尼克尔森答案与纠错版solutions manual.pdf
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CHAPTER 2
THE MATHEMATICS OF OPTIMIZATION
The problems in this chapter are primarily mathematical. They are intended to give students some practice
with taking derivatives and using the Lagrangian techniques, but the problems in themselves offer few
economic insights. Consequently, no commentary is provided. All of the problems are relatively simple
and instructors might choose from among them on the basis of how they wish to approach the teaching of
the optimization methods in class. Solutions 2 2
2.1 U( x, y) 4 x 3 y U U a. = 8x , = 6y x y b. 8, 12 U U c. dU dx + dy = 8x dx + 6y dy x y dy d. for dU 0 8x dx 6y dy 0 dx dy 8x 4x = = dx 6y 3y e. x 1, y 2 U 4 1 3 4 16 dy 4(1) f. 2 / 3 dx 3(2) g. U = 16 contour line is an ellipse centered at the origin. With equat