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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)Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Find the steady-state capital-labor ratio, real GDP per worker, investment per worker and consumption per worker for this economy.At k*(GOLD), when population growth and depreciation are non-zero, what is true? a. MPK = depreciation + population growth b. MPK = population growth + capital growth c. MPK = depreciation + capital growth d. MPK = depreciation + population growth + capital growth
- Which of the following statements are correct? state which ones are definitely incorrect and why. a. Capital grows when investment is higher than depreciation b. The growth rate of capital increases when investment is higher than depreciation c. For a given rate of depreciation of capital, a rise in the ratio of investment to capital will raise the growth rate of capital d. There are no rich countries wth low investment ratios, and no poor countries with high investment ratios e. A country can only invest more than it saves if it borrows from abroad. f. The scatter diagram of capital output ratios vs investment rates does not show a perfect correlation. Therefore there is something wrong with the model of the way capital grows g. A country that increases its saving rate will be able to have more rapid growth of capital for as long as it maintains this higher savig rate h. A country that increases its saving rate will be able to have more rapid…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, z is given as 2, s is 0.14, depreciation rate is 0.06, and growth rate of labour is 0.08. Calculate the steady-state capital per worker for this economy
- Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.Consider the Production Function: Y=√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?Consider the Production Function: Y=0.5√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?
- Assume that the production function for a country is given by Y=√K and annual investment is given by the function I=γ×YI where γ=0.280, and that the yearly depreciation rate is 4.67%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking.Population Growth Population growth in the US has, for a very long time been about 1% per year.Take the production function to be y = k0.5, where y and k are output andcapital per capita. The depreciation rate is about 10% per year and the savingsrate is about 20%. 1. What is the steady state capital per capita rate?2. From one period to the next, at what rate does total capital (not percapita) grow.3. If the population growth rate grew to 1.5%, how much would steady statecapital per capita change? Then how much is total capital changing atthis steady state?Question 1:- Suppose a country has a gross savings rate of 25%, a depreciation rate of 2%, and an incremental capital output ratio (lCOR) of 2.2. Using the Harrod-Domar growth model, a) find the implied rate of growth of total GDP in the country. b) How much would the rate of savings have to increase to raise the growth rate of total GDP to 10%? c) Is your answer consistent with the Harrod-Domar model? Explain.