# profit_func - 3 Profit Function(p = max py yY 3.1...

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

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.

Unformatted text preview: 3 Profit Function (p) = max py. yY 3.1 Properties 1. If p0 pi, p0 po for all i (inputs) and o (outo i puts), then (p0) (p). 2. Homogeneous of degree 1: for t > 0, (tp) = t(p). 3. Convex in p: for p00 = tp + (1 - t)p0, t [0, 1], (p00) t(p) + (1 - t)(p0). 4. Continuous in p for p 0 (when defined). 3.2 Supply and Demand 3.2.1 Example: Hotelling's Lemma: For all i = 1, . . . , n, for pi > 0, yi (p) = The LeChatelier principle: (p, wx, wz ) = max py - wxx - wz z. y,x,z (p) . pi (1) wx, wz are fixed. Short-run: z is fixed. Proof: Special case of Envelope Theorem. Suppose z = z(p)L-R level, Envelope Theorem: For the problem M(a) = max f (z, a) z h(p) = LR(p) - SR(p, z ) = SR(p, z(p)) - SR(p, z ) 0. We have p = arg min h(p), p we have dM (a) f (x, a) . = da a x=x(a) Substitution matrix: Eq. (1) implies h(p) = 0, (SOC): y(p) = D(p) = Dy(p) = D2(p), (p) convex = Dy(p)symm., pos. semi-def.. 2 LR(p) 2 SR(p, z ) - 0, p2 p2 dy(p) dy(p, z ) - 0. dp dp ...
View Full Document

## This note was uploaded on 03/18/2012 for the course ECON 201 taught by Professor Çakmak during the Spring '10 term at Middle East Technical University.

### Page1 / 2

profit_func - 3 Profit Function(p = max py yY 3.1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}