How is technology introduced in the extended Solow model?
Output is produced using
Y
=
F
(
K
,
A
N
)
Y=F(K,AN), where (A) is technology and (AN) is labour in efficiency units.
What are “efficiency units” of labour?
Labour adjusted for technology: (AN), meaning each worker becomes more productive as (A) rises
Define capital and output per effective (efficiency‑unit) worker.
k
K
/
(
A
N
)
k=K/(AN) is capital per effective worker;
y
=
Y
/
(
A
N
)
y=Y/(AN) is output per effective worker
Write the law of motion for capital per effective worker in the extended Solow model with population growth and tech progress.
Δk=sf(k)−(n+g
A
+δ)k, where
g
A
g
A
is the growth rate of technology.
What is the steady‑state (balanced growth) condition per effective worker?
sf(k
∗
)=(n+g
A
+δ)k
∗
.
On the balanced growth path, what are the long‑run growth rates of output per worker and total output?
Output per worker grows at rate
g
A
g
A
; total output grows at rate
n
+
g
A
n+g
A
.
Does the saving rate affect the long‑run growth rate of output per worker in the extended Solow model?
No. The saving rate affects the level of output per worker and the speed of convergence, but long‑run growth of output per worker is determined by the tech growth rate
g
A
g
A
.
What is the Solow residual (total factor productivity, TFP)?
The part of output growth not explained by growth in labour and capital; it is used as a measure of technological progress.
What are economic institutions in the context of growth?
Rules, organisations and norms (e.g. property rights, legal systems, regulation) that shape incentives for investment, innovation and production.
Why do good institutions promote economic growth?
They protect property rights, enforce contracts and limit corruption, encouraging investment in physical and human capital and technology, which raises TFP and growth.
