Consider the Solow model with Neoclassical Production Function and constant productivity. (a). Derive the condition for the Golden Rule level of capital per worker (b). Provide economic intuition for the condition.
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Consider the Solow model with Neoclassical Production Function and constant productivity.
(a). Derive the condition for the Golden Rule level of capital per worker
(b). Provide economic intuition for the condition.
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- Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y =Y/L, as a function of capital per person, k =K/L.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 termConsider the Solow model with a production function Y(t) = A*K(t)αL(t)1-α, Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and the population growth rate n?
- Consider the Solow model with a production function Y(t) = A*K(t)^α*L(t)^(1-α), Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and (e) the population growth rate n?Consider the Solow model without technological progress and an economy with the following production function, Y=A[Kα+Gα]1/α where α<1, K is private capital and G is public capital that is used freely and provided by the government. The level of technology A is fixed and assumed to be equal to 1. A. Does this production function feature constant returns to scale? Explain. In order to finance public capital, the government taxes all investment on private capital at the rate 0<τ<1. So, the revenue raised by the government in each period is sKYt(1−τ) where sK is the private savings rate so that sKYt is pre-tax private savings. Public investment towards public capital is a constant fraction sG of total revenue. Then, the accumulation equations for private and public capital, respectively, are, Kt+1−Kt=sKYt(1−τ)−δKt Gt+1−Gt=sG(sKYtτ)−δGt where δ is the common depreciation rate B. Consider a balanced growth path where the growth rates of private capital is equal to the growth…Suppose in a Solow model, we have the following parameter values: n = 0, s = 0.2, a = 0.33. 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 deadly pandemic hits the economy at time t=1. As a result, the population at time t =1 is 10% lower than the population at time t=0. The pandemic is a one-time shock so that population growth rate remains the same, i.e., from t-2 onward, the population remains the same as the population at time t=1. The total capital stock, however, is unchanged so that K, Ko. What is the growth rate of per-capita capital in percentage (rounded to the 2 decimal places, e.g., answer 1.08 if your calculation shows the growth rate is 0.01079) at time t=3 from time t=2? %3!
- 1. Consider an economy that operates under competitive markets and meets the assumptions of the Solow model. The production function is given as follows: Y(t) = K (t) 0.3 (A(t)L(t)) ⁰.7 Assume a saving rate of 15%, labor force growth rate of 2% and depreciation rate of 5% and effectiveness of labor growth rate of 8%. a. Show that the production function exhibit constant return to scale? b. Derive the production function for output per capita. c. Derive the production function for output per effective unit of labor. d. Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor. e. Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor. f. Solve for steady state level of capital per unit of effective labor. g. Find steady state level of output per unit of effective labor. h. Find growth rate of output and output per worker on the balanced growth path. i. Which one would…Explain in detail the difference between endogenous variables and Exogenous variables. Use an example for each from the Solow modeIn this question, you will explore how changes in the saving rate and the rate of technological progress affect an economy’s growth. In addition, you will examine how the golden rule saving rate depends on the production function. Consider the Solow (neoclassical) growth model with aggregate production function Y = K^alpha(AN)^(1-alpha). Each period lasts a year.
- In the absence of technological progress, an increase in the saving rate will affect which of the following variables in the long run in the Solow model? output per worker capital per worker the level of investment all of the aboveProblem 1. Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, 8, and a population growth rate, n. The production function is given by Y = AK + BK³3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function. • (i) Does this production function exhibit constant returns to scale? Explain why. (ii) Does it exhibit diminishing returns to physical capital? Explain why. • (ii) Express output per person, y =- -, as a function of capital per person, k =. • (iv) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (v) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. • (vi) Suppose first that sA 8 + n. Draw the savings and depreciation curves, making sure to label the steady state level of capital(if it exists). Under these…Solow model is important because it implies that An economy that uses the neoclassical production function cannot grow at a positive rate forever. All the answers are implications of Solow model. An increase in savings results in a higher long-run economic growth. Heterogeneous economies will absolutely converge so that poor countries can catch-up rich countries in long-run.