Mathematical economics Essay Dissertation Help

1.In what ways is the stone-Geary utility hnction鲈 ven by
v〓 (冯 一 洱
(艿2一 豸20)’2superior to伍 e Cobb-Douglas utility hnction
勿 =Ch,Fl(豸2)′
2,where尼 +屁 =1on both血 nctions?Exp!ain yow ansWer。
2.Provide an econo∏ lic interpretation ofthe3-Good linear expenditure system。
F91冯 =F91豸10+刀l◇卿 一F91而
20) (7)
10-`2豸20) (8)
凡 九
〓 p丿%0+尼 ◇留 一 n艿10T凫 豸20) CD
3.The utⅡty-of-wealth hnctons for three individuals are showrl below:
Person1∶ 笏 = y
Person2: 笏 = 0· 8`
Person3∶ 纫 = y2
Classi夕 伍ese individuals wi伍 respect to their attitudes towards Ⅱsk。 Provide an
intuitive exp1anation ofthe risk-attitude ofeach individual。
4.Describe in Words the meaning ofdecreasing,∞ nstant and increasing Ⅱsolute
risk aversion。 Given the exponential utility hnction E/【 购=-eaw;a>o
a)Does the functon exhibh positive mar红nal utⅡty and risk averson?
bJ Does伍 e hnction h叩 e decreasing absolute risk aversion?
c,Does the血nGtion have∞nstant absolute risk aversio田

5.suppose an individual with a utility亠 of-weal伍 mncti。n勿 =J/1/2faces the
following Ⅱsky prospect,
Calculate the‘ cα忉inty equilˇ `almr wealth to thk GaInble。 What、 maximum
prelllil】 m this person would be wⅡ Ⅱng to pay an insurance company to proteGt
against this speciflc risk?show your calculations。
6.Derive伍e demand funcuons。btained iom maximizing伍e utility hnction
u=xρ饧su凵 ectto budget constr缸 nm=2×1+4劫 。show thatthe demand血 nctions
sati呻 the⑶ homogeneity andthe fb)negativity properties。
7.DescⅡbe whatthe prospect-theory states and explain in what ways it dffers
各om the expected util” 仇eory。 Explain which of伍 ese theoⅡ es is be⒒ er。
8.One ofthe central elements ofprospect theory is the idea ofloss aversion。
Explain the concept ofloss aversion and how it differs frorn risk aversion。 C;ive
one example ofa real、vorld phenomenon that can be explained by loss aversion。
9.Distinguish between systematic and l1nsystematiG risk ofa portfolo。 What role‘
does systematic risk play in the cap⒈ 刀d asρet pⅡcing Fnodel?ExplaⅡ l your answer。
10.Demonstrate that Wickse11’s law,together wi伍 伍e assumptions ofpositive
marginal productivities,and the law ofdhninishing rnarginal producjv⒒ ies
guarantee that isoquants`vⅡ l have the desirable convex-to-the-origin shape。
Descrbe the ecOnom忆 m∞血ng ofconve虹ty ofisoquants。

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