Due Date: Oct31, Monday – between 9 & 11 AM in room S 2.132 Please keep a copy of your assignment and show all your work clearly.

(1) Mr. J. Bond, a retired movie actor, consumes only grapes and the composite good Y (i.e. price of Y is £1). His income consists of £10000 a year from his investment fund plus the proceeds of whatever he sells of the 2000 bushels of grapes he harvests annually from his vineyard in Tuscany. Last year, grapes sold at £2 per bushel and Bond consumed all 2000 bushels of his grapes, in addition to 10,000 units of Y. This year, the price of grapes is £3 per bushel (and the price of the composite good Y is the same as before). If Bond has well-behaved preferences, will his consumption of grapes this year be greater than, less than or the same as last year’s? How about his consumption of the composite good? (Hint: Graph both years’ budget constraints and think about whether last year’s bundle is affordable to Mr. R).

(2) Suppose Carmela’s income is £100 per week, which she allocates between sandwiches and books. Sandwiches cost £2 each. Books cost £10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to £5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Carmela might have more than one utility-maximizing solution?

(3) Fiona requires a minimum level of consumption, to derive additional utility. For Fiona, U(X,Y) = 0 if X+Y<5
= X+Y otherwise.
Which of our usual assumptions about well-behaved preferences are violated in Fiona’s case?

(4) Consider the following utility functions over goods A and B. U = AB, and V = A2B. Compute the MRS for each of these functions, and evaluate these at the point (3,4). Explain whether these functions represent the same preference ordering....

...NATIONAL BOARD FOR HIGHER MATHEMATICS
AND
HOMI BHABHA CENTRE FOR SCIENCE EDUCATION
TATA INSTITUTE OF FUNDAMENTAL RESEARCH
Pre-REGIONAL MATHEMATICAL OLYMPIAD, 2013
Mumbai Region
October 20, 2013
QUESTION PAPER SET: A
• There are 20 questions in this question paper. Each question carries 5 marks.
• Answer all questions.
• Time allotted: 2 hours.
QUESTIONS
1. What is the smallest positive integer k such that k(33 + 43 + 53 ) = an for some positive
integers a and n, with n > 1?...

...“Problems Encountered by Irregular Students on their Academic Subjects”
Chapter 1
Introduction to the Study
Students encounters many and different problems during their school years. These problems vary differently during their study years. It could be as simple as missing a homework or getting late in class. Or it could be as severe as getting dropped in a certain subject or worse failed the subject.
Several of these...

...33-48, July-September 2012 33
The Position of Rough
Set in Soft Set:
A Topological Approach
Tutut Herawan, Universiti Malaysia Pahang, Malaysia
ABSTRACT
In this paper, the author presents the concept of topological space that must be used to show a relation between rough set and soft set. There are two main results presented; firstly, a construction of a quasi-discrete
topology using indiscernibility (equivalence) relation...

...A STUDY ON PROBLEMS AND PROSPECTS OF GARMENT INDUSTRY
AT TIRUPUR DISTRICT
1. Name of the company
2. Type of ownership (please tick respective one)
a) Solo partnership [ ] b) Partnership [ ]
c) Pvt ltd company [ ] d) Public limited company [ ] e) others [ ]
3. Are you focusing on: - [ ] export / [ ] domestic market [ ] both
4. How long you engage in garment industry
a) Below 5 yrs [ ] b) 5 yrs – 10 yrs [ ]
c) 10 yrs – 15 yrs [ ]...

...Vicente, San Pedro, Laguna
Problems Encountered by 3rd Year and 4th Year Students of
Amazing Grace School while Selecting Course in
College this SY 2011-2012
By:
Acupan, Cheyanne Kleir T.
Amuan, Mark Benjamin D.G.
Galang, Allan Gerold M.
Manalo, John Daniel T.
Pinpin, Jose Maria Emmanuellee
Remoquillo, Katrina L.
To, Efraim Julian M.
2011-2012
A Partial Requirement for Graduation in High School SY 2011-2012
Introduction
Various...

...-------------------------------------------------
Set (mathematics)
From Wikipedia, the free encyclopedia
This article is about what mathematicians call "intuitive" or "naive" set theory. For a more detailed account, see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory.
An example of a Venn diagram
The intersection of two sets is made up with the objects contained in...

...Eady
Problems Facing Human Services Clients
Human service professionals have a very rewarding career. They are given the opportunity in more ways than one to provide help to those who are in need of it. While this profession can be rewarding, unfortunately, this area of expertise can be emotionally exhausting because of the many problems that the human service clients face and the lack of resources that are available to them. These...

...Essay 1
Set And Subset of Assemblages
Devanshi Purohit
Each assemblage is an emergent entity which can combine with others to produce ever larger assemblages; both assemblages and their component parts are thus characterized by reciprocal relations of exteriority (Parr, 2005). This statement poses a question that whether it can be considered that each assemblage is made up of smaller assemblages as well as there is a larger universal assemblage that each assemblage is a...