Swinnerton-Dyer Conjecture by A. Wiles A polynomial relation f (x‚ y) = 0 in two variables defines a curve C0 . If the coefficients of the polynomial are rational numbers then one can ask for solutions of the equation f (x‚ y) = 0 with x‚ y ∈ Q‚ in other words for rational points on the curve. The set of all such points is denoted C0 (Q). If we consider a non-singular projective model C of the curve then topologically C is classified by its genus‚ and we call this the genus of C0 also. Note that C0
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cardinal approach 5.6 Consumer’s surplus 5.7 The ordinal utility approach to consumer behaviour: the indifference curve approach 5.8 Consumer’s budget constraint 5.9 Consumer’s equilibrium in the ordinal utility approach 5.10 Special cases 5.11 Price-consumption curve 5.12 Income-consumption curve 5.13 Price‚ substitution‚ and income effects 5.14 Derivation of the demand curve for a good 5.15 Inferior goods and Giffen goods 5.16 Let us sum up 5.17 Some key words 5.18 Some useful books
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ECM002 Business Economics Instructions: Please answer four out of the following six following questions: Question 1. Suppose Cola- Sol and Miniranda are the only two companies producing a particular type of cola drink in the soft drink industry. Both companies are considering launching a new drink with a light lemon twist. They can launch their products either at a low price or at a high price. The expected net payoffs are the following: If both companies choose a high price strategy‚ Cola-
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Topic 6 - The Theory of Consumer Behavior – the theory of utility • The theory of consumer behaviour may be analysed by either utility theory and / or indifference curve analysis. • Note: this course only requires students to be aware of utility theory. Indifference curve analysis is undertaken in year 2 and is not a requirement of this course Basic Principles of the theory of Consumer Behaviour • Consumers are rational optimisers • Consumers seek to maximise total utility • Utility is achieved
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Minicase 4 Yield Curve Hypotheses and the Effects of Economic Events CONCEPTS IN THIS CASE term structure of interest rates default risk risk premium yield curve expectations hypotheses segmented markets theory preferred habitat theory liquidity premium theory Your employer (a bank) has decided to offer five-year loans to its small business customers. You have been presented the task of determining what the appropriate minimum interest rate should be for the most creditworthy customer
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indifference curve(tangent to the income budget line or MRS = |w/p|). At this point A‚ the individual will work Ls1 hours‚ enjoy La leisure hours and enjoy an income of Ca. Assuming the individual has attained a source of non-labour income‚ for example inheritance or lottery winnings‚ represented by vertical distance ZX on the graph. The income budget constraint will now become a kinked line KXZ. The presence of non-labour income allows the individual to reach a higher indifference curve and the new
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−−−−−−−−−−−−−−−−−−− 4dx A B C = + + (x + 2)(x2 − 4) x − 2 x + 2 (x + 2)2 Then 4 = A(x + 2)2 + B(x2 − 4) + C(x − 2) which 1 implies A = −B = − C = 4 . Therefore 4 4dx 1 1 x−2 = ln + +C (x + 2)(x2 − 4) 4 x+2 x+2 3 dx Lorentz curves For 0 x 1‚ L(x) is the percentage of total income
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___________________________________________________________________________________________________ 1. Monopolistic competition: definition; characteristics 1-17 2. Demand curve 18-24 3. Price-output behavior 25-78 4. Efficiency aspects 79-88 5. Oligopoly: definition; characteristics 89-112 6. Concentration ratio; Herfindahl Index 113-140 7. Game theory 141-156 8. Kinked-demand curve model 157-176 9. Collusion; cartels; price leadership 177-194 10. Advertising 195-200 11. Efficiency aspects 201-204 12. Review of four
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Experiment 9: Growth curve of Serratia marcescens Abstract Bacteria grows by binary fission. The aim of this experiment is to follow the growth of Serratia marcescens in nutrient broth at 37oCby recording the changes in turbidity (cloudiness) by measuring the absorbance of visible light (600 nm) and also to prove that there is an increase in the cell number and not just in mass during the growth. In the experiment we measure the full growth curve of Serratia marcescens by measuring the absorbance
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creating as set of contour plots of DM’s implied utility function. Figure 1 plots a set of "indifference curves" assuming a utility function of U = X Y. FIGURE 1 U=X^1Y^1 100 U= 1 U= 8100 U= 6400 U= 4900 U= 3600 U= 2500 Y 60 80 40 U= 1600 U= 900 U= 400 U= 100 0 20 0 20 40 X 1 60 80 100 Marginal Rate of Substitution The slope of the indifference curve is called DM’s Marginal Rate of Substitution (MRS) and provides information with respect to tradeoff’s
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