DSE 2013 Doubts

Posted by ViV on May 29, 2014; 1:42pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2013-Doubts-tp7590991.html

The next TWO questions are based on the following model:
Suppose that there are two goods, which are imperfect substitutes of each other. Let p1, p2
denote the price of good 1 and good 2, respectively. Demand of good 1 and
good 2 are as follows
D1(p1, p2) = a - p1 + bp2; D2(p1; p2) = a - p2 + bp1
where a > 0 and 1 > b > 0. Both of the goods can be produced at cost c per
unit.
QUESTION 7. Find the equilibrium prices, when good 1 and good 2 are
produced by two different monopolists.
(a) p1 = p2 = a+c/2-b

(b) p1 = p2 = a+c/1-b

(c) p1 = a+c/2-b, p2 = a+c/1-b

(d) p1 = a+c/1-b,  p2 = a+c/2-b

QUESTION 8. Find the equilibrium prices, when both the goods are pro-
duced by single monopolist.
(a) p1 = p2 = a+c-bc/2-b

(b) p1 = p2 = a+c-bc/1-b

(c) p1 = p2 = a+c-bc/2(1-b)

(d) p1 = p2 = a+c-bc/2



Suppose three players, 1, 2 and 3, use the following procedure to allocate 9 indivisible
coins. Player 1 proposes an allocation (x1; x2; x3) where xi is the number of
coins given to player i. Players 2 and 3 vote on the proposal, saying either
Y (Yes) or N (No). If there are two Y votes, then the proposed allocation
is implemented. If there are two N votes, the proposal is rejected. If there
is one Y vote and one N vote, then player 1 gets to vote Y or N. Now, the
proposal is accepted if there are two Y votes and rejected if there are two N
votes.
If 1's proposal is rejected, then 2 makes a proposal. Now, only 3 votes
Y or N. If 3 votes Y, then 2's proposal is accepted. If 3 votes N, then the
proposal is rejected and the allocation (3; 3; 3) is implemented.
Assume that, if the expected allocation to be received by a particular
player by voting Y or N is identical, then the player votes N.

QUESTION 28. If 1's proposal is rejected and 2 gets to make a proposal,
her proposal will be
(a) (0; 5; 4)
(b) (0; 4; 5)
(c) (0; 6; 3)
(d) (0; 3; 6)
QUESTION 29. 1's proposal will be
(a) (5; 0; 4)
(b) (4; 0; 5)
(c) (3; 6; 0)
(d) (6; 3; 0)
Just solve 29 only.

QUESTION 42. A bowl contains 5 chips, 3 marked $1 and 2 marked $4.
A player draws 2 chips at random and is paid the sum of the values of the
chips. The player's expected gain (in $) is
(a) less than 2
(b) 3
(c) above 3 and less than 4
(d) above 4 and less than 5

QUESTION 44. A certain club consists of 5 men and 5 women. A 5-
member committee consisting of 2 men and 3 women has to be constituted.
Also, suppose that Mrs. F refuses to work with Mr. M. How many ways are there of constituting a 5-member committee that ensures that both of them
do not work together?
(a) 50
(b) 76
(c) 108
(d) None of the above

QUESTION 45. Suppose, you are an editor of a magazine. Everyday you
get two letters from your correspondents. Each letter is as likely to be from
a male as from a female correspondent. The letters are delivered by a post-
man, who brings one letter at a time. Moreover, he has a `ladies rst' policy;
he delivers letter from a female rst, if there is such a letter. Suppose you
have already received the rst letter for today and it is from a female corre-
spondent. What is the probability that the second letter will also be from a
female?
(a) 1/2
(b) 1/4
(c) 1/3
(d) 2/3

QUESTION 46. On an average, a waiter gets no tip from two of his cus-
tomers on Saturdays. What is the probability that on next Saturday, he will
get no tip from three of his customers?
(a) (9/2)e^-3
(b) 2e^-3
(c) (4/3)e^-2
(d) 3e^-2