On Dictatorship, Economic Development and Stability

there exists an implicit function q_t+1 = f (k_t ,q_t) if F has continuous partial derivatives
F_qt+ι, F_kt, F_qt, and if ∂F∕∂q_t+1 = 0. Both conditions are verified if q_t+1 = 1 and q_t = 0.
As only the values between 0 and 1 are of interest, we can define an interval ]0, 1[ for q
to ensure that F admits the implicit function q_{t +1} = f (k_t,q_t).

The linearized system of (40)-(41) is the following:

with

lβ (1 -α )
(1+ β )(1 -qt )²

where,

Υ = (αqt)^1-σ [lβ(1 - α)]^{- 1}-^σ i ^q ■ A. '    '    - l (1 - qt)^α)

^σqt+1 _ (1 -qt)^α f σ___αqt ´     ^qt+1^l(1+β)α

^{(1 -σ})qt       qt    ∖(^{1 -σ})   ^{1 -}qt / ^{(1 -}qt+1)^{a[lβ(1 -α})]^α

l [(1+β )(1 -qt )]^α

^{a [ lβ (1 -α )] α (1 -}qt +1⁾²

Therefore, the Jacobian matrix is:

42

<<   41   42   43   44   45   46   47   >>

More intriguing information