Question 11 Assume a country produces output according to a production function: Y = the growth rate of A is 1%, what is the growth rate of A² 1% O 2% O3% O 4% Question 2 What is the steady state level of capital per effective worker in the last question (with A growing at 1%) if population growth is 2%, depreciation is 6%, and s-0.5 16 O 25 36 AK/L/21 000
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- 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].2. Solow-Swan Model (a) You will demonstrate the importance of diminishing returns to capital in the Solow-Swanmodel. Draw a Solow-Swan diagram in which there are constant returns to capital. Thiswould happen if the production function were Yt= AKt, where A = 1. Furthermore,assume that the sum of population growth and the depreciation rate is greater than thesaving rate. Does the economy converge to a steady state in this case? To answer thisquestion, you should draw a Solow-Swan diagram in terms of output per person, as we didin class. Use this diagram to explain why the economy converges to a steady state or doesnot. (b) Assume, instead, that the sum of population growth and the depreciation rate is equal tothe saving rate. In this case, are there any steady states? If yes, describe the steady-statelevels of capital per person. If no, explain why not. (Note: Diagram is not needed for thispart.)Country A and country B both have the production function Y = F(K, L) = K1/3L2/3 Does this production function have constant returns to scale? Explain. Find Solow’s production function, y = f (k)? Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. Find the steady-state level of capital per worker for each country, then find the steady-state levels of income per worker and consumption per worker. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator (or, better yet, a computer spreadsheet) to show how the capital stock per worker will evolve over time in both countries. For…
- Suppose that 10 workers were required in 2010 to produce 40,000 bushels of wheat on a 1,000-acre farm. a. What is the average output per acre? Per worker? b. If in 2020 only 8 workers produce 44,000 bushels of wheat on that same 1,000-acre farm, what will be the average output per acre? Per worker? c. By what percentage does productivity (output per worker) increase over those 10 years? Over those 10 years, what is the average annual percentage increase in productivity?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.7 Assume a Cobb-Douglas production function, where © =0.5 and A = 1. If AN/N = 0.06, d = 0.04, and s = 0.2, what is the steady state value of capital per capita ??
- A country produces output using a production function: Y = F(K, L) = AxK0.5 L0.5 where L is labour, K is capital and A is total factor productivity. Prove that this function exhibits constant returns to scale. Assume that A = 3 and its growth rate is zero. The country has a population growth of 1.5% per year (0.015) and capital depreciates at a rate of 10% (0.10) per year. If the country saves 30% (0.3) of national income, find the steady state levels of capital per worker, as well as consumption and income per worker in the Solow growth model corresponding to this country. What would be the rate of growth of GDP per capita in steady state? Calculate the “Golden Rule” level of capital stock in steady state. Is this economy dynamically efficient?Suppose that the economy is summarized by the following: Technology (Production Function): Yt = 10 (Kt)0.3 (Lte)0.7 Consumption function: Ct = 0.8Yt Depreciation rate: 8% (i.e. δ= 0.08) Population growth: 2% (i.e. n = 0.02) Technological growth: 4% (i.e. g = 0.04) 1. Assuming that in 2013 the US economy is in the steady state and L2013 = Le2013 = 8, what is the value of ke2014, ye2014, ce2014 , k2014, y2014, and c2014 ?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…
- Suppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.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.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?