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AMS/ECON 11A - Syllabus Week Notes (09-25-16)

by: Adriana Chavez

AMS/ECON 11A - Syllabus Week Notes (09-25-16) AMS11A

Marketplace > University of California - Santa Cruz > Economics > AMS11A > AMS ECON 11A Syllabus Week Notes 09 25 16
Adriana Chavez
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About this Document

These notes cover the material given on the first day of class. Modeling economics and the three types of equations used to express how economic values relate.
Math Methods for Economics
Jonathan Katznelson
Class Notes
Math, Calculus, Precalculus, Radicals, AMS, AMS11A, Econ, Economics, Econ11A




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This 3 page Class Notes was uploaded by Adriana Chavez on Monday September 26, 2016. The Class Notes belongs to AMS11A at University of California - Santa Cruz taught by Jonathan Katznelson in Fall 2016. Since its upload, it has received 18 views. For similar materials see Math Methods for Economics in Economics at University of California - Santa Cruz.


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Date Created: 09/26/16
Friday, September 23, 2016 AMS/ECON 11A - Syllabus Week Housekeeping - NO Make-Up Quizzes, Lowest quiz score will be dropped - Carla - MSI Learning Tutor - Office Hours: WF 10:00 - 11:30am Modeling Economics - What is Modeling Economics? • Using equations to describe how different economic variables relate to e/o - Three Types of Equations • Identities - Always True - Definitions • ex. r = pq Functional Realtionships • - In the form: y = f(x) • ex. q = √(400 - 0.5p) if p = 600 q = √(100) = 10 or r = pq r = p √(400 - 0.5p) Revenue is expressed as a FUNCTION of price. For what value of p is r defined? Because negative numbers under the radical are undefined/imaginary, and revenue MUST always be a nonnegative, √(400 - 0.5p) ≥ 0 p ≥ 0 } 1 Friday, September 23, 2016 q ≥ 0 } r = pq ≥ 0 q = √(400 - 0.5p) ≤ 0 400 - 0.5p ≤ 0 400 ≤ 0.5p 400 ÷ 0.5 ≤ p p ≤ 800 r is defined as a function of p if p ≤ 800. This revenue function only defines prices between 0 ≤ p ≤ 800. Always positive values between the two. 0 800 • Equilibrium Equations - Balanced, not moving • Supply/Demand relationship demonstrates Market Equilibrium - q = f(p) ← Demand - q = g(p) ← Supply • ex. q = √(400 - 0.5p) ← Demand Equation q = 5 + p∕120 ← Supply Equation qdemand= q supply √(400 - 0.5p) = 5 + p∕120 400 - 0.5p = 25 + p∕12 + (p∕120) ←Square both sides 2 2 (1∕120) p + (7∕12)p - 375 = 0 ← Set the equation equal to 0 p = -7∕12 ± √((49∕122) +1500∕120 ) ← Factor using Quadratic Equation 2∕120 2 2 Friday, September 23, 2016 p = -7∕12 ± 1∕12 √(49 + 15) ← Simplify by taking (1∕12) out from the √ 2∕120 2 -7 ± √(64) ← Simplify 2∕1200 -7 ± 8 ← Simplify 1∕600 p = 600 or p = -15.600 p ≥ 0; therefore, -15.600 cannot be an answer. 3


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