Solow Growth Model: Cobb-Douglas Production Function. Suppose that production is described by thefollowing constant returns to scale technology: Ya) Derive an expression for steady-state k and steady-state c.b) What value of steady-state k maximizes steady-state c?c) What value of steady-state s, ensures that steady-state c is maximized?KªN1-a

Solow Growth Model: Cobb-Douglas Production Function. Suppose that production is described by the following constant returns to scale technology: Y = KªN²-« a) Derive an expression for steady-state k and steady-state c. b) What value of steady-state k maximizes steady-state c? c) What value of steady-state s, ensures that steady-state c is maximized?

Solow Growth Model: Cobb-Douglas Production Function. Suppose that production is described by the following constant returns to scale technology: Y = KªN²-« a) Derive an expression for steady-state k and steady-state c. b) What value of steady-state k maximizes steady-state c? c) What value of steady-state s, ensures that steady-state c is maximized?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter20: Economic Growth In The Global Economy

Section: Chapter Questions

Problem 5P

See similar textbooks

Similar questions

Consider the Solow growth model in which we allow for long-run techno- logical progress. Assume N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the pop- ulation growth rate. Assume that z = 1 for simplicity, and there is labour-augmenting technological progress. The production technology is given by Y = F(k,bN) where Y is the output of the consumption good, K is the current period capital stock, b denotes the number of units of “human capital” per worker, and bN is the “efficiency units” of labour. Assume that b′ = (1 + β)b where β > 0 is the growth rate in human capital. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. The production function F exhibits constant returns to scale. (a) Define a variable k as the quantity of capital per efficieny units of labor (as opposed to quantity of capital per labour). Using equilibrium conditions derive the…
Identify two assumptions of the basic Solow Growth Model. b. Why are these assumptions important in supporting the Solow Model? c. You are given the following information about an economy.Y = C + IY = F(K, L) The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns.s = saving rate (assume this is constant) per yearδ= depreciation rate (assume this is a constant) per yeary = Y/Lk = K/Lk* = steady state of capital per worker (K/L) and sf(k) < δk.i. What is sf(k)? ii. What is δk? iii. Interpret the meaning of sf(k) < δk? iv. Graphically illustrate sf(k), δk, and k*. Indicate on your graph where sf(k) < δk. v. Explain what happens in this economy when sf(k) < δk.
Assume that the economy’s production function is Cobb Douglas so per-capita output is ? = k^α, where k is per-capita capital. Using the Solow growth model, explain the impact of the loss of capital on the growth rate of per-capita output in the years following the disaster.
Consider the Solow growth model with neither technological nor population change. The parameters of the model are given by s=0.3 (savings rate) and δ=0.08(depreciation rate). Let k denote capital per worker; y output per worker; Solve for output per worker (y*) in the steady state. Show your derivations.
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?
Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.
Please aid in answering the underlined questions in BOLD Question 4:a. Identify two assumptions of the basic Solow Growth Model. b. Why are these assumptions important in supporting the Solow Model? c. You are given the following information about an economy.Y = C + IY = F(K, L)The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns.s = saving rate (assume this is constant) per yearδ= depreciation rate (assume this is a constant) per yeary = Y/Lk = K/Lk* = steady state of capital per worker (K/L) and sf(k) < δk.i. What is sf(k)? ii. What is δk?iii. Interpret the meaning of sf(k) < δk? iv. Graphically illustrate sf(k), δk, and k*. Indicate on your graph where sf(k) < δk.v. Explain what happens in this economy when sf(k) < δk.
Consider 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?
In this problem, we distinguish between labor and population in the Solow growth model. A proportion of the population, a, between zero and one, works. The production function is now written as Y = A(K^1/3)[(aL)^2/3] (a) How does an increase in a from 0.3 to 0.6 change steady state GDP? (b) Does it change the steady-state capital? Explain. (c) Suppose a rises steadily over time. How do you think would affect the growth rate of GDP?
select the correct one(s) a) Suppose s = 0.15, Y = 4200, K = 6100, n = 0.03, g=0.03 and δ= 0.10. This makes national saving smaller than steady-state investment, so that the amount of capital per effective worker will be falling. b) In the graph of the Solow growth model, at any point to the left of the steady-state intersection we have national saving per effective labour greater than steady-state investment per person, causing (K/AL) to increase. c) In the Solow growth model, an increase in the marginal propensity to consume shifts the steady-state investment line downward with the implied change in the capital stock resulting in a higher standard of living in the long run.
In the Solow growth model, suppose that the per-worker production function is given by y=zk2/3 . The saving rate is s, depreciation rate is d, and population growth rate is n. Calculate the per capita capital (k) and output per worker (y) in the steady state.
(III) Consider a version of the Solow growth model without technological change covered in lecture with a rate of population growth of zero (i.e. n=0). Assume that the country has been at the BGP for many years and that suddenly at time t ̅ there is a onetime increase in its population. Show how the economy will adjust to a new BGP by working with the modified system (per capita/worker variables). Show how capital per worker adjusts to the new Steady State level and how its growth rate changes over time.