经济最有化相关问题，求高人解答

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

1、
Show in a diagram the opportunity sets for the classical maximizing problem in two variables with one constraint, where the constraint is :
①
②
③
④

2.Prove that:
①The two problems
              
subject to

x
               
subject to

x
have the same solutions.

②If
is a strictly concave function then the stationary point is a strict local maximum.

3. Solve diagrammatically, using contours, preference directions, and opportunity sets, the following problems:
①
subject to ;
②
subject to

4. Consider the problem of maximizing a quadratic from subject to the condition that the sum of the squares of the instrument variables equals unity;
               
subject to

x

Where A is a given symmetric matrix. Show that if
is the solution,then
equals the largest characteristic root of A. Illustrate the result geometrically if .Under what circumstances is

5. Consider the problem:

subject to

①Solve the problem geometrically.
②Show that the method of Lagrange multipliers does not work in this case. Why does not it work?

6. The portfolio selection problem is an example of a vector maximum problem. In this problem an investor must choose a portfolio ,where
is the proportion of his assets invested in the
security,
and The investor’s objectives relate to “return” and “risk”. The return on the portfolio is measured by the mean return, as given by the linear form:
            
Where
is a given row vector of mean returns on the
securities. The risk on the portfolio is measured by the variance, as given by the quadratic form:
                     
Where is a given
matrix of variances and covariances of returns, assumed positive definite. A portfolio is efficient if there is no other portfolio with either a higher and lower risk, a higher return at the same level of risk, or a lower risk at the same level of return.
①Show that the problem of maximizing return where the maximum risk is specified as :
      
Subject to

x
yields an efficient portfolio and
that the set of solutions to this problem for all
yields all efficient portfolios. What are the Kuhn-Tucker conditions for this problem?


②Show that if the minimum return were specified as
then the problem:
  
subject to

X
yields an efficient portfolio. What are the Kuhn-Tucker conditions for this problem?

7. Prove that the solution to the linear programming maximum problem
is a sub additive
function of the vector of objective constants c and a superadditive function of the vector of constraint constants,b,that is :

Where
and
are two
dimensional row vectors and
and
are two
dimensional colum vectors.

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：高人解答 Opportunity Dimensional Covariances Programming 经济 解答 高人