Review Questions 1Yuya Takahashi7=26=20126.96.36.199.5.6. Consider the market for orange juice. Demand and supply are summarized as follows:Dt=°+±Pt+²Xt+"tSt=³+´Pt+µZt+ut;whereXtis the price of apple juice at timetandZtis the price of orange at timet: "tandutare thedemand and supply shock, respectively. The equilibrium price and quantity traded are determined inthis model.(°; ±; ²; ³; ´; µ)is the set of parameters in the model.(a) What can we expect about signs of(±; ²; ´; µ)?The own price elasticity is expected to be negative;± <0:Meanwhile, since apple juice is a com-plement, the cross price elasticity should be positive;² >0:We usually expect the supply functionto be positively sloped, so´ >0:Finally, a high value ofZtis considered to be a negative supplyshock, soµis expected to be negative.(b) One analyst wanted to estimate±:He collected data on the quantity traded and the price in thismarket for many years;fQt; PtgTt=1:Then he ran OLS, regressingQton constant,Pt, andXt.Then, he obtained the positive estimate for±!Explain possible reasons of why this happened.As was shown in p.21 of lecture note 2, the coe¢ cient ofPin the proposed regression is not±:Aswe can infer from the graph, if the demand shock (") is much more volatile than the supply shock(u), it°s possible that we observe a positive coe¢ cient on P.(c) How would you estimate±?Clearly state a set of conditions that should hold for your estimationstrategy to work.Solve the supply and demand:Pt=³°°±°´+µ±°´Zt°²±°´Xt+ut°"t±°´Qt=±³°°´±°´+±µ±°´Zt°´²±°´Xt+±ut°´"t±°´:1
This shows thatPand"are correlate, soPis endogenous in the demand equation. At the sametime, this solution showsZa/ects the equilibrium price. Therefore, if
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- Spring '08
- Supply And Demand, OLS, zt