25 Matching Annotations
  1. Jan 2020
  2. Dec 2019
    1. What does SPNE predict (use backwards induction)?

      could you please explain this a bit more?

    2. Shepherd A: 120−2sA−sB

      is this the partial differential of the function above?

    3. The payoff from staying Silent (cooperating) in each period is: −2×(1+g+g2+g3+...)−2×(1+g+g2+g3+...)-2 \times (1 + g + g^2 + g^3 + ... ) Here I get -2 in each period, starting today. Discounting this, we add up -2 (today), −2g−2g-2g (next period), −2g2−2g2-2g^2 (the period after next), etc, as represented above. The payoff from Confessing right away (after which both players Confess always) is: −1−3×(g+g2+g3+...)−1−3×(g+g2+g3+...) -1 -3 \times (g + g^2 + g^3 + ... ) Formula for a geometric series (where 0<g<10<g<10<g<1): g+g2+g3+g4...=g/(1−g)g+g2+g3+g4...=g/(1−g)g + g^2 + g^3 + g^4 ... = g/(1-g) Note on Maths: The standard derivation of this, which is pretty neat, is in the text. This formula is an important one in economics (and beyond), particularly for discounting a constant stream of payoffs, e.g., stock dividends Thus cooperation in a single period is ‘weakly preferred’ (at least as good) if (−2)×(1+g+g2+g3+...)≥(−1)+−3×(g+g2+g3+...)(−2)×(1+g+g2+g3+...)≥(−1)+−3×(g+g2+g3+...)(-2) \times (1 + g + g^2 + g^3 + ... ) \geq (-1) + -3 \times (g + g^2 + g^3 + ...) g+g2+g3+...≥1g+g2+g3+...≥1g + g^2 + g^3 + ... \geq 1 Note on the intuition for the second formula: the left side is loss of future payoffs (-3 vs -2 forever from next period, so a loss of 1 per period starting tomorrow). The right side is gain in ‘the present’ period (getting -1 rather than -2), so it is un-discounted. g/(1−g)≥1g/(1−g)≥1g/(1-g) \geq 1 g≥12

      2019-20: you will not be asked to do this computation on the final exam, but you should understand the general idea

    1. Bee2024 finishing insurance problem from sixth problem set

      May be helpful in revising

    1. Power rule

      I will give you the formula for the power rule on an exam, but it wouldn't hurt to practice it!

    1. Nash proved that if we allow mixed strategies, then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium.

      It always has at least one Nash equilibrium (but it may only be a NE in mixed strategies).

    1. More volatile underlying assets will translate to higher options premiums, because with volatility there is a greater probability that the options will end up in-the-money at expiration.

      That's interesting

    1. The option is European and can only be exercised at expiration.No dividends are paid out during the life of the option.Markets are efficient (i.e., market movements cannot be predicted).There are no transaction costs in buying the option.The risk-free rate and volatility of the underlying are known and constant.The returns on the underlying are normally distributed.

      Some of the assumptions underlying the Black-Scholes model. Do these limit its realism and predictive power?

    1. In low-income countries the vast majority are unwilling to pay for effective drugs simply because they are unable to pay. Low-income nations need more price discrimination—and vastly lower prices—if they are ever to afford the world's most effective medicines.

      Does price discrimination help poor countries here? Which countries have more price-inelastic demand? Does PD increase social welfare for this case?

    1. She found a German seller offering packs of the same nappies she buys in Luxembourg for the same price she normally pays. Looking more closely at the unit price, however, Nadine realised that the German packs contained 140 nappies, whereas the packs in Luxembourg had only 90, making them much more expensive. She switched straight away to buying all her nappies from the German shop.

      If this was price discrimination... which country's consumers likely had the higher price elasticity?

    1. I think that the preservation of these documents could be seen as providing pure public good. We value that these have been preserved for posterity even if we don't visit the Magna Carta ourselves. What do you think?

  3. Nov 2019
    1. 3. Now draw the farmers’ ‘best response functions’ in a diagram.

      Worth covering in tutorial starting from here, focusing on intuition rather than algebra and calculus

    2. Do parts A and B; part C is optional enrichment

      Worth covering A-B in tutorial if time permits

    1. This second assumption, called diminishing marginal utility, will imply ‘risk aversion’!

      A student asked

      I want to ask why risk-averse has a decreasing marginal utility? Thank you.


      If someone has a decreasing marginal utility of income and they maximise expected utility then they will be risk averse.

      This is something that takes a long time to fully explain, and I try to give an explanation in the web-book and in lecture (and again in tomorrow's lecture).

      One simple intuition.: Risk averse essentially means "I will never take any fair gamble".

      E.g., "I'll never accept a bet with an equal chance of losing or gaining some amount X." How does diminishing MU of income explain this? If I have diminishing MU of income then my utility is increasing in income at a decreasing rate.

      The first units of income (e.g., going from 0 income to 15k income) add more utility than the later units of income (e.g., going from 15k income to 30k income) , which adds more than even later increments (e.g., going from 30k to 45k), etc.

      So "an equal chance of losing or gaining X" would not be attractive to such a person. Why not? Because relative to any point "losing X" reduces my utility more than "gaining X" increases it.

      E.g., in the above example, if you started at 15K income you wouldn't want to have an equal chance of losing or gaining 15K in income. Having 0 income would be terrible, while having 30k income would be better, but not 'that much' better. As we said, the utility difference between 0 and 15K is much greater than the utility difference between 15k and 30k... because of the assumption of diminishing marginal utility. So it's better to have 15k for sure than to have a 50/50 chance of 0k or 30k.

      The 'utility loss from losing 15k' is greater than the 'utility gain from gaining 15k'. As expected utility weights the utility of each outcome by its probability and sums these, in considering a 1/2 chance of losing 15k and a 1/2 chance of gaining 15k these probabilities weight equally, so I only need to consider "does the utility cost of losing 15k exceed the utility gain from gaining 15k" in this example. Because of diminishing MU, we know it does not. Nor does it for any "equal chance of losing or gaining some amount X". Thus this person is risk-averse.

      I hope this helps. Looking at the 'utility of income' diagrams may also be helpful.

    1. Two statistics about reducing your risk of an early death made headlines around the world recently. The first seems to be a great reason to add a four-legged friend to your life. It suggests that owning a dog is tied to lowering your chance of dying early by nearly a quarter. The second statistic claims that even a minimal amount of running is linked to reducing your risk of premature death by up to 30%. Ruth Alexander finds out what’s behind these numbers and we hear from epidemiologist, Gideon Meyerowitz-Katz.

      It's amazing that statistics like these... (seemingly without even minimal obvious controls for age etc.) get reported so naively in the media. Note that one of the interviewees suggests one approach that would provide evidence on the impact of pets on longevity ... random dog assignment. He seems to doubt the health benefits; I don't know, it seems plausible to me, but I'd like to see some real evidence.