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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 by 10%.

(c) An earthquake destroys 75% of the capital stock.

(d) A more generous immigration policy leads the population to double.


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Answer #1

We need to first determine the steady state level of capital per capita:

(n + d)k* = sz(k ∗ ) 1/3

k* = (sz/ n+d) 3/2

= ( 0.2×1 / 0+0.1) 3/2 = 2 3/2 ≈ 2.8284

y ∗ = z(k ∗ ) 1/3 = 21/2 ≈ 1.4142

growth rate of GDP is then 3.2%

a. When investment rate doubles:

First, using the fact that (n+d)k*=sz(k*)1/3

then the initial steady state capital per worker , k* is 23/2.

The initial steady output per worker is given by

y*=z(k*)1/3 = 21/2\sim1.41.

Given that the investment rate doubles, the new output per worker level is

zk'1/3

where k' = (1-d)k* + sz(k*)1/3 with s=0.4.

Hence the new level of output per worker is 1.46

and the growth rate is3.3%.

b) When the productivity level rises by 10%.

z = 1 × 1.1 = 1.1. Then,

(1 + n)k' = szk 1/3 + (1 − d)k

k' = 0.2 × 1.1 × 20.5 + 0.9 × 23/2

= 2.8567

y' = z(k' ) 1/3 = 1.1 × 2.8567 = 1.5608

growth rate of GDP is then 10.4%

c)

k = 0.25 × k ∗ = 0.25 × 23/2 = 0.7071

and y = 1 × 0.70711/3 = 0.8909.

Then, (1 + n)k' = szk1/3 + (1 − d)k

k' = 0.2 × 1 × 0.70711/3 + 0.9 × 0.7071 = 0.8146

y' = z(k' ) 1/3 = 1 × 0.81461/3 = 0.9339

growth rate of GDP is then 4.8%


answered by: Fullynn
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Answer #2

Thanx for answering but it still not clear 


Fasit

oppgave 9-10 kapittel 5.JPG

answered by: Kris0.0
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