Question on Harrod-Domar Growth Model. Show (complete mathematical solution) how the net savings rate and the capital-output ratio affect the GDP growth rate.
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Question on Harrod-Domar Growth Model.
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- Question 3Consider an economy described by the production function:Y = F(K, L) = K0.3 L0.7 a. What is the per-worker production function?b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.c. Assume that the depreciation rate is 10 percent per year. Make a table showing steadystate capital per worker, output per worker, and consumption per worker for saving ratesof 0 percent, 10 percent, 20 percent, 30 percent, and so on. (You will need a calculator with an exponent key for this.) What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?Consider an economy with the following aggregate production function: Y = 3K1/3(AL)2/3 Capital grows through investment but also decays due to wear and tear at a constant rate δ per period. Assume that A is growing at the exogenous rate g, that L is growing at the exogenous rate n, and that households save a constant proportion s of their income. (a ) Find the steady state level of the capital per effective worker (k*), output per effective worker (y*) and consumption per effective worker (c*) - in terms of the parameters of the model. (B) What is the level of k (k**) that maximizes consumption? (C) Given a depreciation rate of 7%, population growth rate of 2%, technological progress of 1% and a saving rate of 30%, calculate the steady state levels of k, y and c. (D) To move to the level of capital that maximizes consumption, how should the saving rate be changed? Explain. (E) Calculate the saving rate needed to reach the golden rule level of capital per effective worker.Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is yt = 2.2kt^0.5, where y is output per worker and k is capital per worker. The depreciation rate of capital is 10% per year a- Households initially consume 80% of income and save the remaining 20% of income. There is no government spending. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker? b-Suppose saving rate decreases to 10% permanently. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?
- 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 ?Consider an economy described by the production function: Y = F(K, L) = K^0,3L^0,7 A. What is the per-worker production function? B. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.9 Based on the production function Y = AKaG1-a (with G representing public expenditure, and the remaining variables and parameters representing usual values), show, using the necessary assumptions the value of the tax amount that maximizes the economic growth rate. Then, represent graphically the situation.
- The saving rate (gross domestic saving as a % of GDP) in Australia, a small open economy, was 15% in 2011 while the investment rate (domestic investment as a % of GDP) was 25%. As a result, there was net outflow of capital from Australia in 2011. Is this true, false or uncertain? Please provide your explaination.Consider an economy A described by the production function: Y = F(K, L) = K0.3L0.7. In economy B, everything is similar to economy A, except, saving rate is 40%. Explain how steady state output per worker, consumption per worker and golden rule level of capital stock will differ from those of country AIf labor input increases by 2 per cent and capital stock increases by 3 per cent per annum, what will be the GDP growth rate? Assume the multi- factor activity or efficiency factor is 2, labor share in national income is 70%, and capital share is 30%: a. 2.023b. 4.20c. 5.023d. 5.30
- Between Foreign Direct Investment (net inflows %) and Real GDP Growth ( %): A. Identify the independent and dependent variable and explain Between Foreign Direct investment (net inflows %) and Real GDP per capita (constant %) a. Identify the independent and dependent variable and explainConsider an economy in which the labour force grows by 2.7 percent per annum, physical capital grows by 4 percent per annum and human capital grows by 1.8 percent per annum. Suppose 45 percent of national income goes to labour and 40 percent to capital. Use a constant returns to scale production function to answer the following growth accounting questions: (a) If the Solow residual were zero what rate of growth would the economy achieve? (b) The country's actual rate of growth has been 4.5 percent per annum, which is faster than the growth rate generated by the accumulation of capital and labour stocks. Calculate the value of the residual.Consider an Economy in steady state, with a Cobb Douglas Production function. They have a savings rate of 45% and a capital share of 2/7. Technological progress is 1%, population growth is 3%, and Depreciation is 5%. 1. Derive the Production function per effective worker and solve for steady state capital, output, and consumption per effective worker. 2. What is MPK in the steady state? Is this country saving too much or too little? How do you know? 3. What should you lower or raise the saving rate to, in order to reach the golden rule steady state