Macroeconomics Exam Review 252

Macroeconomics Exam Review 252 - c 2001 Michael Carter All...

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6.8 Supermodularity of Π( x ,?, w ) follows from Exercises 2.50 and 2.51. To show strictly increasing diFerences, consider two price vectors w 2 w 1 Π( x w 1 ) Π( x w 2 )= ? ± =1 ( ± 1 ± ) ² ± ? ± =1 ( ± 2 ± ) ² ± = ? ± =1 ( ± 2 ± ± 1 ± ) ² ± Since w 2 w 1 , w 2 w 1 0 and ± ? ± =1 ( ± 2 ± ± 1 ± ) ² ± is strictly increasing in x . 6.9 ±or any ? 2 ? 1 , ³ 2 = ´ ( ? 2 ) ´ ( ? 1 ³ 1 and µ ( ³ 1 ) µ ( ³ 2 ) is increasing in and therefore ( µ ( ´ ( ? 2 ) ) µ ( ´ ( ? 1 ) )) is increasing in . 6.10 The ²rm’s optimization problem is max ² ∈ℜ + ¶?³ µ ( ³ ) The objective function ´ ( ³,?,¶ ¶?³ µ ( ³ ) is supermodular in ³ (Exercise 2.49) displays strictly increasing diFerences in ( ³,¶ )s ince ´ ( ³ 2 ,?,¶ ) ´ ( ³ 1 ¶? ( ³ 2 ³ 1 ) ( µ ( ³ 2 ) µ ( ³ 1 ) ) is strictly increasing in for ³ 2 1 . Therefore (Corollary 2.1.2), the ²rm’s output correspondence is strongly increasing and every selection is increasing (Exercise 2.45). Therefore, the ²rm’s output increases as
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

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