SOLOW MODEL

Question 1

2 differences between solow and model of production

Answer 1

Model of production = static, capital exogenous.

Solow = dynamic, endogenous K accumulation.

Question 2

Solow model equation

Answer 2

Yt = F(Kt, L) = A bar Kt^a L^1-a

Question 3

3 exogenous parameters in solow equation

Answer 3

A bar = no technological growth
L bar = no population change
alpha

Question 4

Returns to scale solow

Answer 4

CRS

Question 5

Resource constraint solow

Answer 5

Ct + It = Yt

Question 6

Investment function solow

Answer 6

It = s bar Yt

Question 7

Consumption function solow

Answer 7

Ct = (1 - s bar)Yt

Question 8

Capital accumulation equation solow

Answer 8

Kt+1 = Kt + It - dKt
change Kt+1 = It - dKt
change Kt+1 = sbar Yt - dKt

Question 9

wage rate = solow

Answer 9

wt = MPLt = (1-a) Yt/L bar

Question 10

rental rate = solow

Answer 10

rt = MPKt = a Yt/Kt

Question 11

6 endogenous variables solow

Answer 11

Yt, Kt, Ct, It, wt, rt

Question 12

6 parameters solow

Answer 12

L bar, alpha, s bar, d bar, K0 bar, A bar

Question 13

Requirement for K0 bar

Answer 13

K0 bar > 0 otherwise nothing happens.

Question 14

How do we solve the dynamic solow model/

Answer 14

Must solve at every point in time = cannot do algebraically.

1. solve graphically
2. solve for LR

Question 15

When is capital growing solow?

Answer 15

When sbar Yt > d bar Kt

Question 16

Steady state condition solow

Answer 16

s bar Yt = d bar Kt

Question 17

What does the investment function look like graphically? Why?

Answer 17

Concave as just a scaled version of the production function which is concave due to diminishing MPK and fixed L.

Question 18

How many steady states?

Answer 18

actually 2 - also one where K0=0 but this is unstable as any small change in economy –> K*

Question 19

Transition dynamics =

Answer 19

The process that takes the economy from its initial level of capital to the steady state.

Question 20

Kt* =

Answer 20

Kt* = L bar (s bar A bar / d bar) ^1/1-a

Question 21

Kt* is increasing in

Answer 21

A bar
L bar
s bar

Question 22

Kt* is decreasing in

Answer 22

depreciation rate d bar

Question 23

Yt*=

Answer 23

Yt* = A bar ^1/1-a (s bar / d bar)^a/1-a L bar

Question 24

per worker yt* =

Answer 24

yt* = A bar ^1/1-a (s bar / d bar)^a/1-a

Question 25

How does exponent on A bar differ in solow to production model? Why?

Answer 25

1 / 1 - a is greater than 1

Higher productivity has additional effects on output through its indirect effect on increasing K accumulation.

Question 26

Why do we have a steady state?

Answer 26

Diminishing MPK as K rises
Depreciation rate constant
So net investment eventually = 0

Question 27

Does solow generate LR growth?

Answer 27

NO - all endogenous variables are constant at the steady state.

Question 28

Is Solow data consistent in terms of its growth prediction?

Answer 28

NO - data show economies do grow over the long run = solow fails to explain this.

Question 29

How does rise in s bar affect economy SR and LR?

Answer 29

Investment curve pivots up
At K*, net investment > 0 so K grows
Eventually reach new steady state with higher level of K, higher output.
Growth in K and Y only temporary.

Question 30

How could increasing S bar have a trade off in solow?

Answer 30

Could reduce consumption in the LR

Question 31

How does rise in d bar affect economy SR and LR?

Answer 31

depreciation curve pivots up
at K*, net investment < 0 so K declines
Eventually new steady state with lower K and lower Y. -VE growth in K and Y only temporary.

Question 32

Impact of higher L bar on steady state

Answer 32

higher L bar = increased MPK = higher K*

But in per worker terms, no change - in LR back to old steady state.

Question 33

What does solow predict about convergence? Why?

Answer 33

CONDITIONAL CONVERGENCE
change Kt+1 / Kt = s bar A bar (L/Kt)^1-a - d bar
Higher Kt = lower growth rate
So countries with lower GDP = grow faster
Conditional on converging to same steady state - same d bar, s bar, A bar, L bar

Question 34

Is solow’s predicting regarding convergence data consistent?

Answer 34

YES - OECD countries with lower GDP = grow faster. This is not the case for world data, but still consistent as clearly not converging to same steady state.

Question 35

Does solow explain LR differences in GDP levels across countries well?

Answer 35

NO - higher S bar of rich not enough to explain GDP per worker differences. And d bar could actually be higher for richer countries.

Question 36

Why is d bar higher or richer countries?

Answer 36

Because faster process of innovation

Question 37

So is solow a good model?

Answer 37

NO - we need a new model which explains technological change since most of cross-country differences in GDP per capita due to A.