Daily question

[deepti]

1) 2OOO+1800/I.O4+1600/1.O4 SQ+1400/CUBE1.O4+........................2OO/1.O4 POWER 9=9824.05

2)2000+1800/1.05+............................200/1.05 POWER9=9569.15

[Aastha]

Ans 2) equillibrium quantity is 6 apples, equillibrium price Rs.8

market demand will be the horizontal summation of the individual demand curves.
therefore addind demand's of A & B we get the market demand as: P= 50- 3q/4
 
market supply is given by: P=2+Q
 
At equillibrium Q=q therefore equating market demand and market supply we get
50-3q/4=Q+2; 50-3q= 4Q+8 ; 42=7Q
therefore Q= 42/7=6 apples
 
P= 2+6=Rs.8

[Amit Goyal]

1st-4th Mar, 2009
WARP says that if a consumer chooses commodity bundle A when she can afford bundle B from any budget in which she can afford A. Check if WARP holds or not:
1) (x,y) = (2,3) and (p(x),p(y))=(1,4) ; (x’,y’) = (5,2) and (p(x’),p(y’))=(1,5)
2) (x,y) = (2,3) and (p(x),p(y))=(2,1) ; (x’,y’) = (3,2) and (p(x’),p(y’))=(1,2)
3) (x,y) = (2,3) and (p(x),p(y))=(1,2) ; (x’,y’) = (3,2) and (p(x’),p(y’))=(2,1)

Kamal has been given a free ticket to attend a classical music concert. If Kamal had to pay for the ticket, he would have paid up to Rs. 300/- to attend the concert. On the same evening, Kamal’s alternative entertainment option is a film music and dance event for which tickets are priced at Rs. 200/- each. Suppose also that Kamal is willing to pay up to Rs. X to attend the film music and dance event. What does Kamal do, i.e., does he attend the classical music concert, or does he attend the film music and dance show, or does he do neither? Justify your answer.

Suppose there are two consumers A and B. Both consumers have a unit demand for the good. Consumer A has valuation $50 for it and consumer B's valuation is $20. What will be the monopolist price and quantity if he produces the good at 0 marginal cost? What will happen under duopoly i.e if there are two firms? What will be competitive output and quantity? Comment on DWL in three market structures.

You have 10 chocolates to divide among three individuals(A,B and C). All 3 prefer more chocolates to less.Find all the Pareto efficient allocations. Suppose individual A has 0 chocolates and the other two has 5 chocolates each. Find the competitive equilibrium price and allocation. Is the equilibrium pareto efficient?

[Khushboo]

Show that P(A ∩ B ∩ C) = P(A).P(B).P(C) does not necessarily imply that A, B and C are all pairwise independent.


It is prooved by an example:
Suppose 8 tickets numbered 111, 121, 122, 122, 211, 212, 212, 221 are placed in a hat nd stirred. One of them is then drawn at random. The events are:
 
   A : the 1st digit on the ticket drawn will be 1,
   B : the 2nd digit on the ticket drawn will be 1,  
   C : the 3rd digit on the ticket drawn will be 1.

then, A = 111, 121, 122, 122
       P(A) = 4/8

       B = 111, 211, 212, 212
      P(B) = 4/8

      C = 111, 121, 211, 221
      P(C) = 4/8

     (A∩B∩C) = 111
     P(A∩B∩C) = 1/8

So,  P(A∩B∩C) = P(A).P(B).P(C) = 1/8

P(A ∩ B ∩ C) = P(A).P(B).P(C) does not necessarily imply that A, B are pairwise independent.

 As,
     P(A∩B) is not equal to P(A).P(B)  [ 1/8 is not equal to 4/8 . 4/8 ]
     

[ankita]

income elasticity is 1 for the goods.

equlibrium price is 8 and qty is 6.

[deepti]

1)all  d 3 cases r stsfyng warp.....

4)all d alloctns r pareto effcnt....as all of d 3 ind lyk choclt n if v tk choclt 4m one and gv it to another den  v r mkng one indvdl btr off and mkng anthe worse off.......

cmptv eq:if v tk price>o den incm of A IS  0 n incm of  B  and C  is 5p....

both b and c wld lyk 2 spnd dere incm on chclt therefore dd 5 choclt while a vl nt dd any chclt.....mkt is also clearng

thrfore 4 al prices >o dere is cmptv eq..........

[Kanika]

1.The third case does nit satisfy warp

[Khushboo]

1-  a) satisfy WARP
     b) satisfy WARP
     c) satisfy WARP

2-  the maximum value of Film music & dance event is X
    therefore, Kamal gt a surplus on Film music & dance event is (X-200) and maximum value on Classical music is 300, therefore, surplus on Classical music concert is 300.
   
   There is no any such situation arise that he will do neither, all depend on the value of Film music & dance event  bcz
   If X > 500, then he will attend Film music & dance event.
   If X < 500, then he will attend Classical music concert.
   If X = 500, then he will either attend Film music & dance event or he will attend Classical music concert.

3- Any allocation in which 10 choclates r distributed is pareto efficient. this is so bcz any movement from this allocation makes atleast 1 individual worse off. All d prices greater dan 0 shows competitive equilibrium.

[deepti]

2)price of classical music concert is 0 and his max wiilingness to pay is 300 thus his consumer surlus is 300..

price of film music and dance show is 200  and maximum willingness to pay is x thus his surlus is x-200..

now if x>500 then he will go to film music and dance show

if x<500 then he will go to classical music concert....

if x=500 then he can choose either of the two...

[farha]

suppose there r 2 prsns A nd B.at the beginning of the game A has 'a' dollars nd B has 'b' dollars.each time a loser has to pay 1 dollar to the winner.each players expectation is zero.they will play until each player bcme ruined.find the probability that A will win B's 'b' dollar before he loses his all 'a' dollars.

[Amit Goyal]

5-7 March, 2009
Answer Farha's question. You can assume that they toss a fair coin everytime, if its head then A wins and if its tail then B wins.

We have following data for two countries.
In country A, 80 labor-hrs  are required to produce one unit of x and 90 labor-hrs  are required to produce one unit of y.
In country B, 120 labor-hrs  are required to produce one unit of x and 100 labor-hrs  are required to produce one unit of y.
Fill in the blanks:
Country ___ will export x and country ___ will export y.

Let A and B be events having positive probability. State whether each of the following statements is        i) necessarily true, ii) necessarily false, or iii) possibly true
(a) If A and B are mutually exclusive, then they are independent.
(b) If A and B are independent, then they are mutually exclusive.
(c) P(A)=P(B)=0.6, and A and B are mutually exclusive.
(d) P(A)=P(B)=0.6, and A and B are independent.

[varun]

ans.1 the first and second case satisfy warp but third case dont.

[varun]

ans.2 in no way he will choose neither of options .

 case 1 if X > 700 then he will choose dance and film
         2 if X< 700 then concert
         3  if x700 then any of two

[farha]

srry that ques was incomplete........MR. Adam nd MS. Smith r bettng on repeatd flips of a coin.at the start of d game Mr. Adam has 'a' dollars nd Ms. Smith has 'b' dollars,at each flip the loser pays the winner 1 dollar nd the game continues until either player is ruined.each players expectation is zero.fnd the prob that Mr. Adam will win Ms. Smith's  'b' dollars before he loses his 'a' dollars.

[Kanika]

country a will export good x and country b will export good y.

The first two statements are necessarily false given p(a) and p(b)>0,the third statement is necessarily false and the fourth staetement is possibiliy true

[deepti]

4)  MU OF G/MU OF L=PRICE OF G /PRICE OF L

WE GET 2L/3G=1/PRICE OF L


BUDGET EQUATION :PG+WR=W(TOTAL TIME AVAILABLE FOR LEISSURE)


G+WR=10W

2/3RW+WR=10W

R=6

THUS 4 ANY WAGES HE WOULD WORK FOR 4 HRS ONLY

[deepti]

statement a ,b ,c are necessarily false and statement d is possibly true

[Khushboo]

Try to solve these questions
1- A consumer consumes electricity (Xe) and other goods (Xo). The price of other goods is unity, To consume electricity the consumer has to pay a rental charge R and a per unit price p. However, p increases with the quantity of electricity consumed according to the function p = 1/2 Xe. The utility function of the consumer is U = Xe + Xo and his income is I>R.
a) Draw the budget line of the consumer.
b) If R = 0 and I = 1, find the optimum consumption bundle.
c) Find the maximum R that the electricity company can extract from the consumer.



2- Experience shows that 20% of the ppl reserving tables at a certain restaurant never show up. If the restaurant has 50 tables and takes 52 reservations, then the probability that it will be able to accommodate everyone is what?

[Khushboo]

  Statement a, b, c are necessarily false and statement d is possibly true.

[farha]

country A is specialised in the production of x.nd country B is specialised in the production of y.therefore...country A will export x nd country B will export y.