ajaz_eco_204_2012_2013_chapter_16_Market_Power

We could try to guess the functional form by

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Unformatted text preview: roduct: # of liquid ozs. Sold in store that week Brand Y product # of liquid ozs. Sold in store that week Price/liquid oz. of brand X product Price/liquid oz. of brand Y product Retailer’s Marginal Cost/liquid oz. of brand X product Retailer Marginal Cost/liquid oz. of brand Y product Suppose we want to estimate a simple demand model for the diet variety of brand X: () To do this we would first have to “guess” the functional form of ( ). We could try to guess the functional form by inspecting a scatter plot of vs. : 9 ECO 204 Chapter 16: Analysis of Firms with Market Power (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Are these points best described by a linear or a non-linear model? Frankly, it’s hard to glean an obvious functional form from this scatterplot. For convenience, let’s assume that the functional form is linear in parameters so that the regression demand model becomes: Here , are the, as yet, unknown parameters of this model and is the “error” term which, loosely speaking, encompasses omitted variables affecting quantity. As described earlier, we can estimate the parameters , by regressing (the dependent variable) on a constant and (the independent variable) by minimizing the sum of squared errors (aka OLS or “Ordinary Least Squares”): We can get algebraic expressions for , ∑( ∑ , ) by solving the FOCs simultaneously (see optional proof below): ̅̅...
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