Solow–Swan Growth Model

Exercises

Solow–Swan Growth Model

Exercises

Work through the prompts first, then compare against the solutions once you are ready.

Exercise 1

Steady-State Calculation An economy has production function

Y = K^{1/3}(AL)^{2/3}

, with

s = 0.25

,

n = 0.01

,

g = 0.02

,

\delta = 0.05

.

(a)
Find $k^*$ , $y^*$ , and $c^*$ .
(b)
Find the steady-state capital-output ratio.
(c)
What is the steady-state growth rate of $Y/L$ ?

Exercise 2

Golden Rule Using the same parameters as Exercise 1 (

n=0.01, g=0.02, \delta=0.05

).

(a)
Find the Golden Rule capital per effective worker $k^*_{GR}$ .
(b)
Find the Golden Rule savings rate $s_{GR}$ .
(c)
Is the economy in Exercise 1 above or below the Golden Rule?

Exercise 3

Comparative Statics Starting from the steady state in Exercise 1,

s

rises permanently from

0.25

to

0.36

.

(a)
Calculate the new $k^{**}$ and $y^{**}$ .
(b)
By what percentage does steady-state output per effective worker increase?
(c)
What happens to the growth rate of $Y/L$ in the long run?

Exercise 4

Growth Accounting Economy:

\hat{Y} = 4.0\%

,

\hat{K} = 5.0\%

,

\hat{L} = 2.0\%

,

\alpha = 0.35

.

(a)
Compute the Solow residual.
(b)
What fraction of output growth is accounted for by TFP?
(c)
What fraction is accounted for by capital deepening ( $K/L$ growth)?

Exercise 5

Speed of Convergence Parameters:

\alpha = 1/3

,

n = 0.01

,

g = 0.02

,

\delta = 0.05

.

(a)
What is the annual convergence speed $|\lambda|$ ?
(b)
How many years until the economy closes 90% of the gap?