Dear Prof De Fraja,
Before I move onto some questions about the module, I’d like to thank you for teaching it in a most enjoyable way – the references to the practicality of the content were particularly interesting.
I might be making a typical blunder by thinking this, but with the Paashe price index, the slides state that the ‘usual price index proposed for indexation is the Paasche quantity index (the Consumer’ Price Index)’. However, at least for me, the Paasche price index makes more sense: the CPI shows the weighted change in price, but doesn’t take into account that consumers may change their choices after the change and thus do not need full indexation to receive the same utility. Wouldn’t the price index be a better representation of CPI given that here prices change, while the quantity remains constant?
On slide 78 of section 3 to derive the slope of the budget constraint we bring the two states Cna and Ca together by eliminating K. Perhaps this is rather pedantic of me, but is there any reason that k is eliminated rather than gamma or m (income) or is it just coincidence?
On slide 81 of section 3 we analyse how a consumer’s risk attitude can alter whether they prefer the utility of the expected value or the expected utility. You highlighted the point that to do this we are using a cardinal concept of utility which is potentially impossible to have, philosophically speaking. I just wanted to check that my understanding of why this is cardinal is correct.
We are using a cardinal concept of utility because we are not just ranking bundles given their utility score, but using the score to come up with an ‘average’ (when finding the expected utility) and then comparing that to the U(EM). This is because an ordinal utility function doesn’t have any linear relationship to the ‘true’ utility amounts (if we assume this is theoretically possible), but just ranks them in the correct order. Therefore, if we found this average using an ordinal utility function there is no suggestion that this will be in the correct position in the ranking.
On the topic of Mixed Strategy Nash Equilibria I have consulted the textbook, youtube and your notes, but am still puzzled by one thing. A player will beindifferent between strategies if their predictions about the other player’s probability of choosing strategies makes their own pay-off’s equal to each other. If this player is indifferent then what incentivises them to assign probabilities to their strategies that will make the other player indifferent and so make it a Nash Equilibirum. If the player is indifferent then they receive no additional payoff from assigning probabilities to their strategies that makes a Nash Equilibrium unlike in a Pure Strategy where deviating would give a lower pay-off. What is the inventive to each player to keep the system in a Nash Equilibrium? Gibbons argued when introducing the topic to think that the other player is a mind-reader and thus if you changed your probabilities (because you are indifferent) the other player would know this and thus would no longer be indifferent and the Nash Equilibria would break down making you worse-off. This doesn’t seem like a reasonable assumption to make, however is this indeed the case because we assume ‘common knowledge’ in these models? In practical applications of game theory are additional assumptions introduced in mixed games that take account of this? (I’m sorry, that was one a long one…)
Thank you very much for answering these questions for me, I do have other’s but I will go and see my assigned tutor first about them in his office hour.
Kind Regards,
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First of all thanks for the kind words about my lectures. I love the human viewpoint of economics (this is why I dislike the way the subject is taught at A-levels), and I am pleased when I can convey this to students.
As to your questions.
There is not a “better” index. Each measure different things, and for each an argument can be made one way or the other. In the end, you have to choose one. In practice, of course life is further complicated by the fact that the basket itself changes for year to year (cassette tape players, and CD and VCR and DVD players are replaced by mp3 downloads, etc)
Cardinal utility implies that it makes sense to say that you prefer one basket three times more than another. This does not make sense, hence we do not use cardinal utility when comparing baskets of goods. Just as you cannot say that an oven is twice as hot as another. Instead you can say that a dog weighs twice as another. When we compare lotteries, however, we are in a slightly different position than when we compare baskets of bread and wine, as things are anchored down by the concept of certainty equivalent, so we can say whether a person is risk averse, or even that a person is more risk averse than another.
You are of course right in arguing that, since I am indifferent between strategies, why should I bother randomise with the exact probability to ensure indifference of my opponent. One story is the “mind reader” you report from Gibbons. Another is indifference given beliefs. Suppose you are playing a football match in a minor league in Tajikistan, and you are called to kick a penalty. You know that every Tajikistan goalkeepers always dive to the same side, and so there are two kinds of Tajikistani goalkeeper, those that dive to the right and those that dive to the left. You problem is that you don’t know which type you face. There is only one proportion of the two types that makes indifferent between kicking left and right, and you will do so if that is the proportion in the population, which you have learnt before going over to play this match. People have shown that you can have an evolutionary story which will ensure that proportions of type evolve in the exact right proportion through slow genetic mutations.
Microeconomic Theory L12302 