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ch06-differential-calculus (1)

# ch06-differential-calculus (1) - Basics of Differential...

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Basics of Differential Calculus Professor Erkut Ozbay Economics 300

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Why differential calculus? Models explain economic behavior with system of equations What happens if a variable changes? Comparative statics determines marginal change in economic behavior How does change in tax rate alter consumption? How does change in NBA collective bargaining agreement impact share of NBA revenues going to players? parity of teams across league?
Why differential calculus? Economic models assume rational optimizers Consumers maximize utility Producers maximize profits NBA owners maximize combination of wins and profits Optimization uses calculus to evaluate tradeoffs How much to consume? Consume until marginal utility = price How much to produce? Produce until marginal revenue = marginal cost Which free agents to go for?

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Average rate of change over [x 0 ,x 1 ] 1 0 1 0 1 0 1 0 ( ) ( ) , where and f x f x y x x x x x x y y y - - - -
Average rate of change examples 1 0 1 0 ( ) ( ) f x f x y x x x - - 1 0 1 0 : bx bx y y a bx b x x x - = + = = - 2 2 2 1 0 1 0 1 0 1 0 1 0 1 0 ( )( ) : x x x x x x y y x x x x x x x x - - + = = = = + - -

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6 y x = 3 y x = 2 y x =
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ch06-differential-calculus (1) - Basics of Differential...

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