(h) (6 points) Explain why a Bertrand competition in di/erentiated product markets with identical°rms (identical cost functions) does not achieve thep=MCcondition.(i) (6 points) Consider a two-°rm industry producing two di/erentiated products indexed byi= 1;2:The inverse demand functions are given byp1=3°2q1°q2p2=3°q1°2q2:Assuming zero production cost, calculate Cournot-Nash equilibrium prices (pC1; pC2).(j) (6 points) Consider the market for tomatoes, which we assume is a homogeneous product. You havedata on the quantity and the price of tomatoes over 100 weeks. You want to estimate the demandfunction for tomatoes (i.e., the e/ect of price on the quantity demanded). Explain why regressingthe observed quantity on the price (and on other demand shifters) by OLS is NOT likely to giveyou the right price coe¢ cient in the demand function.(k) (6 points) Explain why a high market share does not necessarily mean a high market power (youdo not have to cover every aspect of the problem; you can focus on a speci°c case and/or you canuse any example to make your point clear).2. (34 points in total)Download the dataset ps1. The °le includes hypothetical data on 1000 °rms. Foreach °rm, there are observed output (Y), capital input (K), labor input (L), wage rate that the °rmpays (w),and productivity shock (°).We would like to estimate °rms±production function in thisindustry:Y°i=CK°iL±i°iwhereY°iis the true output andCis a constant. Our interest is to estimate°and±:Taking log givesy°i=c+°ki+±li+²i:wherec= lnC,y°i= lnY°i; ki= lnKi; li= lnLi;and²i= ln °i:We observe output with a measurementerror"i;yi=y°i+"i;wherey
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