Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Economics of Migration: Class Problem Set 2

Suphanit Piyapromdee

1. Assume that firms produce output using high and low skill labor Yt  = At  [甘htLht(p) ＋Làt(p)]1/p

where Let  with e ∈ {h) à} is the aggregate labor input of workers of skill e in time t; 女E = 1/(1 − p) is the elasticity of substitution between skill groups;甘et is the relative productivity level of skilled to unskilled labor.

Within each skill group, workers differ by age (or experience)

Let  = ╱αeYL Yte(|) ＋L Ote(|)、1/|

where a ∈ {Y) O} denotes young and old, and one of the αea  is normalized to one; 女A = 1/(1 − |) is the elasticity of substitution between age groups.

Within each age group, workers differ by immigration status

Leat  = ╱Nea(6)t＋ βeat(M)M  tea(6)、1/6

where N denotes natives and M denotes immigrants, and βea(N)t  is normalized to one.

(a)  (optional) Assume perfect competition, verify that labor demand takes the fol- lowing form

lnWea(s)t  = lnAt ＋ 女E(1)  lnLt ＋ln甘et ＋lnαea＋ lnβe(s)at

＋ ╱  女A(1)  − 女E(1)  ← lnLet ＋ ╱  女(1)I  − 女A(1) ← lnLeat − 女(1)I lnSeat

where S ∈ {N) M} is an immigrant status.

(b) How would you estimate 女E ) 女A ) 女I and 甘ht ) αeY ) βeat(M)?

(c)  Suppose we have an influx of high skill immigrants. Show why the imperfect substitutability between immigrants and natives leads to a smaller effect of im- migration on wages of high skill natives than on wages of high skill immigrants.

(d) If we want to make the model richer by adding more characteristics of workers e.g. gender and countries of origin, discuss what problems we may have.