6. Using the Solow Model, determine graphically, the steady state for capital and output when there is an: (a) a permanent decrease in the savings rate (b) a permanent decrease in A (c) a permanent increase in the depreciation rate.
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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…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…1. Suppose an economy experiences both positive population growth (8 ) and technological progress (84 ). The capital depreciation rate is d . The saving rate is exogenously given as s. (a) Draw a diagram with variables in per effective worker terms to show how a steady state level of capital per effective worker (K/AN) is determined. Also explain your answers in words. (b) We further assume that the aggregate production function is given by Y= K“(AN)™, where o12. 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 correct3. Plot production function, savings function, and depreciation function in a slow model and graphically show the effects (transition) of steady state capital in following situations: (a) Contractionary monetary policy = real interest rate increases = increased level of savings. (b) Increase in the population growth rates. (c) Increase in the technology parameter.1. Suppose that the aggregate production function in the Solow-Swan model has the Cobb- Douglas form, y = ka. Also, assume a = 0.35, saving rate s = 15%, population growth n = 5%, technology growth g = 10%, and no depreciation ổ = 0%. (a) Show that f'(k) > 0, f"(k) < 0, and the Inada conditions limp-of"(k) = o and limz f'(k) = 0 are satisfied. (b) What are the numerical steady-state values of y* and e*? Show your workings. (c) Why is the steady state unique? (d) Assume labour and capital are paid their marginal products and the economy is on a balanced growth path at time t = 0: i) What is the real wage w(0) if A(0) = 1? ii) What is the growth rate of wages w/w along the balanced growth path? iii) What is the return to "working" capital r? iv) What are the shares of income going to capital and to labour? v) If the depreciation rate were positive (e.g., 6 = 10%), explain what would hap- pen to the return to "working" capital r and the shares of income going to (both "working" and…4. If the production function is given by Y=K2L'3 and the saving rate saving rate (s) equals the depreciation rate (8). Find the numerical values of the steady state capital and output?Let the production function be Q = K0.®L0.2 Solow's assumptions are K = sQ – 6K The symbols s represents a (constant) marginal propensity to save, n, a (constant) rate of growth of labor and 8 constant depreciation rate. (a) Derive the fundamental equation of Solow growth model for given production function. (b) Sketch graph of with k on the vertical axis and k on the horizontal take n = 0.01, s = 0.3, 8 = 0.1.10. In the steady state in a Solow model including effective/productive workers, the growth of output per effective worker is: G 0 N+G Depreciation rate Savings ratewhich one(s) is true (a) If an economy can raise its annual real GDP growth rate from 3.8 percent to 4.5 percent, its real GDP doubling time is reduced by 15 years. (b) Suppose that the government passes a law requiring households to increase savings 10% above previous levels. According to Solow's growth theory, in the long run output per capita will grow less rapidly. (c) If an economy has a real GDP doubling-time of 48 years, this will be increased to 56 years if annual GDP growth is reduced by 3.2 percentage points. (d) If K = 3000, n = 0.02, and depreciation, δ= 0.04 and g =0.03, then investment of 320 will hold (K/AL) constant.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.Problem 2 In class, we argued that if people could accumulate human as well as physical capital, the production function would look like the "AK" production function. 66 (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and population growth are 8 and n respectively, what would the growth rate of the economy be? (b) What would be the macroeconomic consequences of increasing the savings. rate in this economy? Explain using the model and intuitively. (c) What would be the consequences of an increase in fertility in this economy? Are these consequences good or bad? Is this answer unambiguous? (d) How are human and physical capital different from one another in the way they evolve from period to period? (e) Does human capital have an upper limit? If it does, what is the resulting production function when this is reached and the growth rate of the economy? If it doesn't have a limit, what is the resulting growth rate of output…SEE MORE QUESTIONS