(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K >0 The population grows at the exogenously given rate n, so that N n)N (a) Derive the per worker production function, where y-Y/N is output per worker and k = K/N is capital per worker (b) Derive the aggregate accumulation equation for capital per worker expressed solely as a function of k. k', A, and parameters (s. θ, d, n). Recall the law of motion for...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K > 0 n > The population grows at the exogenously given rate n, so that N,-(1 + n) (a) Derive the per worker production function, where y - Y/N is output per worker and k- K/N is capital per worker (b) Derive the aggregate accumulation equation for capital per worker expressed solely as a function of k, k', A. and parameters (s, θ, d, n). Recall...
An economy is described by the solow model, it has he following production function: Y= F(K,EL) K5 (EL) 0.5 E grows at rate g; L grows at rate n ; depreciation rate is ô. Savings rate is a constant s 1- We will fill in the model (in terms of Y, s) C= (in terms of Y, s Y = (in terms of C and I only) 2- This is the first year of our country's founding, the country is...
Question 3 : Solow model with long-run TFP growth [20 marks] Suppose output is given by Y = K}(AN) As in the basic model, the workforce grows at rate n, capital depreciates at rate d and the savings rate is s. In addition, suppose that TFP grows at a constant rate g. That is: ΔΑ A9 We will refer to the product AN as the "effective workforce". It follows that the effective workforce grows at rate n+g. a. Express the...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3 Lš where K, is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation KH = (1-d) * Kit It: where d is the depreciation rate. Every person saves share s of his income and, therefore, aggregate saving is St-s...
A and B only Consider the Solow growth model with the following production function where y is output. K is capital, s is the productivity and is labor. Assume that 0 < α < 1 Further, suppose that labor grows at a constant rate n. That is. 1 + n. Also, assume that capital depreciates at rate d and that gross investment in capital is fraction s of output. a Letting k-N, obtain the law of motion for capital accumulation...
In the Solow model, suppose the per worker production function is y: 4 k . Suppose s : 009, n-o 07, and d-012. Calculate the steady-state equilibrium capital-labor ratio. k(Round to two decimal places.)
Suppose the production function is given by ? = ?^a?'^1-a, where Y is output; K is capital stock and N is Labor (look Appendix in Chapter 16). a. Is this production function characterized by constant return to scale? How? Show the work. b. Write this production function as a relationship between output per worker and capital per worker. c. If saving (S) equals investment (I), and S = sY, where s is saving rate, what is the corresponding investment per...
2. Suppose an economy described by the Solow model has the following production function and capital law of motion, with the variables as defined in class: Y =K^(1/2)(LE)^(1/2) ∆k = sy − (δ + n + g)k The economy has a saving rate of 24 percent, a depreciation rate of 3 percent, a population growth rate of 2 percent, and a growth rate of labor productivity of 1 percent. (a) At what rate do total output (Y ), output per...
In the Solow model, suppose the per worker production function is y = 60. Suppose s + 0.11, n = 0.06, and d = 0.08. Calculate the steady-state equilibrium capital-labor ratio. k = 22.22. (Round to two decimal places.) Calculate the steady-state level of output per worker. y= (Round to two decimal places.)