Q&A final
You will find below my answers to the questions you e-mailed me to regis.renault@u-cergy.fr. If you want to ask more questions, just send them to the same address "Q&A final" as the e-mail's subject. I will answer them in the same way.
March 19
Q I am reviewing for the exam and have a question about the Chapter 1. When do we need the FOC=0 and the second order condition >0. Is it the FOC of the profit? What's these rules for?
A When you max a function you need a FOC, which usually is that first deriv. is zero (but not always). But this condition is not sufficient (just necessary). It is however sufficient if the function is quasiconcave. To estaglish that this is the case, we check that whenever first deriv. is zero then the second deriv. is <0. Here we show that if demand is \rho-concave with \rho>-1, then profit is quasiconcave (with constant marginal cost, or actually with increasing marg. Cost as you were supposed to show in problem 1).
Q And referring to the CHapter4 and 5 in the slides, what are the chapters in the book?
A You can find material related to chapter 4 in Tirole’s book (chapters 2 and 7). Chapter 5 is based on my chapter on “Firm pricing with consumer search” (nothing in Tirole).
Q Did we cover "pricing and quantity discrimination" (price discrimication with resespect to the customer type)
A We did not do the formal analysis (writing down the maximization problem with all the IC and IR constraints and solve it). We did however, discuss the main issues using a picture. Similar pictures can be found in my chapter on price discrimination with Simon Anderson, which I believe can be downloaded online on his website http://economics.virginia.edu/people/sa9w under other research papers.
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Q I also tried to review the previois problem sets, but also would like to know whether we covered the topic in relation to white burgandy question (firm location choice)
(I couldnt attend the class on 9 Feb and couldn't catch what's been covered on that day.)
A You should be able to analyze a Hotelling model with one firm at each end of the segment although we have not spent much time on this (you should know the case with linear transport costs). But we have not done the product information disclosure problem, which was in that particular application.
Q In Varian model, price distribution can be written as F(P). Could you please explain how to interpret this distribustion? Given that F(r) =1, F(p_low)=0, then I can consider this the probability that the price is lower than p-value?
A The distribution function of a random variable, usually denoted F, is defined as the probability that the random variable falls below some level: F(x) is the probability that RV X is <= x. That is a definition from probability theory. It applies to price distributions in mixed strategies and to the distribution of the match value in a random utility model. So I guess the answer to your question is yes.
Q similary, in the discrete choice with random utility, F distribution can be derived. But here I wonder why F(ei - (Pi - Pj/m)^(1/n-1) rather than F(ei)?
A I am not sure why you have ^[1/(n-1). It should be to the power (n-1). Thee are (n-1) competing products. So the probability that they are all worse than product I (so the consumer buys product i) is the probability that one of them is worse than I, raised to the power (n-1) (because of the assumption that the \epsilon_j’s are i.i.d.).
It is the same as when you look for a symmetric mixed strategy with n firms: the probability that the price of one firm is less than the price of its (n-1) competitors is (1-F(-)]^(n-1).