미시경제학 9판 솔루션 (Micro economic theory 9th ed , Nicholson)

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
2.1
U ( x, y ) ? 4 x 2 ? 3 y 2 ?U ?U a. 〓 8x , 〓 6y ?x ?y b. 8, 12 ?U ?U c. dU ? dx + dy 〓 8 x dx + 6 y dy ?x ?y dy for dU ? 0 8 x dx ? 6 y dy ? 0 d. dx dy ?8 x ?4 x 〓 〓 dx 6 y 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 equation 4 x 2 ? 3 y 2 ? 16 , slope of the line at (x, y) is

dy 4x . ?? dx 3y

2.2

a.

Profits are given by ? ? R ? C ? ?2q 2 ? 40q ? 100 d? * ? ? 4q ? 40 q ? 10 d…