Lecture 2

# Lecture 2 - Vineet Goyal Lines Quantitative Skills Review...

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QSRP - Chapters 3, 4 and 5 1 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Quantitative Skills Review Program (QSRP) Chapters 3, 4 and 5

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QSRP - Chapters 3, 4 and 5 2 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Lines Steepness = ratio of rate of change of y wrt x Constant everywhere for lines Slope Slope of a line passing thru (x1,y1) and (x2,y2) m = (y2-y1) / (x2-x1) Special cases Vertical lines Horizontal lines 1 2 3 4 1 2 3 4 5 6 7 (1,3) (3,7) y x
QSRP - Chapters 3, 4 and 5 3 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Ex: Price-Quantity Relationship Price-Quantity curve as shown Interpret slope (2,4) (8,1)

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QSRP - Chapters 3, 4 and 5 4 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Parallel lines, Perpendicular lines Parallel lines have same slope (or both vertical) m1 = m2 Perpendicular lines have slopes that are negative reciprocals of each other m1 = -1/m2 Or if one is vertical and the other is horizontal
QSRP - Chapters 3, 4 and 5 5 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Equations of lines Point-slope form Data: (x1,y1) and m m = (y-y1)/(x-x1) i.e. y – y1 = m (x – x1) Any example Data: (x1,y1) and (x2,y2) Find slope and use any 1 point Slope-intercept form Data: (0,b) and m y = m x + b General equation of line a x + b y + c = 0

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QSRP - Chapters 3, 4 and 5 6 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Applications of lines Example 1 (pg 124 of text) Linear demand and supply curves @ \$58, D = 100, S = 120 @ \$54, D = 200, S = 60 What is the equilibrium price? Example 6 (pg 128 of text)
QSRP - Chapters 3, 4 and 5 7 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Parabola: Quadratic Functions Quadratic function f(x) = ax 2 +bx+c, a≠0 Note: y-intercept = c Graph of quadratic function: Parabola Pg 131 of text Axis of symmetry Vertex = (-b/2a, f(-b/2a)) Minimum if a > 0 Maximum if a < 0 Restricted quadratic functions: one-to-one

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QSRP - Chapters 3, 4 and 5 8 Vineet Goyal Systems Logarithmi c functions Math of finance Parabolas Lines Exponential functions Application of quadratic functions Maximum Revenue (ex. 6 p. 135, text) The demand function is p=1000-2q Find maximum total revenue Decision Variable q – quantity to produce Objective function: Max p * q = (1000-2q)q = -2q 2 + 1000q
9 Vineet Goyal

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Lecture 2 - Vineet Goyal Lines Quantitative Skills Review...

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