eco204_summer_2009_practice_problem_11_solution

# eco204_summer_2009_practice_problem_11_solution -...

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University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 11 Solutions Please help improve the course by sending me an e mail about typos or suggestions for improvements Note: Please don’t memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you’ll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Note : This practice problem is based on the lecture on the estimation of demand, production and cost functions. The main point was to contrast the ECO 204 microeconomic theory approach with the ECO 220 econometric approach. I have purposely kept the discussion of econometrics to a minimum-- the intention is to give you an idea of the essential connections between ECO 204 and ECO 220. I am therefore subsuming many issues that you will see in ECO 220 (such as omitted variable bias). I also urge you to come back to this practice problem when you do regression analysis in ECO 220. I will contrast the two approaches through a discussion of demand estimation. In consumer theory, we assumed (“axiom”) that the consumer’s preferences are known and represented by a utility function from which we can perform the UMP and derive demand equations. Here are some utility functions and associated demands for good 1: 1

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University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Utility Function Demand for Good 1 U = Q 1 α Q 2 β Q 1 = { α /( α + β )} Y/P 1 U = min(Q 1 , Q 2 ) Q 1 = Y/(P 1 + P 2 ) U = Q 1 + Q 2 If P 1 > P 2 : Q 1 = 0 If P 1 < P 2 : Q 1 = Y/P 1 P 1 = P 2 , Q 1 = [0, Y/P 1 ] U = log(Q 1 ) + Q 2 Q 1 = P 2 /P 1 U = (Q 1 - α ) 2 /2 β + Q 2 Q 1 = α - β P 1 In particular, note how the first non-linear demand equation (Q 1 = { α /( α + β )} Y/P 1 ) has constant elasticity of -1, while the last linear demand equation (Q 1 = α - β P 1 ) does not have constant elasticity. The econometrician (ECO 220) is faced with a different problem. She has consumer data (Q, P and Y) and wants to know the demand equation which best “fits” the data 1 . In real life, however, we don’t know the consumer’s preferences. Hence, to estimate a consumer’s demand equation, the econometrician has to make some assumptions. The econometrician conjectures (i.e. guesses) the equation of the demand equation. For example, she guesses the equation is linear or non-linear. If she suspects demand is linear, then she suspects the equation is: Q 1 = β 0 + β 1 P 1 and she’ll estimate the parameters β 0 and β 1 from data on Q 1 and P 1 . But what if she suspects demand is non-linear? After all, there are an infinite number of non-
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