{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

601-compstats

# 601-compstats - E 601 1 Comparative statics Suppose an...

This preview shows pages 1–2. Sign up to view the full content.

E frqrplfv 601 1 Comparative statics Suppose an agent is maximizing her objective function f ( x, a ) , where x is the choice variable and a is a parameter. Assuming the maximization problem is well- behaved, and all we are interested in is the sign of dx/da then the method of com- parative statics (the implicit function theorem) tells us that Sign dx da = Sign 2 f ( x, a ) a x . The fi rst-order condition for this problem is f ( x, a ) x = 0 which implicitly de fi nes the optimal level of x as a function of a . Taking a total di ff erential of this equation obtain 2 f ( x, a ) x 2 dx + 2 f ( x, a ) a x da = 0 or dx da = 2 f ( x, a ) / a x 2 f ( x, a ) / x 2 The result follows immediate from this equation and that the second-order con- ditions for the maximization require 2 f ( x, a ) / x 2 < 0 . EXAMPLE Consider a two-period life-cycle model of a single individual whose endowment is e 1 in period 1 and half the time e 2 + δ in period 2 and half the time e 2 δ in period 2 , where δ is a positive number. The individual must use an asset that pays a known real rate of return, r, to carry purchasing power across the periods. With no uncertainty, her lifetime utility function is U = v

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern