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quotient rule of differentiation: d TC(y)) Y A MC(y)y-TC(y) ACADE ² ways positive the sign of the derivative thus depends on MClas TOld. fip B = dTC (y) y - TC(y) y² dy Oxbridge

quotient rule of differentiation: d TC(y)) Y A MC(y)y-TC(y) ACADE ² ways positive the sign of the derivative thus depends on MClas TOld. fip B = dTC (y) y - TC(y) y² dy Oxbridge

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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re risi osts crease AC AVC MC MC>AC ISION ALXAC Starts! 15 (P VISION ACADE turning points. Through the quotient rule of differentiation: (TC (y)) average fired costs (diminishing). Cost curves. The average cost curve (AC), the average vari- able cost curve (AVC), and the Oxbriday m2 AC marginal cost curve (MC). where average cost can be expressed differently: d dy Y . Mathematically, whether AC is increasing or decreasing depends on the derivative of average cost: dAC (y) dy = VISION ACADEMY dAC(y) _d (TC(y)) = dy dy Mcxbrid AC Elite Camp 11 dTC(y) y-TC(y) dy y² 1. If MC(y)y - TC(y) > 0⇒ MC(y) > AC(y), then 2. If MC(y)y - TC(y) <0⇒ MC(y) < AC(y), then 3. If MC(y)y - TC(y) = 0 MC(y) = AC(y), then Since y² is always positive, the sign of the derivative thus depends on MC(y)y - TC(y): ACADE 2 dAC (y) dy - 17- dAC (y) dy I AVC dAC (y) dy Oxbridge Flie Camp 168# MC(y)y - TC(y) > 0; < 0; VISION ACA Oxbridge VISION Elite Camp VIS This = 0. proves mathematically that MC(y) intersects AC(y) at the minimum of of the later. A similar logic follows for average variable costs. E NON ACADEMY • The area under the MC(y) curve is variable cost. The total cost of producing each additional unit is the total variable cost used in production.
Transcribed Image Text:re risi osts crease AC AVC MC MC>AC ISION ALXAC Starts! 15 (P VISION ACADE turning points. Through the quotient rule of differentiation: (TC (y)) average fired costs (diminishing). Cost curves. The average cost curve (AC), the average vari- able cost curve (AVC), and the Oxbriday m2 AC marginal cost curve (MC). where average cost can be expressed differently: d dy Y . Mathematically, whether AC is increasing or decreasing depends on the derivative of average cost: dAC (y) dy = VISION ACADEMY dAC(y) _d (TC(y)) = dy dy Mcxbrid AC Elite Camp 11 dTC(y) y-TC(y) dy y² 1. If MC(y)y - TC(y) > 0⇒ MC(y) > AC(y), then 2. If MC(y)y - TC(y) <0⇒ MC(y) < AC(y), then 3. If MC(y)y - TC(y) = 0 MC(y) = AC(y), then Since y² is always positive, the sign of the derivative thus depends on MC(y)y - TC(y): ACADE 2 dAC (y) dy - 17- dAC (y) dy I AVC dAC (y) dy Oxbridge Flie Camp 168# MC(y)y - TC(y) > 0; < 0; VISION ACA Oxbridge VISION Elite Camp VIS This = 0. proves mathematically that MC(y) intersects AC(y) at the minimum of of the later. A similar logic follows for average variable costs. E NON ACADEMY • The area under the MC(y) curve is variable cost. The total cost of producing each additional unit is the total variable cost used in production.
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