calculus_review_203_2010

calculus_review_203_2010 - Econ 203 Calculus Review p. 1...

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Econ 203 Calculus Review p. 1 Economics 203: Intermediate Microeconomics Calculus Review Functions, Graphs and Coordinates Functions: A function f , is a rule assigning a value y for each value x . The following illustration shows the graph of the function yf x = () . If x=x 0 , then we follow the arrow from x 0 up the graph of the function to get the value of y, specifically y 0 , which is given by the height of the function at x 0 .
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Econ 203 Calculus Review p. 2 Graphs and Coordinates: Typically, economists use 2-dimensional graphs to depict functional relationships. Graphs gives us a visual format to easily grasp the information regarding a functional relationship. However, graphs may be less precise than algebraic representation of functions, and may even be misleading. Figure (a) illustrates some basics. We designate the horizontal axis as the x axis and the vertical axis as the y axis. Each point in the (x,y) plane is characterized by a pair of numbers(x 0 ,y 0 ) with x always coming first.
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Econ 203 Calculus Review p. 3 Types of Functions: Function’s characteristics : linear and positive slope throughout.
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Econ 203 Calculus Review p. 4 Function’s characteristics: non-linear and decreasing throughout.
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Econ 203 Calculus Review p. 5 Functions’ characteristics : linear, non-decreasing, constant or horizontal. Simultaneous non-increasing and non-decreasing.
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Econ 203 Calculus Review p. 6 Function’s characteristics: decreasing and increasing, non- linear function.
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Econ 203 Calculus Review p. 7 Note: Linear functions are represented in slope-intercept form: ya b x =+ , where '' a represents the vertical intercept and b represents the slope of the function. Such parameters can take on any positive, negative or zero value. Nonlinear functions can take on a much wider range of forms. For example: yx ye x = = = 3 log( ) (logarithmic function) (exponential function) In all of theses functions, the slope of the function changes as x changes.
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Econ 203 Calculus Review p. 8 Conventions: Typically the horizontal axis of a diagram depicts the independent (x) variable and the vertical axis depicts the “dependent” (y) variable. However, it has become conventional to draw market demand and supply curves with the quantity on the horizontal axis and price of the vertical axis even though we are assuming that the quantity demanded of a good is a function of its price: D = f (p).
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Econ 203 Calculus Review p. 9 The budget constraint for an individual who has a budget of M dollars and spends it all on only two goods, X and Y, which have fixed prices, is illustrated next:
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calculus_review_203_2010 - Econ 203 Calculus Review p. 1...

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