Macroeconomics Exam Review 135

Macroeconomics Exam Review 135 - c 2001 Michael Carter All...

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The inverse satisFes the equation ( ²³ )( ´µ ¶· ) = ( 10 01 ) In particular, this means that ´ and satisfy the equation ( ´ ) = ( 1 0 ) By Cramer’s rule (Exercise 3.103) ´ = ) ) ) ) 1 ± 0 ³ ) ) ) ) ) ) ) ) ) ) ) ) = ³ Δ where Δ = ±² . Similarly = ) ) ) ) ? 1 ² 0 ) ) ) ) ) ) ) ) ) ) ) ) = ² Δ µ and · are determined analogously. 3.105 A portfolio is duplicable if and only if there is a di±erent portfolio y = x such that ¸ x = ¸ y or ¸ ( x y )= 0 There exists a duplicable portfolio if and only if this homogeneous system has a non- trivial solution, that is if rank ¸<´ . 3.106 State ¯ ¹ is insurable if there is a solution to the linear system ¸ x = e ¯ ? (3.42) where e ¯ ? is the ¯ ¹ -th unit vector (the ¯ ¹ Arrow-Debreu security). (3.42) has a solution
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