The depreciation rate of capital in the US is 8 = 0.043 and the population growth rate is g₁ = 0.007. Moreover, Y/K is around 0.35 on average over the last 60 years in the US (see the graph. below). If the saving rate is s= 0.2 in the US, then find the long-run growth rate of average income in the US according to the Solow's model. (Note: To cross-check Compare your theoretical result with the actual growth rate of average income in the US which is 2%.)
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- Two countries, X & Y both have the production function f(k) = k0.5 but X starts with an initial k of 4 while Y starts with initial k of 16. Both of the countries have the same values for these exogeneous variables: s = 0.2, A = 1, depreciation rate = 0.05, n = 0, L0 = 10. As you can see, X starts out with just 25% as much capital as Y. How many periods does it take before X has at least 50% as much capital as Y? (A spreadsheet will help a lot with this)If the production function is given by Yt=Kt 2/3Lt 1/3 and the saving rate (s) equals the depreciation rate (õ). Find the numerical values of the steady-state capital and output?If techology grows at a rate of 1% per period- how fast does output per worker grow in the long run or steady state if the production function is Y = A*(K^0.5) *(L^0.5)
- In an economy with population growth rate at gn, technology growth rate at gå and depreciation rate at 8. The change in capital per effective worker k is given by the equation: O sf(k)(8 + 9A + 9N)k Of(k) - (8 + 9N)k ○ f(k) - (8 + 9A + 9N)k f(k) + (8 + 9A +9N)k O sf (k) + (8 + 9A + 9N)kIn 1998, Brazil had a per capita GDP of about $4,500, compared to per capita GDP of about $28,000 in the US. (A) If per capita growth were to average 2% per year indefinitely in the US and 5% per year in Brazil, how many years would it take Brazil to catch up with the US? (B) Using the assumptions of the Cobb-Douglas production function, how fast would capital stock have to grow for per capita GDP to rise 5% per year? How does that compare with capital stock growth of 3% per year in the US (assume technology advances 1% per year in both countries)? (C) In mature industrialized societies, the capital/output ratio is approximately 3.0. If the average depreciation rate is 0.04, what would be the current saving and investment ratio in the US? What would it be in Brazil if per capita GDP rose 5% per year?For the following questions, you will need the following formula: let Xo be the initial value, X, be the value after t periods and g be the growth rate by period, then Xt = X₁ (1 + g)t. You may also need the log properties: log(a³) = blog(a) and log(ab) = log(a) + log(b). The properties imply: log(X) = log(X₁) + tlog(1+g). a. Suppose the initial real per capita GDP for countries A and B is 15 thousand dollars. If the annual growth rates of countries A and B are respectively 3.6% and 5.6%, what is the the ratio XB/XA after 39 years? Round your answer to the nearest first decimal. Number b. Suppose the annual growth rates of countries A and B are respectively 3.6% and 5.6%. How many years it will take for each country to double their respective real per capita GDP? Round your answer to the nearest first decimal. Country A: Number Country B: Number c. Suppose the initial real per capita GDP of countries A, B and C are respectively 10, 10 and 50 thousand dollars. If their annual growth…
- Suppose the two nations start out in 2016 with identical levels of output per worker hour say, $100 per hour. In the first nation, labor productivity growth by 1% per year. In the second girls by 2% per year. Use a calculator or a spreadsheet to determine how much output per hour each nation will be producing 20 years later, assuming the labor productivity growth rates do not change. Then, determine how much each will be producing per hour 100 years later. What do your results tell you about the effects of small differences in productivity growth rates?If the production function is y = k³, s == .4, and & = .2, what is the steady-state level of: k yThe 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…
- 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…If real GDP per capita for Nelsonville grew from $8 trillion to $16 trillion between 2000 and 2020, then which of the following was the approximate annual growth rate? A) 8% B) 5.5% C) 20% D) 7.5% E) 3.5%Suppose there is a country called Solowland whose output (Y) is produced using capital (K), labour (L) according to the following aggregate production function: 13 Y = AK^(1/4) L^(3/4) where A is Total Factor Productivity (TFP). The rate of population growth (n) is 2.5% per year (0.025). The rate of depreciation of capital is 15% per year (0.15). Total factor productivity equals 20 (A=20) and we assume there is no technical progress (growth rate of A is zero).a)Show, analytically, that the production function displays diminishing marginal product of capital and labour and constant returns to scale. Explain your answer. b)If Solowlands savings rate (s) is 20% (0.20), find its steady state capital stock per capita, income per capita, consumption per capita and investment per capita. c)Suppose there is another county, Swanland where output is also produced by a diminishing returns production function using capital, labour, and technology. In this country, population growth is just 0.5%…