Suppose an economy described by the Solow model has the following production function:
1/2 1/2 Y=K (LE) .
a. For this economy, what is f(k)?
b. Use your answer to part (a) to solve for the steady-state value of y as a function of s, n, g, and ?.
c. Two neighboring economies have the above production function,
but they have different parameter values. Atlantis has a saving
rate of 28 percent and a population growth rate of
1 percent per year. Xanadu has a saving rate of 10 percent and a
population growth rate of 4 percent per year. In both countries, g
= 0.02 and ? = 0.04. Find the steady-state value of
d. y for each country.
Suppose an economy described by the Solow model has the following production function: 1/2 1/2 Y=K...
Economic Growth II-End of Chapter Problem Suppose an economy described by the Solow model has the following production function: Y-K (LE a. For this economy, what is f(k)? f(k) b. Use your answer in part a to solve for the steady-state value of y as a function of s, n, g, and 6. y Suppose two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 28% per year and a...
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...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The population grows at the exogenously given rate n, so that N-(1+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, ,A, and parameters (s,8, d,n). Recall the law of motion for capital: (e) Show...
1. Assume that an economy described by a Solow model has a per-worker production function given by y- k05, where y is output per worker and k is capital stock per worker (capital-labor ratio). Assume also that the depreciation rate δ is 5%. This economy has no technological progress and no population growth (n 0). Both capital and labor are paid for their marginal products and the economy has been in a steady state with capital stock per worker at...
An economy has a Cobb-Douglas production function: Y = K"(LE)!-a The economy has a capital share of 0.25, a saving rate of 40 percent, a depreciation rate of 3.00 percent, a rate of population growth of 0.75 percent, and a rate of labor- augmenting technological change of 2.0 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital.
(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...
An economy has a Cobb-Douglas production function: Y = K°(LE)1-a The economy has a capital share of 0.25, a saving rate of 43 percent, a depreciation rate of 3.00 percent, a rate of population growth of 4.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = 2.83 y* * = 1.30 =...
(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...
1. An economy has the production function y = 20k1/2. The current capital stock is 256 and the depreciation rate is 8 percent, and the population growth rate is 2 percent. For income per person to grow, the saving rate must exceed Question 1 options: 6 percent 8 percent 10 percent 12 percent Question 2 (1 point) 2. According to the Solow model, if an economy decreases its saving rate, then in the new steady state, compared to the old...
Solow Growth Model: Consider an economy with the following features: • Y = K 0.25 0.75 • 8 = 0.02 • n=0 . g=0 i. Does the production function exhibit decreasing, constant, or increasing returns to scale? How do you know? ii. Determine MPK. Tii. Does the production function exhibit increasing, constant, or diminishing marginal product of labour? How do you know? iv. Re-express the production function in per worker terms. v. Determine the value of k in three periods...