12 Y = AK3L3Suppose you add a variable rate of population growth to a two-sector model of growth. Draw and properly label a graph on how the production function, investment requirement line, and saving line look like. Does the addition of the variable rate of population growth to this model help you explain anything that a simpler two-sector model with a fixed rate of growth, or a one sector model with variable population growth, cannot? Expound.
- 4. On January 12th 2010 a devastating earthquake with a magnitude of 7.3 struck Haiti. As a result, about 40% of the capital stock of Haiti was destroyed. Assume the economy was at its steady state before the earthquake hit. Use the Solow Diagram to illustrate how the economy was impacted. Draw a graph showing how output evolves over time and explain what happens to the level and growth rate of per capita GDP.Small differences in growth rates in the size of the economy, over several decades, will result in big differences in the size of the economy. Pretend we start in 1950 and the U.S. growth in real GDP has been around 3.15%. This has resulted in real GDP growing 8 times over this 70-year period (1950 to 2020). If real GDP growth had been 4.0%, real GDP would be times larger. a. 8 (about the same growth as with 3.15% growth) b. 10 С. 14 d. 16The measure of GDP for economic growth is not always perfect.Describe any two problems that are associated with GDP as ameasure of economic growth