Diaspora remittances and reduction of unemployment

Munich Personal RePEc Archive

Diaspora remittances and reduction of unemployment

Jellal, Mohamed

Al Makrîzi Institut D’économie, rabat , Morocco

25 August 2014

Online at https://mpra.ub.uni-muenchen.de/58114/

MPRA Paper No. 58114, posted 25 Aug 2014 13:38 UTC

𝑐1,𝑡 +𝑠_𝑡 = 𝑤_𝑟 1− 𝑢_𝑡 +𝑢_𝑡(𝑤_𝑖 +𝑀) 𝑐1,𝑡 𝑠_𝑡 𝑤_𝑟 𝑢_𝑡 𝑤_𝑖 𝑀

𝑤_∗

𝑤_𝑖 < 𝑤_∗ < 𝑤_𝑟

𝑐2,𝑡+1 = 1 + 𝑟_𝑡+1 𝑠_𝑡 𝑐2,𝑡+1 𝑟_𝑡+1

𝑁_𝑡 𝑛

𝑈_𝑡 = 𝑙𝑜𝑔 𝑐1,𝑡 +𝛽𝑙𝑜𝑔 𝑐2,𝑡+1

𝛽

𝑀𝑎𝑥 𝑈_𝑡 = 𝑙𝑜𝑔 𝑐1,𝑡 +𝛽𝑙𝑜𝑔 𝑐2,𝑡+1

𝑐1,𝑡 +𝑠_𝑡 = 𝑤_𝑟 1− 𝑢_𝑡 +𝑢_𝑡(𝑤_𝑖 +𝑀) 𝑐2,𝑡+1 = 1 +𝑟_𝑡+1 𝑠_𝑡

𝑠_𝑡(𝑀) = 𝛽

1 +𝛽 𝑤_𝑟 1− 𝑢_𝑡 +𝑢_𝑡(𝑤_𝑖 +𝑀

𝑀

𝑀 𝑀^′ 𝑤_𝑖 < 0

𝑆𝑖𝑔𝑛 𝑑𝑠_𝑡(𝑀)

𝑑𝑢_𝑡 = 𝑆𝑖𝑔𝑛 𝑤_𝑖 +𝑀 − 𝑤_𝑟

𝑑𝑠_𝑡(𝑀)

𝑑𝑢_𝑡 > 0 𝑀 > 𝑤_𝑟 − 𝑤_𝑖

𝑑𝑠_𝑡(𝑀)

𝑑𝑢_𝑡 ≤ 0 𝑀 ≤ 𝑤_𝑟 − 𝑤_𝑖

𝑑²𝑠_𝑡(𝑀) 𝑑𝑢_𝑡𝑑𝑤_𝑟 ≤ 0

𝐿_𝑡 𝐾_𝑡

𝑌_𝑡 = 𝐴𝐾_𝑡^𝛼𝐿¹_𝑡^−𝛼 𝐴

Π_𝑡 = 𝐴𝑘_𝑡^𝛼 1 − 𝑢_𝑡 ^1−𝛼 − 𝑤_𝑟 1 − 𝑢_𝑡 −(1 +𝑟_𝑡)𝑘_𝑡 𝑘_𝑡 = ^𝐾𝑡

𝑁_𝑡 𝑢_𝑡 = 1−_𝑁^𝐿𝑡

𝑡

𝑢_𝑡 = 1− 1 − 𝛼 𝐴 𝑤_𝑟

𝛼1

.𝑘_𝑡

𝑙_𝑡 = 1− 𝑢_𝑡

𝑢_𝑡 = 1− ^{1−𝛼 𝐴}_𝑤

𝑟 1 𝛼 .𝑘_𝑡

𝑑𝑢_𝑡

𝑑𝑤_𝑟 > 0 ^𝑑𝑢𝑡

𝑑𝐴 < 0 ^𝑑𝑢𝑡

𝑑𝑘_𝑡 < 0

𝐾_𝑡+1 = 𝑁_𝑡𝑠_𝑡 = ^𝑁𝑡+1

𝑛 𝑠_𝑡

𝑘_𝑡+1 = ^𝛽

𝑛 1+𝛽 𝑤_𝑟 1− 𝑢_𝑡 +𝑢_𝑡(𝑤_𝑖 +𝑀

𝑤_∗ = ^𝛽

𝑛 1+𝛽 𝛼

1−𝛼 1− 𝛼 𝐴 ^1−𝛼1

𝑢_𝑡 = 1− ^{1−𝛼 𝐴}_𝑤

𝑟 1

𝛼 .𝑘_𝑡 = 0 𝑤_∗ = 1− 𝛼 𝐴𝑘_𝑡^𝛼

𝑘_𝑡+1 = 𝛽

𝑛 1 +𝛽 1− 𝛼 𝐴𝑘_𝑡^𝛼

𝑘 = 1− 𝛼 𝐴 𝛽 𝑛 1 +𝛽

1 1−𝛼

𝑤_∗ = 1− 𝛼 𝐴 1− 𝛼 𝐴 𝛽 𝑛 1 +𝛽

1 1−𝛼

𝛼

𝑘_𝑡+1 = ^𝛽

𝑛 1+𝛽 𝑤_𝑟 + 1 − ^{1−𝛼 𝐴}_𝑤

𝑟 1

𝛼 .𝑘_𝑡 (𝑤_𝑖 +𝑀 − 𝑤_𝑟)

𝑢_𝑡+1 = 1− ^{1−𝛼 𝐴}_𝑤

𝑟 1

𝛼 .𝑘_𝑡+1

𝑢(𝑀) = 1 − ^{1−𝛼 𝐴}_𝑤

𝑟 1

𝛼 . ^{𝛽 𝑤𝑖+𝑀}

1+𝛽 𝑛+𝛽 𝑤^𝑖+𝑀−𝑤_𝑟 ^{1−𝛼 𝐴}_{𝑤 𝑟} 1 𝛼

𝑢_𝑡 = 1− ^{1−𝛼 𝐴}_𝑤

𝑟 1 𝛼 .𝑘_𝑡 𝑘_𝑡+1 = ^𝛽

𝑛 1+𝛽 𝑤_𝑟 + 1 − ^{1−𝛼 𝐴}_𝑤

𝑟 1

𝛼 .𝑘_𝑡 (𝑤_𝑖 +𝑀 − 𝑤_𝑟)

𝑘_𝑡+1 = 𝑘_𝑡 = 𝑘 ∀𝑡

𝑘(𝑀) = 𝛽 𝑤^𝑖 +𝑀

1 +𝛽 𝑛+𝛽 𝑤^𝑖 +𝑀 − 𝑤_𝑟 1 − 𝛼 𝐴 𝑤_𝑟

𝛼1

𝑢(𝑀) = 1− ^{1−𝛼 𝐴}_𝑤

𝑟 1

𝛼 𝑘(𝑀)

𝑢^′ 𝑀 = − 1− 𝛼 𝐴 𝑤_𝑟

𝛼1

𝑘^′ 𝑀 < 0

𝑘^′ 𝑀 > 0.

𝑘(𝑀) = 𝛽 𝑤^𝑖 +𝑀

1 +𝛽 𝑛+𝛽 𝑤^𝑖 +𝑀 − 𝑤_𝑟 1 − 𝛼 𝐴 𝑤_𝑟

𝛼1

𝑆𝑖𝑔𝑛 𝑘^′ 𝑀 = 𝑆𝑖𝑔𝑛 1 +𝛽 𝑛 − 𝛽 1− 𝛼 𝐴 𝑤_𝑟

𝛼1

.𝑤_𝑟

𝑘^′ 𝑀 > 0

𝑤_𝑟 > 𝛽 𝑛 1 +𝛽

𝛼 1−𝛼

1 − 𝛼 𝐴 ^1−𝛼1

𝑤_∗ = 𝛽 𝑛 1 +𝛽

𝛼 1−𝛼

1− 𝛼 𝐴 ^1−𝛼1 𝑤_𝑟 > 𝑤_∗ 𝑘^′ 𝑀 > 0

∀ 0 < 𝑀 < +∞

𝑢 𝑀 =

1 + 𝛽 𝑛 − 𝛽 1− 𝛼 𝐴 𝑤_𝑟

𝛼1

.𝑤_𝑟 1 +𝛽 𝑛+𝛽 𝑤^𝑖 +𝑀 − 𝑤_𝑟 1− 𝛼 𝐴

𝑤_𝑟

𝛼1

> 0

𝑤_𝑟 > 𝑤_∗ 1 +𝛽 𝑛 − 𝛽 ^{1−𝛼 𝐴}_𝑤

𝑟 1

𝛼 .𝑤_𝑟 > 0 𝑢 𝑀 > 0 ∀𝑀 < +∞