1 / 8

Economics 214

Economics 214. Lecture 8 Introduction to Functions Cont. Necessary & Sufficient Conditions. Symbol  means “implies” PQ means “if P then Q,” “P implies Q,” “P only if Q.” P is a sufficient condition for Q, for if P holds then if follows that Q holds.

conlan
Download Presentation

Economics 214

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Economics 214 Lecture 8 Introduction to Functions Cont.

  2. Necessary & Sufficient Conditions • Symbol  means “implies” • PQ means “if P then Q,” “P implies Q,” “P only if Q.” P is a sufficient condition for Q, for if P holds then if follows that Q holds. • This expression also shows that Q is a necessary condition for P cause P can only hold if Q holds.

  3. Example of Necessary and Sufficient Conditions • f strictly concave  f concave

  4. If and only if

  5. Power Functions

  6. Rules of Exponents

  7. Power functions with p equal even integer • F(0)=0 • If k>0, then f(x) reaches a global minimum at x=0. If k<0, then f(x) reaches global maximum at x=0. • These functions are symmetric about the vertical axis. They are strictly convex if k>0 or strictly concave if k<0.

  8. Figure 2.13 Power Functions in Which the Exponent Is a Positive Even Number

More Related