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- 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%…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)QUESTION 2 Assume we have a Cobb-Douglas production function of Y-KO505 Assume K-160, L-40, a-025, 6-0.10, and initial k-4.0. Derive the steady-state level of capital (k) (calculate unt Ak is at a level where the first 2 decimal points are 0. 1024
- 1. Country A has a capital-labor ratio that is initially twice as big as that of country B, but neither is yet in a steady state. Both countries have the same production function: f(k) = 6k^1/2 Country A has a 10% saving rate, 10% population growth rate, and 5% depreciation rate, while country B has a 20% saving rate, 10% population growth rate, and 20% depreciation rate. a. Calculate the steady-state capital-labor ratio for each country. Does the initial capital-labor ratio affect your results? b. Calculate output per worker and consumption per worker for each country. Which country has the highest output per worker? The highest consumption per worker?Assume that the saving rate s is equal to 24%, the population growth rate n is 2% and the depreciation rate d is 2%. Assume also that output per worker is given by: y = k0.5. Then, output per worker in steady state is equal to: 05 36 O 100 064. If the production function is given by Y=K2L'3 and the saving rate saving rate (s) equals the depreciation rate (8). Find the numerical values of the steady state capital and output?
- Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].Suppose that two countries share identical technology, depreciation rate, saving rate, and population growth. However, these two countries started off with different levels of capital stock. Which of the following is/are true? (i) The country with initially smaller capital stock grows more quickly to reach the steady state compared to the country with initially larger capital stock. (ii) The country with initially smaller capital stock will have a smaller capital stock in the steady state compared to the country with initially larger capital stock. (iii) Both countries will grow at the same rate in reaching the steady state. O a. Both (i) and (ii). O b. Only (iii). O c. Only (i). O d. Cannot tell. Need more information.Consider the Solow model (Y-AK1/4L3/4). Suppose that the productivity parameter is A=500, the depreciation rate is d=1/10, the savings (investment) rate is s=0.30, and the labor force is constant and equal to 2 million. ÊÊWhat is the steady state capital stock (K)? Please choose the closest answer." a. b. 48200 million C. 34341 million d. 15930 million 18340 million
- In the Saul model, if the per capita production function is y=k^0.7, the savings rate is 0.2, and the depreciation rate(8) is 0.1, then the steady-state level of capital per worker (k') equals O O O A. B. C. D. 4.85 8.05 10.08. 11.12In Wonderland production per worker (y) depends on capital per worker() such the y=10vk. Every year 15% of the capital stock depreciates, while workers in Wonderland save 10% of their income. Every year the population grows ratas te of 3% (c) The country of Neverland is identical to Wonderland in terms of output per worker, the savings rate, the depreciation rate and population growth. They differ in one respect: Wonderland has capital per worker of 10, whereas Neverland has capital per worker of 20. Which country experiences a higher growth rate of output per worker and how will their growth rates evolve over time?J 7 Given a production function Yt = AKt1 /3L2 /3 , if K0=8, A = 2, L = 4, s = 0.2, and d = 0.05: (a) Calculate the steady-state level of capital and output. (b) Calculate K1 , I 1 , Y1 and C1 .