# Mathematical economics Essay Dissertation Help

1.In what ways is the stone-Geary utility hnction鲈 ven by
v〓 (冯 一 洱
0)尼
(艿2一 豸20)’2superior to伍 e Cobb-Douglas utility hnction

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
0^F92豸
20) (7)
F92豸2=F92豸20+’2◇%一
`1豸
10-`2豸20) (8)

〓 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:
1/2
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,
C=(40,160;0.1,0.9)
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

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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