چکیده:
The present paper contributes to the theoretical analysis of the human capital investment and participation decision of heterogeneous workers in the search and matching framework. Its aim is to characterize the equilibrium and to identify the efficiency. Here, the paper studies search equilibrium and matching to consider the participation decision of heterogeneous workers who have different inherent ability levels. The productivity investment decision is endogenous and wages are determined by the Nash bargain among participants.
خلاصه ماشینی:
"With fixed participation, Hosios (1990) showed that the wage rule decentralizes the efficient labor market allocation if and only if the bargaining power of the worker equals the elasticity of the number of aggregate matches with respect to the number of individuals searching for the jobs.
Substituting (3) and (4) into (2) gives, UiA)ɸ+ m(ɵ))=δEi+ɸ)UiA+Ei) for i=t,h (6) which implies that (ɸ+δ)Ei UiA= (ɵ) (7) m Lets define E+UA i i λi= (8) ηi Substituting (7) into (8) and rearranging in terms of Ei gives, m(ɵ) Ei=λiηi () (9) ɸ+δ+mɵ Substituting (9) into (1) the planner problem reduces to m(ɵ) λhηhm(ɵ) m,λa,xɵP=ɸ+λtηδt+m(ɵ)xt+ɸ+δ+m(ɵ)xh xii +|ηt−λtηtm(ɵ)()|b+ (10) ɸ+δ+mɵ |ηh−ɸλ+hηδh+m(mɵ())|b−k()+ɸ+δ(λtηt)+(λhηh) ɵ(ɸ+δ) ɵ mɵ −ɸ[ηtλtC(xt;at)]−ɸ[ηhλhC(xh;ah)] I can rewrite (11) function as: λiηim(ɵ) xim,λai,xɵP=Ƹi=l,hɸ+δ+m(ɵ) xi +Ƹ|ηi−ɸλ+iηδi+m(mɵ)(ɵ)|b− (11) i=l,h k(ɵɵ()ɸ++ɸδ)+δƸ)λiηi)−ƸɸLηiλiC(xi;ai)] m i=l,h i=l,h Appendix 2: Optimal Policies Using the Lagrangian Method I can solve this standard optimization problem as: This problem satisfies the following first order conditions: ∂P∂C m(ɵ) ∂x=∂x− ) )=0 (1) i i ɸɸ+δ+m(ɵ) ∂P ɸ(ɸ+δ+m(ɵ)) kɵ(ɸ+δ) ∂λi=xi−b− m(ɵ) C(xi;ai)−m(ɵ) (2) =0 ∂ɵP=k−(m(ɵ)+ɸm+'(δɵ)−m'(ɵ)ɵ)[λη+ληxt λtηt tt hh +λλh+ηλh xh−b]=0 (3) tηt hηh Rearranging (12) ɸηiλi=(m(ɵ)+ɸ)UiA−δ)ηiλi−UiA) (4) ηiλi=(ɸm(+ɵ)δ+1)Ui (5) A Consider those individuals that are indifferent to participate in labor market, from the participation constraint lets substitute xi−b into above market and planner free entry conditions then: '(ɵ)ɸ k=()m()[ΠC(xt;at) mɵ−m'ɵɵ (6) +(1−Π)C(xh;ah)] Ptanner sotution k=(1−βɵβ)ɸ[ΠC(xt;at) (7) +(1−Π)C(xh;ah)]Market sotution when the worker is indifferent to participate equality holds then m'(ɵ)ɸ (1−β)ɸ (ɵ) '(ɵ)ɵ=βɵ m−m then m'(ɵ) 1−β (ɵ) '(ɵ)ɵ=βɵ m−m dividing both sides by m(ɵ) m' m(ɵ) 1−β 'ɵ= (ɵ)ɵ 1−mm(ɵ)βm'(ɵ) m m,(ɵ)ɵ Rearranging the terms proves that Hosios Condition, i."