DSE 2009 Q. 26 and 27

Posted by Nag27 on Apr 20, 2013; 5:25am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2009-Q-26-and-27-tp7580134.html

Hi, Can anyone explain the solution of Q. No 26 and 27 in the DSE 2009 paper? The question and the options underneath are as follows:


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^(1/5) y^(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 fellowship and additional 250 as book grant. Naturally, book
grant can only be spent on books.
Scheme 2: 1000 as scholarship and gets one movie free on each book they purchase.
Believing that books and movies are perfectly divisible, compute the optimal
consumption bundle under each scheme.

26. 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, 50 movies)


27. 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)

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I don't understand how to include the 250 books grant into the optimisation problem.