Growth rates in the Solow model (I):

Question

Question

Growth rates in the Solow model (I):

(a) Use the production function in equation (5.6) (Y=AK^1/3L^2/3)and the rules for computing

growth rates from page 53 of Chapter 3 to write the growth rate of per

capita GDP as a function of the growth rate of the capital stock. (Hint:

Because the labor force is constant, the growth rates of GDP and per

capita GDP are the same.)

(b) Combine this result with the last equation in footnote 7 (Section 5.9) to

get a solution for the growth rate of per capita GDP as a function of the

current level of capital Kt

. Be sure to write your answer in terms of

Kt and parameters of the model only. For example, use the fact that s Y ∗/K ∗ = d

.

As

Add a comment Improve this question Transcribed image text

Answer 1

Similar Homework Help Questions

Growth rates in the Solow model

Growth rates in the Solow model (II): Suppose an economy begins in steady state and is characterized by the following parameter values: s 0.2, d 0.1, A 1, L 100. Apply your answer to question 8 to calculate the growth of per capita GDP in the period immediately after each of the changes listed below. (Hint: Since the economy begins in steady state, its growth rate is initially zero and Kt K*.)(a) The investment rate doubles.(b) The productivity level rises...
Growth rates in the Solow model

Growth rates in the Solow model (II): Suppose an economy begins in steady state and is characterized by the following parameter values: s 0.2, d 0.1, A 1, L 100. Apply your answer to question 9 to calculate the growth of per capita GDP in the period immediately after each of the changes listed below. (Hint: Since the economy begins in steady state, its growth rate is initially zero and Kt K*.)(a) The investment rate doubles.(b) The productivity level rises...
1. Consider the simple version of the Solow Growth Model discussed in class summarized by these...

1. Consider the simple version of the Solow Growth Model discussed in class summarized by these four equations: Consumers save a fraction s of output: 1 = sy Capital grows as follows: K' = 1 + (1 - 8)K Firms use capital to make output: Y = AK 0.3 There is no government or trade: Y = C+/ where Y is GDP, / is investment, C is consumption, s is the savings rate, K is the capital stock this year,...

Consider the Solow growth model with depreciation rate and population growth rate n. The equation of...

Consider the Solow growth model with depreciation rate and population growth rate n. The equation of motion for the capital stock and the per worker production function in this economy are given by: Ak= s(f(k) - (8 + n) k y= f(k) = k1/4 a). Suppose adoption of modern birth control methods in a developing country causes the population growth rate to decrease. What happens in the main Solow diagram: what curve(s) shin, what happens to the steady- state level...
MALTHUS AND SOLOW GROWTH MODEL

Malthusian Model of Growth Notation: Yt Aggregate output; Nt Population size; L¯ Land (fixed); ct Per capita consumption Production: Aggregate production function is Yt = F(Nt , Lt) = zN2/3 t L 1/3 t Population Dynamics: Nt+1 = g(ct)Nt Population growth function: g(ct) = (3ct) 1/3 Parameter Values: Land: L¯ = 1000 for all t. Productivity parameter: z = 1 ...
Consider the Solow growth model that we developed in class. Output at time t is given...

Consider the Solow growth model that we developed in class. Output at time t is given by the production function Y AK Lt, where A is total factor productivity, Kt is total capital at timet and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and Y, + 1, where Ct is consumption and I is investment at tim. Every agent saves s share of...

Consider the Solow growth model. Output at time t is given by the production function Yt...

Consider the Solow growth model. Output at time t is given by the production function Yt = AK 1 3 t L 2 3 where Kt 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 Kt+1 = (1 − d) ∗ Kt + It , where d is the depreciation rate. Every person saves...
Consider the Solow growth model. Output at time t is given by the production function Yt...

Consider the Solow growth model. Output at time t is given by the production function Yt = AKt3 L3 , where A is total factor productivity, Kt is total capital at time t and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and Yt = Ct + It where Ct is consumption and It is investment at time t. Every agent saves s share...
12. What happens with no diminishing returns? Consider a Solow model where the production function no...

12. What happens with no diminishing returns? Consider a Solow model where the production function no longer exhibits diminishing returns to capital accu- mulation. This is not particularly realistic, for reasons discussed in Chapter 4. But it is interesting to consider this case nonetheless because of what it tells us about the workings of the Solow model. Assume the production function is now Y, = AK. The rest of the model is unchanged. (a) Draw the Solow diagram in this...

Consider the Solow growth model that we developed in class. Output at time t is given...

Consider the Solow growth model that we developed in class. Output at time t is given by the production function where A is total factor productivity, Kt is total capital at time t and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and where Ct is consumption and It is investment at time t. Every agent saves s share of his income and consumes...

Growth rates in the Solow model (I):

Homework Answers

Request Answer!

Add Answer to:
Growth rates in the Solow model (I):

Post as a guest

Earn Coins