Loads of Doubts.

Posted by NM on Jun 12, 2014; 7:37pm
URL: http://discussion-forum.276.s1.nabble.com/Loads-of-Doubts-tp7592546.html

Q1.) A consumer has a utility function U(x,y)=max(2x+y,x+3y). He consumes (1,0) in equilibrium. Then which of the following is true?

a. Px =< Py
b. Px =< (3/2)Py
c. Px =< (2/3)Py
d. Px =< Py

(I think the answer should be "d". Not sure though.)

Q2.) A gambler has in his pocket a fair coin and a two-headed coin. He selects one of the coins at random, and when he flips it, it shows heads. Suppose that he flips the same coin a second time and again it shows heads.

Now what is the probability that it is a fair coin?
a) 0
b) 1/4
c) 1/5
d) None of the above

Q3.) 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 1, 2 or 3, 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 is 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.

Q4.) Consider market of a good with the following characteristic: There are three consumers of the good. Set of consumers is denoted by {1, 2, 3}. Each consumer wants to “consume” at most one unit of the good. Good can be bought only in non-negative integer quantities. Consumer i’s valuation of the first unit of the good is given by vi where v1 = 2, v2 = 4, v3 = 7. Given price p, consumer i’s demand correspondence is the following:
    xi(p) = 1 if vi – p  0
           = 0 if vi – p < 0
i.e. consumer will demand the unit for consumption if his valuation for it is greater than or equal to the price. Clearly, market demand function is given by x(p)= Summation(xi(p))
Now consider a monopolist producing the good at cost c per unit.

Suppose c = 0, the profit maximizing monopolist will produce
a) 0
b) 1
c) 2
d) 3

The value of c for which the profit maximizing monopolist produces either 1 or 2 units
a) 1
b) 2
c) 3
d) 4