25.4.1 Decision making of private brokers

The conditional expectation and the conditional variance that the representative private brokers have are

* |
(P2 |
— Pi) Bi + (F~ |
B, |
= (E, [P2]-P1)B1 + |
(F-E, [ |
P2]) B2 | |

E-, |
(A |
-P1)B1 + (F- |
p2; |
Bi |
= (P2-P1)S1 + (P- |
-Pi)B*. |
( |

V'arj |
B, |
= <rliB\ + V«r^ [(p |
~ Pi) ^2 |
, and | |||

Var^ |
(P, |
- Pi) B, + |
P2; |
Bz |
= *%B\. |
We consider a linear equilibrium in the following. Since a linear combination of variables that follow normal distributions also follows normal distributions, the equilibrium prices follow normal distributions. The utility of the representative private broker at ¿=1,2 is Et [Up] = - exP (~pEt [(P2 - P,) Bt + (F- Pi) B2] - ^Vwrt [(P, - Pl)Bl + (F - Pi) B, The first-order condition is 25.4.2 Decision making of nations By the sellout constraint of each nation i Si;2 = Wi;2 and by the market clearing condition Si;2 +MB2+n=0, The variance conditional on the events by the time 1 is equal to Take the expectation of both sides conditional on the events by the time 1, and obtain |

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