DSE DOUBT

[Sris]

 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)


THIS IS FROM DSE 2009...PLZ REPLY

[knowpraveen]

The above maximization problem can be solved by using the Lagrangean multiplier method. So, we will have to maximize the utility function w.r.t the equation Px.X+Py.Y=1000. Now, we obtain the values of X and Y to be at 4 books and 80 movies which is against the constrain provided in Scheme 1. It is given that, the 250 INR has to be spent on books. So, 80x10 = 800 INR is spent on movies which is not possible. So, we bring the number of movies down to 75 and increase the number of books brought by 1, which is the next best alternative which maximizes the utility for the given functions.

Optimal Bundle is (5,75) for scheme 1.

The values of utilities for bundle (4, 80) is 44 and (5,75) is 43.5.

The scheme 2, is a special case of the above problem where we have the optimal bundle as (4,84) because we don't have the 250 INR alloted for books, constraint here.

Optimal Bundle is (4,84) for Scheme 2.

Hope, its clear.

[onionknight]

26. Maximize x^1/5*y^4/5 subject to 50(x-5)+10(y)=750 or 5x+y=100 [x>=5] . This is a simple cobb douglas maximization problem the solution to which is x=4 y=80. But, x must be greater than equal to 5 and hence x=5 y=75.

27. Maximize x^1/5*y^4/5 subject to 50(x)+10(y-x)=1000 or 4x+y=100. This is a simple cobb douglas maximization problem the solution to which is x=5 y=80.

[Sris]

THANK U....

[Sris]

DSE DOUBTS....PLZ SOLVE

1. WHICH OF THE FOLLOWING IS QUASI CONVEX (GIVEN f:R TO R)
A)f(x)= x^2
b) f(x)=cosx
c)f(x)=e^-x
d)f(x)=1/x if x not equal to zero and f(x)=0 if x=0

how to check for quasi convexity...

2.consider a strictly decreasing and differenciable and f:R to R. denote the derivative of f at x belonging to R by Df(x).which of the following is true
a) Df(x)>0 for some x belonging to R
B) Df(x)=0 for some x belonging to R
c) Df(x)=0 for some x belonging to (a,b) where a=0 for some x belonging to R

how to solve this

3. if f: R^n to R is twice differenciable ,concave and homogenous of degree 1 then the hessian matrix of f is
a) negative definite
b)positive definite
c)singular
d)non- singular
 
how to solve this...n from where shud i read to get hold of the topics asked in all d above Q

[knowpraveen]

This should answer the above questions. Cover these areas of Mathematical Economics -

https://www.economics.utoronto.ca/osborne/MathTutorial/QCCF.HTM

[knowpraveen]

Que 3. For a function to be concave, the Hessiant det has to be negative semidefinite ie it will be singular with the second derivatives both either negative or one of them negative.

Que 2. For a strictly decreasing function, the Derivative has to be negative for all possible values of X. There has to be an option D which says Dfx < 0, for all x.

[onionknight]

1.) all convex functions are quasi convex -> e^-x