Loads of Doubts.

[NM]

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

[Arushi :))]

fr 1st u have  written a & d as same ..

[Granpa Simpson]

1) c.

[NM]

My bad. (d) was supposed to be Px < Py

And why (C)?

[Granpa Simpson]

1) the consumer basically has two options of utility to choose from when he is choosing in equilibrium (0,1) it means his utility is dependent on U=2x+y, if he would have chosen y then x+3y wud have been his utility level..now he is choosing x implies MU(x)/Px for 2x+y is greater than or equal to MU(y)/Py for x+3y because if it wud have been the other way round he wud have preferred to consume y and would have been on x+3y..thus from this condition we get:
2/Px>=3/Py
On rearranging you will get the answer as Px<=(3/2)*Py...sorry i misstated as c it wud be b.

[Dreyfus]

For the 4th ques....it must produce 2 units when c=0 and c=1 when it produces either 1 or 2 unit(s)

[NM]

Vaibhav, can you please explain the working? :)

[Dreyfus]

And for q2 I m getting 1/5

[Granpa Simpson]

2) will be 1/5..use Bayes theorem and u will get the answer..Vaibhav did u solve it using Bayes Theorem..??

[Dreyfus]

Yes I used Bayes theorem...

[Dreyfus]

Sry ...its bit tedious for me to type my workings right now.....and u won't be able to understand my writing if I upload the snapshot of my workings.....

[NM]

Why will the monopolist not produce 3 units of the good when c=o? And how did you determine p?

[Granpa Simpson]

The monopolist will not produce 3 units of goods because if he does so he will have to keep his price at Rs. 2 and his revenue will be Rs 6, similarly if he produces one unit it means that his price is set at Rs 7 which will fetch him a revenue of Rs 7 however if he produces 2 units means his price is set at Rs 4, and his revenue is Rs 8..Clearly profit is maximized when he sets his price at Rs 4 since 8>7>6. (It is assumed that the firm being a monopolist will extract the maximum consumer surplus it can).

[NM]

Ohh. Right. Thanks a lot. :)

[SoniaKapoor]

pls explain quest 2

[NM]

I am not using Bayes Theorem. This is a simplified procedure.

We need to calculate Pr(Coin being the fair one given the occurrence of 2 heads) = Pr(F/H) = (Pr(F intersection H)/Pr(H)  

The probability of  choosing the fair coin = 1/2
The probability of obtaining 2 heads in a row = 1/4
Hence, Pr(F intersection H) = 1/2 * 1/4 = 1/8

Now, Pr(H) = 1/2 * (1/2 * 1/2) + 1/2 * 1 = 5/8

Hence, Pr(F/H) = (1/8)/(5/8) = 1/5.

[Granpa Simpson]

NM the one that you have used is Baye's Principle only..

[rmabides]

Baggio, wouldn't monopolist behave like a 3rd degree price discriminator since cost and consequently MC is zero? I think the answer should be three.

[hbk]

2013 ques no 23..how to solve it ?

[hbk]

sorry 2012 ques no 23