ps1sol_09_addon

ps1sol_09_addon - Cornell University Economics 3130 Problem...

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Cornell University Economics 3130 Problem Set 1 Solutions 1. What is Nechyba’s interpretation of what Friedman meant when he said that no one knows how to make a pencil? That no one person knows how to make a pencil from scratch. 2. What are the three basic insights Nechyba attributes to economics? 1) There are many situations in which everyone can win–just because there is a winner does not mean there is a loser, 2) People’s actions are often based on incentives rather than inherent dispositions, and 3) Order can emerge spontaneously without someone designing it. 3. Compute f x (that is, ∂f ∂x ), f y , f xy (that is, 2 f ∂x∂y ), f xx , and f yy for the following functions: (a) f ( x,y ) = 10 x 1 5 y - 1 2 . f x = 2 x - 4 5 y - 1 2 , f y = - 5 x 1 5 y - 3 2 , f xy = - x - 4 5 y - 3 2 , f xx = - 8 5 x - 9 5 y - 1 2 , f yy = 15 2 x 1 5 y - 5 2 (b) f ( x,y ) = 4 e 3 x ln (2 y ). f x = 12 e 3 x ln (2 y ), f y = 4 e 3 x y - 1 , f xy = 12 e 3 x y - 1 , f xx = 36 e 3 x ln (2 y ), f yy = - 4 e 3 x y - 2 (c) f ( x,y ) = 2(2 x - 1) 4 y - 2 . f x = 16(2 x - 1) 3 y - 2 , f y = - 2(2 x - 1) 4 ( y - 2) 2 , f xy = - 16(2 x - 1) 3 ( y - 2) 2 , f xx = 96(2 x - 1) 2 y - 2 , f yy = 4(2 x - 1) 4 ( y - 2) 3 (d) f ( x,y ) = x 3 y . f x = 3 y , f y = x ( ln 3)3 y , f xy = ( ln 3)3 y , f xx = 0, f y = x ( ln 3) 2 3 y 4. Suppose that there are two goods:
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ps1sol_09_addon - Cornell University Economics 3130 Problem...

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