3. AK Model Flashcards
What is the key difference between the NGM and the AK model?
In the AK model, returns to capital are constant. In the NGM returns to capital are decreasing
How does the economy grow under constant returns?
It grows endogenously
Give the Euler equation for the AK model
c(dot)t/ ct = ó(A-delta-rho)
Give the feasibility condition in the AK model
k(dot)t = Akt -ct -(delta+ n)kt
Under linear technology how does consumption per capita grow?
At a constant rate
What needs to hold for the growth rate to be strictly positive
A-delta > rho
What is initial consumption and why?
It must be c0.
-If it is larger than c0 then on a finite time capital and consumption will become zero, violating the Euler equation.
-if it is smaller than c0 then consumption will always be smaller than c0 which can’t be optimal
Properties of the equilibrium
-The growth rate is endogenous
-More productive economies grow faster regardless of development level
-The economy jumps to a steady state at t=0
What does the AK model predict and is this consist with the Kaldor facts?
-It predicts that an economy grows permanently if the interest rate is larger than the subjective discount factor.
-The model is consistent with the Kaldor facts, notice the economy grows without improvement in technology
What is the real interest rate equal to?
rt= A- delta
Consumption grows permanently at a constant rate
What is necessary for the solution to be interior?
Rho> ((ó-1)/ó)(A-delta) + n/ó
c>0
What can we notice about the rate of growth of capital in the steady state?
k(dot)t/kt= g = ó(A-delta-rho)= A-delta-n-c/k
What can we notice about the share of consumption to capital?
c/k= A- delta- n- ó(A- delta- rho)
ct= (A- delta- n- g)kt
Where g= ó(A- delta- rho)>0
What is the technology that produces output in efficiency units in the AK model?
yt= Akt
Alpha=1, gamma=0
What is the transversality condition?
Same as in the NGM
In the limit as t goes to infinity
kt x ct^(-1/ó) x e^(-rho(hat)t)=0
