Consider a risky asset i in a one-period setting. Assume all individuals have time-additive expected utility.

(a) Explain why the price of asset i and the consumption of individual l are related as follows:

 It is technically complicated to include transaction costs and trading restrictions in asset pricing models, but a study of He and Modest (1995) indicates that such imperfections can at least in part explain the equity premium puzzle.

Pi = E[Di]
Rf + e −δl Cov Di, u
l (cl )
u
l (cl 0)

.

(b) Show the approximate relation Pi ≈ E[Di]
Rf − e −δl ARAl(c l 0) Cov 
Di,c l 
.

(c) Show that the price of asset i and aggregate consumption C = L l=1 cl satisfy the approximation Pi ≈ E[Di]
Rf −
⎛
⎝
L l=1 1 e−δl ARAl(cl 0)
⎞
⎠
−1 Cov [Di, C].