micro doubts

[smriti]

suppose that a typical graduate student at the Delhi school of economics lives in a two good world, books(x) and movies (y), with utility function u (x,y) =x raised to power 1/5*y raised to power 4/5, prices of books and movies are 50 and 10 respectively. Suppose the university is considering the following  schemes.
Scheme 1 :750 is paid as scholarship and additional 250 as book grant. Naturally book grant can only be spent on books.
Scheme 2 : 1000 as scholarship and gets one movie fee on each book they purchase.
Believing that books and movies are perfectly divisible. Compute the optimal consumption bundle under each scheme.
      Optimal consumption bundle under scheme 1 is
a) (4 books, 80 movies)
b) (5 books, 75 movies)
c) (6.5 books, 57.5 movies)
d) (10 books, 80 movies)

       Optimal consumption bundle under scheme 2 is
a) (4 books, 80 movies)
b) (4 books, 84 movies )
c) (5 books, 75 movies)
d) (5 books, 80 movies)

16. A consumer has a utility function U(x,y) = 10(x raised to power 2 +4xy + 4y raised to power 2(only y raised to power )+ 20. Which one of the following statements is true?
a) the goods are imperfect substitutes
b) the goods are perfect substitutes
c) the goods are perfect complements
d) none of the above

[mukund sharma]

the answer to the first question under the scheme 1 is (5, 75) as the utility is maximised under the given budget constrained of 1000 rs with 750 as scholarship is spent on the movies and the rest 250 book grant on the books which will maximize his utility.
under scheme 2, since he gets all the thousand rs on the scholarship and gets free movie ticket for each book purchased. he will spend 250 rs to get 5 books and 750rs on 75 movie tickets with also five free on the books hence the utility is maximised at 5 books and 80 movie tickets.

[Smriti]

How to solve? what will be the budget constraint? i AM unable to solve

[a.m]

For the second question i am getting (4,84) someone kindly elaborate !

[Smriti]

under scheme 1 , why will he spend full 750 on movies ? H might want to spend a part of it on books

[mukund sharma]

if he tries to spend any other amount of 750 on books his utility will not be maximized . the best option is that u can go by options

[sweta]

 @A.M.
my ans is comin (4,80) for q2.

as the budget constraint is 50X+ 10Y=1000  and U= x^1/5*y^4/5

solving with the help of langrangian method

x=4 and y =80

i think (though it can be wrong) the same shd b the ans 4 Q1. TOO
@ SMRITI do u hv the ans 4 the ques??