The Advantage of Cooperatives under Asymmetric Cost Information



In particular, di > c" => ¾(c<) ≤ <7l(cz∕), as claimed in the proposition. By
<7,(∙) monotonously decreasing, it follows also that
dqi(di)∕dc,i exists almost
everywhere (a.e.), cf. LafFont and Tirole(1993) p. 63.

Rewriting (2), we get that for all di and d- with di > d-

-(ξ - <)⅛(<) < SiW - SiW) + <  ¾(<) - ⅛ ∙ QiW ≤-Wi - <)¾(ξ)
or equivalently

<⅞(¾(4) - QiW)} < ⅝(cj) - ¾(<⅜') < <(¾(g,.) - ¾(⅛))
Cj - ɑi' ^^ Ci - cj' - di - c"

We see therefore that since ⅛(czl)∕dczl exists (a.e.), so does dsɪ(eɔ/dej. Fur-
thermore, going to the limit
(di → eɔ in (2), we get that

d(¾(ci)-<⅞∙¾(cj))

-----J------- -QiW ≤ θ «•

This shows that the less efficient types earn less profit and it implies
fc? _ _

4^ ɑi ʧi(ɛi) d* J Qi[Ci) dci
which is the last property in the proposition.

We shall now show that the two properties in Proposition 1 implies in-
centive compatibility. Inserting the expression for ¾(.) into the incentive
compatibility constraint (1) we get

A⅛ + ci ∙ ςi(ci) + / qi(ci) d⅛ - ci qi(ci) >

Γci _

ki + ⅛∙qi(di) + J qi(ci) dci - ci ∙ qi(c,i) ∀i,ci,c'.

Reducing and rewriting, we get

,c<z                     ∕*< __                  Γci

/ qdci)dci> / ρi(c')dci+ / qi(ci)dci Vi,ci,di
Jci                    Jci                  Jcti

which holds because qi{.) is weakly decreasing. ■

According to Proposition 1, the less efficient types produce less. Also,
the expected payment is - up to an integration constant - determined en-
tirely from the production scheme. Proposition 1 makes it easy to analyze
alternative organizations as we shall see below.



More intriguing information

1. The name is absent
2. Comparison of Optimal Control Solutions in a Labor Market Model
3. The name is absent
4. The name is absent
5. Towards Learning Affective Body Gesture
6. Altruism and fairness in a public pension system
7. Indirect Effects of Pesticide Regulation and the Food Quality Protection Act
8. The name is absent
9. The name is absent
10. The Functions of Postpartum Depression