SOLOW MODEL Flashcards
2 differences between solow and model of production
Model of production = static, capital exogenous.
Solow = dynamic, endogenous K accumulation.
Solow model equation
Yt = F(Kt, L) = A bar Kt^a L^1-a
3 exogenous parameters in solow equation
A bar = no technological growth
L bar = no population change
alpha
Returns to scale solow
CRS
Resource constraint solow
Ct + It = Yt
Investment function solow
It = s bar Yt
Consumption function solow
Ct = (1 - s bar)Yt
Capital accumulation equation solow
Kt+1 = Kt + It - dKt
change Kt+1 = It - dKt
change Kt+1 = sbar Yt - dKt
wage rate = solow
wt = MPLt = (1-a) Yt/L bar
rental rate = solow
rt = MPKt = a Yt/Kt
6 endogenous variables solow
Yt, Kt, Ct, It, wt, rt
6 parameters solow
L bar, alpha, s bar, d bar, K0 bar, A bar
Requirement for K0 bar
K0 bar > 0 otherwise nothing happens.
How do we solve the dynamic solow model/
Must solve at every point in time = cannot do algebraically.
- solve graphically
- solve for LR
When is capital growing solow?
When sbar Yt > d bar Kt
Steady state condition solow
s bar Yt = d bar Kt
What does the investment function look like graphically? Why?
Concave as just a scaled version of the production function which is concave due to diminishing MPK and fixed L.
How many steady states?
actually 2 - also one where K0=0 but this is unstable as any small change in economy –> K*
Transition dynamics =
The process that takes the economy from its initial level of capital to the steady state.
Kt* =
Kt* = L bar (s bar A bar / d bar) ^1/1-a
Kt* is increasing in
A bar
L bar
s bar
Kt* is decreasing in
depreciation rate d bar
Yt*=
Yt* = A bar ^1/1-a (s bar / d bar)^a/1-a L bar
per worker yt* =
yt* = A bar ^1/1-a (s bar / d bar)^a/1-a
How does exponent on A bar differ in solow to production model? Why?
1 / 1 - a is greater than 1
Higher productivity has additional effects on output through its indirect effect on increasing K accumulation.
Why do we have a steady state?
Diminishing MPK as K rises
Depreciation rate constant
So net investment eventually = 0
Does solow generate LR growth?
NO - all endogenous variables are constant at the steady state.
Is Solow data consistent in terms of its growth prediction?
NO - data show economies do grow over the long run = solow fails to explain this.
How does rise in s bar affect economy SR and LR?
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.
How could increasing S bar have a trade off in solow?
Could reduce consumption in the LR
How does rise in d bar affect economy SR and LR?
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.
Impact of higher L bar on steady state
higher L bar = increased MPK = higher K*
But in per worker terms, no change - in LR back to old steady state.
What does solow predict about convergence? Why?
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
Is solow’s predicting regarding convergence data consistent?
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.
Does solow explain LR differences in GDP levels across countries well?
NO - higher S bar of rich not enough to explain GDP per worker differences. And d bar could actually be higher for richer countries.
Why is d bar higher or richer countries?
Because faster process of innovation
So is solow a good model?
NO - we need a new model which explains technological change since most of cross-country differences in GDP per capita due to A.
