solow model Flashcards
solow growth model
The Solow–Swan model is an economic model of long-run economic growth. It attempts to explain long-run economic growth by looking at capital accumulation, labor or population growth, and increases in productivity largely driven by technological progress.
production function total output
Yt = F(Kt, Lt) = AKtαLt1-α
production function per worker
yt=f(kt)=Aktα
production function assumptions
constant returns to scale, exogenous technology, full employment (L=population, grows at rate n)
capital accumulation total
Kt+1=sYt+(1-S)Kt
capital accumulation per worker
(1+n)kt+1=syt+(1-S)kt
capital accumulation assumptions
no government expenditures, no trade, save a constant proportion s of output Y, full employment (L=population, grows at rate n)
combining both per workers
(1+n)kt+1=sAktα+(1-S)kt
diaganol line
(1+n)kt+1
top curve
f(kt) = Aktα
bottom curve
sAkαt + (1-S)kt
k*
(sA/n+S) ^ 1/(1-α)
y*
A(k*)^α
accumulate more capital per worker
(1+n)k < sA(k)α + (1-S)k
decumulate capital per worker
(1+n)k >sK(k)α+(1-s)k
implications for growth
output per worker in equilibrium is constant, but the total output Y grows at rate n
implications for savings
an increase of savings rate leads to higher steady state levels of k and y
implications for population
high population growth rates lead to lower steady state levels of k and y
income convergence
convergence of income per capita of poor countries to the level of rich countries, obtained by th ehigher growth of the former. the solow model of economic growth predicts income convergence
area of trapezoid
(a+b/2)h
gini
G - 1 - 2S
