Question$1$: $(14$ Marks$)($a$)$ The quantitative success of the economic sciences is disappointing when it is compared with that of physics. Its recurrent inability to predict and avert crises, including the current worldwide credit crunch is obvious. Why is this so$?$ Of course, modeling the madness of people is more difficult than the motion of planets, as Newton once said. But the goal here is to describe the behavior of large populations, for which statistical regularities should emerge. The crucial difference between physical sciences and economics or financial mathematics is rather the relative role of concepts, equations, and empirical data. Classical economics is built on very strong assumptions that quickly become axioms: the rationality of economic agents, the invisible hand and market efficiency, etc. Physicists, on the other hand, have learned to be suspicious of axioms and models. If empirical observation is incompatible with the model, the model must be trashed or amended, even if it is conceptually beautiful or mathematically convenient. So many accepted ideas have been proven wrong in the history of physics that physicists have grown to be critical and queasy about their models. Unfortunately, such healthy scientific revolutions have not yet taken hold in economics, where ideas have solidified into dogmas. In reality, markets are not efficient, humans tend to be over$-$focused in the short term and blind in the long term, and errors get amplified through social pressure and herding, ultimately leading to collective irrationality, panic and crashes. Free markets are wild markets. It is foolish to believe that the market can impose its own self$-$discipline. Reliance on models based on incorrect axioms has clear and large effects. The Black$-$Scholes model assumes that price changes have a Gaussian distribution, i$.$e$.$ the probability of extreme events is deemed negligible. Unwarranted use of this model to hedge the downfall risk on stock markets spiraled into the October $1987$ crash. Ironically, it is the very use of the crash$-$free Black$-$Scholes model that destabilized the market! In the recent subprime crisis of $2008$ also, the problem lay in part in the development of structured financial products that packaged sub$-$prime risk into seemingly respectable high$-$yield investments. The models used to price them were fundamentally flawed: they underestimated the probability of the multiple borrowers would default on their loans simultaneously. In other words, these models again neglected the very possibility of a global crisis, even as they contributed to triggering one. Surprisingly, there is no framework in classical economics to understand wild markets, even though their existence is so obvious to the layman. Physicists, on the other hand, has developed in physics, several models allowing one to understand how small perturbations can lead to wild effects. The theory of complexity, developed in the physics literature over the last thirty years, shows that although a system may have an optimum state $($such as a state of lowest energy, for example$),$ it is sometimes so hard to identify that the system in fact never settles there. This optimal solution is not only elusive, it is also hyper$-$fragile to small changes in the environment, and therefore often irrelevant to understanding what is going on$.$ There are good reasons to believe that this complexity paradigm should apply to economic systems in general and financial markets in particular. Simple ideas of equilibrium and linearity do not work. We need to break away from classical economics and develop altogether new tools, as attempted in a still patchy and disorganized way by behavioral economists and econo$-$physicists. But their fringe endeavor is not taken seriously by mainstream economics. Thus, there is a crucial need to change the mindset of those working in economics and financial engineering. They need to realize that an overly formal and dogmatic education in the economic sciences and financial mathematics is a serious part of the problem. In sum Economic curriculums need to include more natural science so that they can tackle real$-$world problems more accurately and efficiently.$($i$)$What is being explained? $($Title needed$)(2-$marks$)($ii$)$What is the explanation? $($A summary$)(3-$marks$)($iii$)$What conclusion can be drawn about the above explanation? $($Your point of view$)(3-$marks$)($b$)$ A remarkable fact is that many of the great scientists and mathematicians in history have a deep interest in music. Einstein, for example, was a devoted amateur violinist, and Newton is said to have been fascinated by the mathematical structure of musical compositions. If you want your child to pursue a career in science, you would be well advised to do everything you can to develop his or her interest in music.The above passage involves THREE fallacies. Mention each type of fallacy in a detailed way. $(6-$marks$)$