A Appendix.
Proof of Proposition 2.3. 1 We know that if 1 + Rt = R(wt) then Yts
F(Kd,AtLd) and AKt d = k(wt). The competitive wage, wtc, implies:
At Lt
Ktd = Kts and Ltd = Nt, (33)
and, then, wtc satisfies:
Ks
■ = ANY 3,.
Substituting ( 2) and ( 6) in ( 34), and solving the equation for wtc we obtain:
Ss
Wtc = (1 - α)(At)1-α['.. ]α.
If wt > wtc we obtain:
7/ ʌ
k (wt) =
Ktd
AtLd
Kts
> . t,r
AtNt
St-1
AtNt ’
(35)
because k(wt) is increasing in wt. If Kd = St-ι, then, from ( 35), we obtain:
1-α
d d κd At~α^ -t_ 1 d
Ld = . ■-1—- = -------t— < Nt. If, on the contrary, Ld = Nt, then, from
t Atk(wt) [ wt ]— t , ,, t t, , J
[ 1 — α ]
( 35), we have: Ktd = kk(wt)At Nt > Kts .
If wt < wtc we have:
k (wt)
Kd K = St-A
AtLd AtNt AtNt ■
(36)
If Ld = Nt, then, from ( 36), we have: Kd = k(wt)AtNt = [ɪwt-] — —N—— < Kt.
1 α At —
d t d Kd
If, on the. contrary, Kt = St-ι, then, from ( 36), we obtain: Ld = - t^ > > Nt.
Proof of Proposition 3.1. 1 First note that the wage set by the union will
never be lower than the competitive wage. From proposition 2.3.1, if wt < wtc
then Lte = Nt . Thus setting the wage equal to the competitive wage we still have
Lte = Nt and a greater wage. Now we solve the program of the union assuming
A ɪ -s
that Le = -------t-1. It is easy to show that the wt that maximizes the program
t [ιwtα]α
of the union is the wage that maximizes the function:
_1
(37)
St = ((1 - τt)wt - ht)wt α ;
where ht = γt(1-τt-1)wt-1+(1-γt)st. The first order condition for a maximum
of St is:
1 (1 - τt )wt - ht
(1 - τt) - “ ʌ-----W ----t = 0. (38)
Solving ( 38) for wt we obtain:
ht = Yt(1 - τt-1)wt-1 + (1 - Yt)st (39)
(1 - α)(1 - τt) (1 - α)(1 - τt)
18
More intriguing information
1. Regionale Wachstumseffekte der GRW-Förderung? Eine räumlich-ökonometrische Analyse auf Basis deutscher Arbeitsmarktregionen2. The name is absent
3. The name is absent
4. Impact of Ethanol Production on U.S. and Regional Gasoline Prices and On the Profitability of U.S. Oil Refinery Industry
5. THE ANDEAN PRICE BAND SYSTEM: EFFECTS ON PRICES, PROTECTION AND PRODUCER WELFARE
6. Computational Experiments with the Fuzzy Love and Romance
7. The name is absent
8. Constructing the Phylomemetic Tree Case of Study: Indonesian Tradition-Inspired Buildings
9. The name is absent
10. The name is absent