Macroeconomics Exam Review 229

Macroeconomics Exam Review 229 - Solutions for Foundations...

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5.10 The Frst-order conditions for a maximum (or minimum) are ? 1 ± ( ² )=2 ² 1 =0 ? 2 ± ( ² ² 2 which have a unique solution ² 1 = ² 2 = 0. This is the only stationary point of ± . Since the Hessian of ± ³ = ( 20 02 ) is positive deFnite, we deduce (0 , 0) is a strict global minimum of ± (Proposition 4.1, Exercise 5.2). 5.11 The average Frm’s proFt function is Π( ´,µ )= 1 2 ´ µ 1 6 and the Frm’s proFt maximization problem is max ?,± Π( ´ 1 / 6 µ 1 / 3 1 2 ´ µ 1 6 A necessary condition for a proFt maximum is that the proFt function be stationary, that is ? ? Π( 1 6 ´ 5 / 6 µ 1
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