武汉大学数理金融考研复试试题原版

武汉大学经济与管理学院

科目名称：高级宏微观经济学               科目代码：

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1.(30’)Consider the utility function u=file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-11933.png

(1)Find the demand functions for goods 1 and 2 as they depend on prices and wealth.

(2)Find the compensated demand function h(.)

(3)Find the expenditure function, and verify that h(p,u)=file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-29943.pnge(p,u).

(4)Find indirect utility function, and verify Roy’s identity.

2.(30’) Suppose that in a two-commodity world,the consumer’s utility function takes the form u(x)=file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-9991.png.

(1)Show that when file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-1648.png=1，indifference curves become linear.

(2)Show that as file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-14487.pngfile:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-23921.png0, this utility function comes to represent the same preference as the generalized Cobb-Douglas utility function u(x)=file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-30629.png

(3)Show that as file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-7856.pngfile:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-22732.pngfile:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-11313.png,this utility function becomes Leontief-form, u(file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-16008.png)=Min{file:///C:/Users/ADMINI~1/AppData/Local/Temp/ksohtml/wps_clip_image-27873.png}

(4)Compute the Walrasian demand and indirect utility functions for linear utility function as that in(1).

3.(40’)

(1)  State the basic model of new-classical growth model (Solow Model) and its economic implication.

(2)  Why the model is considered as an exogenous model?

(3)  What is the convergence hypothesis implied in this model?