Suppose each investor h has CARA utility with absolute risk aversion h. Assume the information in the

Suppose each investor h has CARA utility with absolute risk aversion αh.

Assume the information in the economy is generated by w˜ m. Assume investor h believes w˜ m is normally distributed with mean μh and variance σ2, where σ is the same for all investors.

(a) Show that the Radon-Nikodym derivative of investor h’s probability Ph with respect to the average probability P is z˜h =

exp*

−(w˜ m−μh)2 2σ2

+

1 H

H h=1 exp*

−(w˜ m−μh)2 2σ2

+

(b) Show that the sharing rule (21.6) is equivalent to w˜ h = τh H h=1 τh τ

logλhαh λhαh 
+ μ2 h − μ2 h 2σ2 
+
τh τ
w˜ m + τh 
H h=1 τh(μh − μh)
τ σ2 
w˜ m .

(c) Show that if investors also disagree about the variance of w˜ m, then the sharing rule (21.6) is quadratic in w˜ m.