On Dictatorship, Economic Development and Stability

Plugging in (35) the expression of τt given by (36), and plugging (36) in (37), we obtain
a system of two equations,

kt+1

lβ (1 — a )

⁽¹ + ^β⁾⁽¹^— Qt⁾

(38)

ltt+1

⁽¹^— Qt+1) Ak^α+1

[(1 + ρ )(1 + β )]¹^-^- Ttkq (1 — t) )¹^-^-

1 ^-~- q a— 1^—

a¹^-^σ q^{- -} kt+1 ^-

(39)

Using (36) and (38) to rearrange the expression (39), we obtain a system equivalent to

(35)-(37):

kt+1

lβ (1 — a )

^{(1 +}^β⁾⁽¹^— Qt )

(40)

qt+1 qt¹

-σ

)++1 g-^-^σ l[(1+ β)(1 — t,)]^α

¹^— Qt+1 A^[^lβ⁽¹^—^a^)]^a

(41)

((1 — tt ) a⁺^aka —l (¹^-^q^t Α¹^-^σ+a )

t^∣√1 l ∖ < l l /QM —— l lβ (1 -a ) A^a¹

^a¹^-^-^{[(1 +} P^{)(1 +}^β^)]¹^-^- 1. β )

Then we take a first-order Taylor expansion around the steady state. To compute the
partial derivatives of q_t₊₁ with respect to k_t and q_t , we use the implicit function theorem.

Given the function F (q_t₊₁, k_t, q_t) = 0, with

F⁽ tt+1 ,kt,Qt ) = tt+ι tt¹^-

^qt +1 ^qt ^- l^[(1+^β⁾⁽¹^—^qt^)]^α

1 — qt+1 A [ lβ (1 — a )]^α

(1 — qt ) ^σ⁺^αkα-

I (1 -qt )¹^-^σ⁺^αA

1 — 1

a¹^-^- [(1+ρ)(1+ β)]¹^-^-

lβ (1 — a )
1+β

More intriguing information

1. Clinical Teaching and OSCE in Pediatrics
2. Are combination forecasts of S&P 500 volatility statistically superior?
3. Whatever happened to competition in space agency procurement? The case of NASA
4. The name is absent
5. Evolution of cognitive function via redeployment of brain areas
6. The name is absent
7. The name is absent
8. Ein pragmatisierter Kalkul des naturlichen Schlieβens nebst Metatheorie
9. The name is absent
10. Benefits of travel time savings for freight transportation : beyond the costs