review questions_ak part2.pdf

review questions_ak part2.pdf - Review Questions 1 Yuya...

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Review Questions 1 Yuya Takahashi 7 = 26 = 2018 1. 2. 3. 4. 5. 6. Consider the market for orange juice. Demand and supply are summarized as follows: D t = ° + ±P t + ²X t + " t S t = ³ + ´P t + µZ t + u t ; where X t is the price of apple juice at time t and Z t is the price of orange at time t: " t and u t are the demand and supply shock, respectively. The equilibrium price and quantity traded are determined in this 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 function to be positively sloped, so ´ > 0 : Finally, a high value of Z t is considered to be a negative supply shock, so µ is expected to be negative. (b) One analyst wanted to estimate ±: He collected data on the quantity traded and the price in this market for many years; f Q t ; P t g T t =1 : Then he ran OLS, regressing Q t on constant, P t , and X t . 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 of P in the proposed regression is not ±: As we 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 estimation strategy to work. Solve the supply and demand: P t = ³ ° ° ± ° ´ + µ ± ° ´ Z t ° ² ± ° ´ X t + u t ° " t ± ° ´ Q t = ±³ ° °´ ± ° ´ + ±µ ± ° ´ Z t ° ´² ± ° ´ X t + ±u t ° ´" t ± ° ´ : 1
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This shows that P and " are correlate, so P is endogenous in the demand equation. At the same time, this solution shows Z a/ects the equilibrium price. Therefore, if
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