Show how an economy described by the Solow model with total factor productivity converges to its steady state values of output effective worker (Hint: substitute A-a = A) using an excel per simulation. Set parameters to the following values: a 0.4 15% 4.5% g 8% 25% ko 10
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- Q5 Suppose in a Solow model, we have the following parameter values: n = 0, s = 0.5, a = 0.3. There is no growth in the total factor productivity so that A, = A = 1. Moreover, we know that at time 0, the economy is at a steady state so that k = k, =1. Now imagine that a foreign power invaded this %3D country. 1% of the population was killed and another 14% of the population fleeded the country to avoid violence. Moreover, 15% of capital stocks were destroyed. All of this happens in period t=1. After that, the war ended and there was no more destruction of capital or loss of population (but the refugee permanently settled outside of the country and will never return0. What is the growth rate of per-capita output in period t =4?Q4) Production Functions and Growth (a) Time is continuous and the production function of the economy is given by (1) Y¢ = ( K¢ )ª( A¿N; )1-« Total factor productivity evolves according to (2) A = egt Ao such that A where the growth rate of technological progress g is exogenous. Population grows at an exogenous rate n according to (3) N{ = ent No with No = 1 such that = n Find an expression for the growth rate of (i) output per capita (Yt / Ni) and (ii) output per effective worker ( Yt/ (A:N:) ). When is the growth rate of (ii) equal to zero?An increase in research productivity: Suppose the economy is on a balanced growth path in the Romer model, and then, in the year 2030, research pro-ductivity z rises immediately and permanently to the new level z r. (a) Solve for the new growth rate of knowledge and yt.(b) Make a graph of yt over time using a ratio scale.
- Please no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain. (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k). (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6. (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…Show how an economy described by the Solow model with total factor productivity converges to its steady state values of output per effective worker (Hint: substitute A}¬- a = A) using an excel simulation. Set parameters to the following values: 0.4 15% a 4.5% 8% 25% 10 koAn economy's production function as follows Y = 8 (K)¹/2 (EL)¹/2 If depreciation rate is 10%, population growth rate is 4%, tech progress grows 6%, and saving rate is 20%. a. b. C. d. e. f. Write production function in term of per effective worker variables. Find steady state capital per effective worker, output per effective worker, consumption per effective worker, investment per effective worker. Find growth rate of capital per worker and output per worker at steady state. Find growth rate of capital stock and total output at steady state. Propose policies to encourage long run growth of total output and living standard? Draw relevant graph for the above questions.
- Derive the expression for the speed of convergence for k in the Solow model. Show this is also the speed of convergence for output y. Interpret.Suppose that the economy's production function is: Y = (K) 0.5 (AN) 0.5, that the savings rate s is equal to 16%, and that the rate of depreciation d is equal to 10%. Suppose further that the number of workers grows at 2% per year and that the rate of technological progress is 4% per year. a) Find the steady state values of the variables listed below: i) The capital stock per effective worker. ii) Output per effective worker. iii) The growth rate of output per effective worker. iv) The growth rate of output per worker. v) The growth rate of output. b) Suppose that the rate of technological progress doubles to 8% per year. Recompute the answers in part a). Explain the differences. c) Now suppose that the rate of technological progress is still equal to 4% per year, but the number of workers now grows at 6% per year. Recompute the answer to part a). Are people better off in part a) or c)? Explain.Assume a production function is Cobb - Douglas in capital and labour. Y = ZF(K, N) = zK\alpha N1-\alpha (a) Derive the per worker production function, y = zf (k) where y = Y/N, k = K/N (b) Use the Solow Model to derive the steady state level of capital per worker, for given s, d and n. (c) Show diagrammatically the impact on the steady state solution of i) a rise in z; ii) a rise in s, using both the Solow Model diagram and time path diagrams of Iny and Inc. (d) Showdiagrammatically (ideallysupplementedwithkeyequations)howtode rive the Golden Rule, and explain why this matters for your answer to part c) ii) (e) Show diagrammatically the impact of a fall in n, in the short and long term
- Consider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.Suppose the economy is on a balanced growth path in the Romer model, and then, in the year 2030, ̄l (lower case L bar) decreasesimmediately and permanently to the new level ̄l′ (lower case L bar one). (a) Solve for the new growth rate of knowledge and yt. (b) Make a graph of yt over time using a ratio scale.Suppose that the per-worker production (labour productivity) function in South Korea is Y over L equals A open parentheses K over L close parentheses to the power of 0.4 end exponent open parentheses H over L close parentheses to the power of 0.6 end exponent. South Korea's labor productivity rises 6% per year, capital-labour ratio rises 5% per year, and human capital per worker rises 2% per year. This information suggests that total factor productivity grows at _________ per year.