M3B Mathematics of Business Department of Mathematics Question Examiner's Comments Q 1 Q 2 Q 3 – Overall result: mean 11.3, standard deviation 4.3. – In question c)(ii) it should rather be "intercept" than "intersection". This was announced orally during the exam. – When you make a case distinction, please beware that the converse of x_1 < x_2 is x_1 ≥ x_2, rather than x_1>2. – Overall result: mean 7.7, standard deviation 4.9. – For c)(iii) Beware that utilities are usually not injective. That is, u(x) = u(y) implies that x ~ y, but not necessarily x=y. – Moreover, that a utility is increasing means that x ≤ y implies u(x) ≤ u(y). However, u(x)≤ u(y) does not necessarily imply that x≤ y (you are in a higher dimensional space!) – In (a) the point was to prove that u(x) ≤ u(y) iff x is less preferred than y. – When you want to prove an equivalence, please make sure that you prove both implications. – When you differentiate a function like in (b)(ii) please don't supress the arguments of the function. The argument is quite important here! – A crucial point for the proof of the inequality at (2) is that you show that the two integrands coincide at the left endpoint of the integration region. Then you can derive by the Slutsky Equation that the integrand on the right hand side grows faster than the one on the left hand side. This means the the integrand on the left hand side will be smaller than the one on the right hand side, such that one obtains the respective result on the level of the integrals. – Overall result: mean 13.5, standard deviation 4.7. – In part (h), neither the supply curve nor the demand curve change. That means the market price and quantity will not be a point were the to curves intersect. That is, because we are not in an equilibrium any more. Indeed, this means that there is a whole range of possible market prices. One can only determine the lower and upper bound of the price and the actual outcome will depend on the negotiation power of either side. – Overall result: mean 9.5, standard deviation 3.9. – For (a)(iii) some of you mentioned a factory that produces pipelines. However, some answers implied that the radius of the pipelines is an input factor. But that's a very abstract input factor. It should rather be the material that is used. – In c) it is not advantagous if you give more than one result and the results are mutually exclusive (something like "GDP increases because of A and GDP decreases because of B") – In part c)(iv) one short-coming only. You couldn't earn more marks with mentioning more short-comings. However, you were supposed to explain that short-coming, not only claim it. Finally, you were asked how to solve the short-coming of GDP as a measure of the county's welfare. You were not asked how to solve a country's welfare problems, that's something else (so answers that suggested to incentivise enviromental behaviour missed the point). Moreover, some of you mentioned that healthcare and education were ignored by GDP. That's not true, only some aspects are ignored that are done without a payment. Q 4 Printed: 27/07/2018 11:46:57
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