Calculate the steady state level of investment in an economy with a savings rate of 15%, population growth of -1%, depreciation of 10%, and a= 2/3
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- Given a saving rate of 5%, a depreciation rate of 1%, and a production function in which y = k0.5where y is output per worker and k is capital per worker, calculate the steady state values fori. capital per worker, ii. output per worker, iii. consumption per workerPlease no written by hand Yt = 3Kt saving rate= 0.24 depreciation ratre=0.03 but savings rate, depreciation rate, and population remain the same.(d) What is the per-worker production function, yt = f(kt)? Define yt = YtLt.(e) Find the equation for the evolution of capital per worker in terms of ktand kt+1Population 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?
- 4.If population growth rate is 0.03, and the depreciation rate is 0.2, then in order to maintain the steady state capital-labor ratio equal to the amount found in Qs. 2, what would be the investment per worker?Q) consider the harrod-domar model in which depreciation and the population growth rate are 2% and 3% respectively. what fraction of income must be saved in order for income to double in 10 years if c=3 Solve it nowConsider an economy for which y = Akθ with the parameter values as listed: A=15, s=0.3, n=0.1, d=0.1 ,θ=0.6. Compute the steady state values for k, y, i, and c based on the parameters up to one decimal point
- Solve for the steady state of K with: An Investment (I) function with a rate of growth of 0.4 times the square root of K and a depreciation (D) function of 0.03 * K. Now graph what this looks like. Hint: you need to set the production function equal to the depreciation function and solve for k.Parameters Equations s =0,20 marginal propensity to save Y=WKr.L1-r Production Function u=0,02 Population growth rate K.=s.f(k)−aK Capital Accumulation b=0,04 Technological growth rate L./L= ? Population Growth a=0,05 Depreciation rate W./W=b Technological Progress S=s.f(k) Savings a. Find steady-state level of capital per effective labor: k* b. Draw a graph and show output function, actual investment and breakeven investment lines. c. Assume that in this economy, people start spending more and therefore marginal propensity to save decline permanently. What will happen to variables in the model (steady-state level capital per effective labor; output growth etc.). d. Instead of reduction in saving assume this time that we face lower fertility rate in the country. What will happen to variables in…Given a saving rate of 5%, a depreciation rate of 1%, and a production function in which y = k0.5where y is output per worker and k is capital per worker, calculate the steady state values forii. output per worker, iii. consumption per worker, iv. Calculate the golden rule steady state level of capital
- Given (5), derive the kt+1-equation and determine the steady state solution(s) for the capital intensitySolow economy where TFP = 1, capital starts off at K0=1, the savings rate is 50%, and the annual depreciation rate of capital is 10%. What is the steady-state capital stock?An economy has the per-worker production function yt=f(kt)=4kt)0.4, where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04. Saving is St=0.5Yt, where St is total national saving and Yt is total output. The slope of the per worker production function is given by f' (kt)=1.6kt-0.6 . What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.