Lecture 7: Solow Swan

Question 1

Two long-run properties Solow-Swan model is based off

Answer 1

1. Amounts of output determiines new investment (per period) - Cobb-Douglas
2. National income accounting:
   Y = C + I (closed economy for simplicity)

Question 2

Solow-Swan capital accumulation formula

Based on the two long run properties

Answer 2

K(t+1) - K(t) = sAF(K(t),L) - depreciationK(t)

Question 3

Draw a labelled Solow-swan diagram

Answer 3

check summary

Question 4

Steady state capital equality when capital is not changing

Answer 4

sAF(K,L) = depreciationK
sY^=depreciationK^
where K=K*
- solve this to find steady state

Question 5

Steady state output and consumption formulas

Answer 5

Y^ = AF(K^, L)
C^ = Y^ - I^
= (1-s)Y^
Where, ^ = *

Question 6

Capital accumulation intensive form (with growing A, labour productivity and L, labour) formula

Answer 6

(1+ga+gl)(k(t+1)-k(t)) = sf(k(t))-(depreciation + ga + gl)kt

Question 7

Steady state per effective worker equality

Answer 7

sf(k^) = (depreciation +ga +gl)k^

where, ^ = *

Question 8

Intensive steady state capital and output formula

Answer 8

K(t) = k^A(t)L(t)
Y(t) = y^A(t)L(t)

where ^ = *

Question 9

Total factor prodctivity (productivity growth)

Answer 9

= 1+ ga

Question 10

Labour force growth

Answer 10

= 1 + gl

Question 11

Labour augmented productivity

Answer 11

= F(K(t), A(t)L(t))

Question 12

Convergence hypothesis

Answer 12

A country should grow faster when it is far below steady state and slower when it is closer to steady state.
Solow swan predicts conditional convergence which suggests convergence is conditional on savings rate, depreciation, labour productivity growth, labour market growth etc. but independent of initial capital per effective worker, k0
- predicts countries with same parameters will have similar long-run outputs per worker - the clubs will converge.

Question 13

alphs and 1-alpha value

Answer 13

alpha = rK/Y
1-alpha = wL/Y