Re: Micro

Posted by arpita lahiri on
URL: http://discussion-forum.276.s1.nabble.com/Micro-tp5202707p5208823.html

(Problems 1-3 are based on the following information) Consider a two-person (A and
B) two good (x and y) competitive exchange economy with externalities. A has utility
function
uA = 2(min{xA, yA}) - xB
B has utility function  
uB = 4xB +4yB
Both have the nonnegative quadrant as a consumption possibility set. A’s initial
endowment is 12 units of x and 12 units of y; and B’s initial endowment is 12 units of
x and no y.
1. Consider the following allocations:  
i) ((xA, yA),(xB, yB)) = ((24, 0), (0, 12))  
ii) ((xA, yA),(xB, yB)) = ((12, 12), (12, 0))  
Which of the following is true about the allocations above?
a) Only i) is pareto efficient  
b) Only ii) is pareto efficient  
c) Both i) and ii) are pareto efficient  
d) None of the above  
 
2. Example(s) of competitive equilibrium allocation is(are)  
a) ((xA, yA),(xB, yB)) = ((24, 0), (0, 12))  
b) ((xA, yA),(xB, yB)) = ((12, 12), (12, 0))  
c) ((xA, yA),(xB, yB)) = ((24, 12), (0, 0))  
d) All of the above  
 
3. An example of competitive equilibrium price is  
a) (4/9, 5/9)  
b) (5/9, 4/9)  
c) (1, 0)  
d) (0, 1)  
 
*Additional exercise(not part of the quiz): Determine the set of all pareto efficient
allocations and competitive equilibria.
 
4. Let X be distributed uniformly on the interval [-1, 1] i.e.  Probability distribution  
function of X is given by F(x) = (x+1)/2 for -1 =  x = 1
Probability distribution function of Y = |X| is given by
a) G(y) = y for 0 = y = 1  
b) G(y) = 1 for 0 = y = 1  
2
c) G(y) = y  for 0 = y = 1  
d) None of the above.  
 
5. There is a pile of 18 matchsticks on a table. Players 1 and 2 take turns in removing  
matchsticks from the pile, starting with player 1. On each turn, a player has to
remove a number of sticks that equals either 1or 2, such that the number of matchsticks that remain on the table equals some non-negative integer. The player,
who cannot do so, when it is his /her turn, loses. Which of the following statements
true?
a) If player 2 plays appropriately, he/she can win regardless of how 1 actually  
plays.
b) If player 1 plays appropriately, he/she can win regardless of how 2 actually  
plays.
c) Both players have a chance to win, if they play correctly.  
d) The outcome of the game cannot be predicted on the basis of the data given.  
 
An n × n chessboard is coloured in the following way: the (i, j) square (that
is, the square on the ith row and jth column) is coloured white if (i + j) is ev
and black if (i + j) is odd. A coin placed on the (i, j) square can be moved to
2 2
(i’, j’) square if (i – i’)  + (j – j’)  is an even number.
i. if a coin can be moved from one square to another, then the squares mus
be of the same colour.
ii. For n even,  it is possible for a coin to travel from the square (1, 1) to th
square (1, n) by a sequence of moves.
Which of the following statements is true?
a) Both i and ii are true.  
b) i is true and ii is false.  
c) i is false and ii is true.  
d) Both i and ii are false.  

how to get the ans