Notes-Chapter 8 - Chapter 8 COMPARATIVE STATIC ANALYSIS OF...

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Chapter 8 COMPARATIVE STATIC ANALYSIS OF GENERAL FUNCTION MODELS Alpha Chiang, Fundamental Methods of Mathematical Economics 3 rd edition
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Comparative Static Analysis Significance: sometimes no explicit reduced form solution can be obtained. Hence, we will have to find the comparative static derivatives directly from the original equation of the model. 0 0 0 0 0 0 ( , ) ( , ) Y C I G C C Y T Y C Y T I G = + + = = + +
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Comparative Static Analysis 0 0 0 ( , , ) Y Y I G T = 0 0 0 At neighborhood of Y the following identical equality will hold: ( , ) Y C Y T I G = + + 0 0 Partial differentiation, ,does not do the job as T can affect C not only directly, but also indirectly via Y. We must resort to total differentiation, based on the notion of total differential Y T s. Because of the general form of the C function, no explicit solution is available.
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Differentials Given a function ( ), Example: '( ) y f x y y x x dy dy dx or dy f x dx dx = ∆ ≡ ÷ ÷
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Example: 2 Given: 3 7 5 The derivative of the function is 6 7 (6 7) y x x dy x dx dy x dx = + - = + = +
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Differentials and Point Elasticity . / / / / / marginal function / average function d y x dQ Q dQ dP dP P Q P dy dx y x ε = =
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Sample Questions Find the differential dy, given Given the import function , express income elasticity of imports in terms of propensities to import Given the consumption function C=a+bY, find the
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Notes-Chapter 8 - Chapter 8 COMPARATIVE STATIC ANALYSIS OF...

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