Basic Solow Model Flashcards
Assumptions
1) Time is ______
2) There is _______ produced in economy
3) No _______ or ________. Y = ___
4) Worker enjoys no _____, and so spends all time _______ supplying ________ . This means individual’s labour supply does not change when price of labour = ____ changes.
5) Aggregate labour force = ___. Labour force grows at ___ %
6) Initial values for ____ and ____ given.
7) No ___ growth –> A(t) = ___
8) ________ production function
1) continuous
2) single good
3) government; international trade –> G = 0 | NX = 0; C + I
4) leisure; inelastically; 1 unit of labour; wage
5) L; n = L-dot(t)/ L(t)
6) K(0); L(0)
7) TFP; 1
8) Cobb-Douglas
per capita = per ______
worker
Y/L = _ K/L = _
y = output per capita = output per worker k = capital per capita = capital per worker
Intensive form
y =
Using assumption (8) Cobb-Douglas production function Y/L = AK^aL^(1-a) / L Using assumption (7) no TFP growth --> A(t) = 1 = K^aL^-a = (K/L)^a = k^a
y = k^a = f(k)
Intensive form has _______ returns to scale.
f(k) = k^a
Suppose k doubles –>
f(2k) = ____
2f(k) = ____
Since 0 < a < 1, 2^a < 2 –> _______ returns to scale
decreasing
(2k)^a = 2^ak^a
2k^a
decreasing
Savings Assumption
Worker saves _____ of income = _
Worker consumes _____ of _____
Aggregate consumption C = _____
constant fraction; s
1-s; income
(1-s)Y
Aggregate savings –> ______ = sY = _____
Investment; Y - C
Capital evolution in discrete time = ______
Delta = _______
For continuous time, take limit of change in time to ____
Capital evolution in continuous time = ______
K_(t+1) - K_t = sY_t - deltaK_t
Depreciation rate of capital
0
K-dot = sY - deltaK
Capital evolution per capita
K-dot = sY - delta*K
Divide by __ –>
K-dot/ L is not equal to ___ = (K/L)-dot
L –> K-dot/L = sy - deltak = sk^a - deltak
k-dot
Capital evolution in intensive form
How to find (K/L)-dot?
Remember the dot means rate of change of that variable = differentiate wrt ____
Use _____ on K(t)/L(t).
k-dot = _______
This is called the ________ of the Solow model
time; quotient rule;
[ L(t)K(t)-dot - K(t)L(t)-dot ]/ L(t)^2
- -> K(t)-dot/L(t) - K(t)/L(t) * L(t)-dot/L(t)
- –> sk^a - delta*k - kn
- —> sk^a - (delta + n)k
fundamental equation
k-dot = sk^a - (delta + n)k
sk^a = _____
(delta + n)k = ______
If sk^a > (delta + n)k, then k _____
If sk^a < (delta + n)k, then k _____
actual investment
breakeven investment
increases
decreases
Steady state is when _______ or ______ which happens when _______
–> k* = ____
There is unique _____ steady state at k = k* and a _____ steady state at _____
k is constant; k-dot = 0;
sk^a = (delta + n)k
k* = [ s/(delta+n) ]^(1/1-a)
positive; trivial; k = 0
Steady state output per capita = y* = _____
Steady state consumption per capita = c* =
k*^a = [ s/(delta+n) ]^ (a/1-a)
1 - s)y* = (1-s) [ s/(delta+n) ]^ (a/1-a
Comparative Statics
Saving rate increases from s to s’
In intensive form:
Production function y = f(k) = k^a curve _______
Actual investment curve sy = sk^a ______
Breakeven investment line (delta + n)k _______
k* _______, y* ________, c* _______
does not change
becomes steeper
does not change
increases
increases
decreases
Why some countries rich, some poor?
rich = high ______
Solow model predicts –> If all countries in steady states, then rich countries have higher y* becos:
1) rich countries have higher ______
2) rich countries have lower ______
This supported by ______
Limitation of Solow model = Limitation of capital accumulation as a source of economic growth:
In the long-run, there is no ______ when TFP is ______. There is only ___________ towards y*.
incomer per capita = y
saving rate (s) = investment rate
population growth rate (n)
empirical data
growth in steady state per capita variables (i.e., no growth in y, k and c*); constant; transitional dynamics
