101 Class 14 W2008

13 2 4 e1 e 2 1 qd 20 3 p 6 1 2 3 8 20 q why

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Unformatted text preview: 20 3 P 4 6 1 2 3 8 20 Q Why Linear Estimators? Demand functions are unlikely to be linear But linear estimators... And nonlinear estimators... are simple are often not bad approximations for reality can sometimes be nonlinear estimation in disguise Linear estimators are certainly a good place to start analysis are complicated often require some knowledge of the precise nature of non linearity Linear estimator as approximation to non-linear function P Q Linear estimators might be nonlinear estimators in disguise Suppose we knew the demand function had the form log Qd = a + b log P + Could estimate the linear function: where p = log P and qd = log Qd ^ ^ ^ qd = a + b p i.e. simply take logarithms of all variables and perform OLS on the transformed data Supply Functions Also work primarily with linear supply functions in this course Simple case: price is the only explanatory variable QS = a + b P b : inverse of the supply curve slope a : intercept on the horizontal axis Always positive May be positive or negative Q = 10 + 5 P s P Slope = 1/5 6 10 40 Q Q = -10 + 5 P s P Slope = 1/5 6 10 20 Q Infinitely elastic supply P Supply function is undefined Slope = 0 P0 Q1 Q2 Q Relatively elastic supply P Qs = a + belastic P 0 < belastic Slope = P/Q = 1/belastic > 0 P2 P1 P Q Q1 Q2 Q Relatively ine...
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