A8. Consider the basic Solow model with production function Y KaN¹-, saving rate of 16% and depreciation rate of 5%. Which of the following is true? An increase in capital income share a will: = (a) decrease steady-state output per worker but leave the steady-state capital/output ratio unchanged (b) decrease steady-state output per worker but increase the steady-state capital/output ratio (c) increase steady-state output per worker but increase the steady-state capital/output ratio (d) increase steady-state output per worker and leave the steady-state capital/output ratio unchanged
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- 1. Consider an economy where the production function is Y = K0.5 (LE)0.5 The depreciation rate is = 0.04, the savings rate is s = 0.2, the popula- tion growth rate is n = 0.03 and technology growth rate is g = 0.03. (a) What is the 'per effective worker' production function? (b) Find the steady state levels of capital per effective worker (k*), in- come per effective worker (y*), investment per effective worker (¿*) and consumption per effective worker (c"). (c) Find the golden rule levels of capital per effective worker (kg), income per effective worker (y), investment per effective worker (it) and consumption per effective worker (c2). Also find sg, that is the level of the savings rate that would lead the economy to the golden rule steady state. (d) Suppose the government pursues policies that change the savings rate from s = 0.2 to sg. What is the immediate effect on income per effective worker and consumption per effective worker? What is the long run effect on income per…12. Consider an economy without technological progress and population growth. The production function is given as Y = K²/³N\/3. Both the saving rate and the capital depreciation rate are assumed to be 0.1. Which of the following saving rate delivers the highest consumption per worker in the steady-state: (a) 1/3 (Ь) 1/2 (c) 2/3 (d) none of above is correctIn an economy with population growth rate at gn, technology growth rate at gå and depreciation rate at 8. The change in capital per effective worker k is given by the equation: O sf(k)(8 + 9A + 9N)k Of(k) - (8 + 9N)k ○ f(k) - (8 + 9A + 9N)k f(k) + (8 + 9A +9N)k O sf (k) + (8 + 9A + 9N)k
- Refer to the figure at right. Which point on the graph shows the optimal combination of inputs? A. Point D, when the production process is capital intensive В. Рoint B C. Point A, when the production process is capital intensive D. All three points, A, B, and D are optimal.QUESTION 2 Assume we have a Cobb-Douglas production function of Y-KO505 Assume K-160, L-40, a-025, 6-0.10, and initial k-4.0. Derive the steady-state level of capital (k) (calculate unt Ak is at a level where the first 2 decimal points are 0. 1024When the savings rate is relatively high, this implies that the steady state level of capital per worker is relatively high and output per worker is relatively low. True Fasle
- 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 workerIn the Solow model with production function Y = K03 L0.7, which of the following saving rates minimizes consumption in steady state? O 0.3 0.7 (0.3+0.7)/2The convergence to a steady-state capital-labour ratio k* is ensured by the fact that if k is at a level Multiple Choice lower than k*, saving will exceed the investment required to maintain constant k, causing k to rise lower than k*, investment will exceed saving, leading to an increase in the capital stock lower than k*, saving will exceed the investment required to maintain a constant k, causing output per capita to decline higher than k*, the rate of depreciation will be higher than the savings rate, causing k to decrease higher than K*, output per capita will continue to increase until a new steady-state equilibrium is reached
- 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…Would you expect capital deepening to result in diminished1etmns? Why or why not? Would you expect improvements in technology to result in diminished returns? Why or why not?The production function for an economy is Y; = 1.5 Kª L(1«), where Y; is total output, K; is total capital, and L; is total labor. Total savings for the economy is given by S; = 0.2 Y. The rate of population growth, n, is 5% and the rate of depreciation, 8, is 10%. Write down the per capita production function. (a) (b) Write down the fundamental equation of Solow-Swan. (c) Imagine that a=0.7. In the long run, what is the growth rate of per capita output, y?? In the long run, what is the growth rate of total output, Y;? (d) In the long run, is there a constant level of capital per person, output per person and consumption per person? If so what are they? If not, why not? (e) Imagine that the depreciation rate increases from 10% to 12%. If the economy is initially in steady state, what are the effects on the levels and growth rates of k, y, and c? () Imagine that a=1. In the long run, what is the growth rate of per capita output, y.? In the long run, what is the growth rate of total…