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Chiang_Ch6

Chiang_Ch6 - Ch.6 ConceptofDerivative 6.1 6.2 6.3 6.4...

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1 Ch. 6 Comparative Statics and the  Concept of Derivative 6.1 The Nature of Comparative Statics 6.2 Rate of Change and the Derivative 6.3 The Derivative and the Slope of a Curve 6.4 The Concept of Limit 6.5 Digression on Inequalities and Absolute Values 6.6 Limit Theorems 6.7 Continuity and Differentiability of a Function

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2 6.1 The Nature of Comparative Statics Comparative statics: a study of different equilibrium states associated with different sets of values of parameters and exogenous variables. Begin by assuming an initial equilibrium is given Examples – Isolated market model (P 0 ,Q 0 ) (shock) (P 1 ,Q 1 ) – National income model (Y 0 , C 0 ) (shock) (Y 1 , C 1 )
3 6.1 Shift in Demand Q P Q s Q d0 Q d1 P 1 P 0 Q 0 Q 1

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4 6.1 Comparative statics Static equilibrium analysis y* =  f (x) Comparative static equilibrium analysis y 1 * - y 0 * =  f (x 1 ) -  f (x 0 )   Where the subscripts 0 and 1 indicate initial  and subsequent points in time respectively
5 6.1 Comparative statics Issues: The rate of change, i.e., the derivative ( Y/ G)

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6 6.2 Rate of Change and the Derivative ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 dx dy x x f x x f x y x x f x x f x y x f x x f y x x x x x x y y y x f x f y y x f y x f y x x o = - - = - + = - + = + = = - = - - = - = = 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 * 0 * 1 1 * 1 0 * 0 lim lim ) 9 derivative the gives quotient difference a of 0 x as limit the Taking ) 8 quotient difference the gives x by sides both Dividing ) 7 3) into 6) and 4) ng Substituti ) 6 such that ) 5 ) 4 Let ) 3 in x change small a for y in change the Find ) 2 ) 1 x of function a is y that of ms equilibriu static two Assume
Macro-economic model (Section 3.5, #1b p. 53) Given  Y = C + I + G 0 • C = a + b(Y-T) • T=d+tY Solving for Y Y* = (a-bd+ I + G 0 )/(1-( b(1-t)))  variable exogenous or parameter a represents x where ? 0 1

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Chiang_Ch6 - Ch.6 ConceptofDerivative 6.1 6.2 6.3 6.4...

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