Daily question

[Amit Goyal]

In this section, i will post a problem in Economics daily that might be a good exercise for you. Feel free to post some problem if you want to challenge others.

[Amit Goyal]

15 Feb 2009
Pick the correct answer from the options.
a) Indifference curves are downward sloping because:
1) Diminishing Marginal rate of substitution of good x for good y.
2) Marginal Utility from both goods is positive.
3) Marginal utility of one good is positive and other good is negative.
4) Prices of both goods are positive.

Do the following problem:
b) Suppose U=xy. Price of x is Rs. 2 and price of y is Rs. 4 and consumer has Rs.600 to spend. Compute the equilibrium bundle. Now suppose price rise to Rs.4. Decompose the total price effect into Substitution effect and Income effect. (Using both Hicksian and Slutsky methods)

[Amit Goyal]

Monty Hall Game
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, pigs. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a pig. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?


Link: http://www.shodor.org/interactivate/activities/SimpleMontyHall/
The activity in the link allows the user to simulate the standard Monty Hall Game.
The user chooses a door, and then another door is opened to reveal a stinking pig. The player must then decide to stick with the original choice or change.

[Khushboo]

1 - Marginal utility of goods is positive    

2 - By Slutsky method, substitution effect is 37.5 and income effect is also 37.5.
     By Hicks method, substitution effect is 43.933 and income effect is 31.06.

     So, total effect is same in both the methods i.e 75.

[Khushboo]

Suppose the 3 doors are A1 , A2, A3 and   B - Host opens the door 3

 If the car is behind 1, then host would open either door 2 or 3.


 So, P[ A1/B ] =  P[B/A1] P[A1] / P[B/A1] P[A1] + P[B/A2] P[A2]
                    =  1/2 * 1/3  /  1/2 * 1/3 + 1 * 1/3
                    =  1/3

 then, P [ A1/B ] = 1/3
         P [ A2/B ] = 2/3

 Therefore, having a car in door 2 has a greater advantage.
 

[gurvinder]

indifference curves are downward sloping because of diminishing rate of marginal substitution between x and y.

[Kanika]

(1)The intial quantities of x and y are =(150,75),the total price effect is 75,By Slutsky the substitution effect is 37.5 and income effect is 37.5,By Hicks,s.e=0 and i.e.=75
(2)Also ic's are downward sloping because both marginal utilities are positive.

[varun]

1. I C are downward sloping as marginal utility from goods is positive.

2. Slutsky se= -37.5
       income effect= -37.5

[Aastha]

A:1 Diminishing marginal rate of substitution of good X for Y.

[Amit Goyal]

16 Feb 2009

To encourage Elmer's promising tennis career, his father offers him a prize if he wins (atleast) two tennis sets in a row in a three set series to be played with his father and the club champion alternately:
father-champion-father or champion-father-champion, according to Elmer's choice. The champion is a bettter player than Elmer's father. Which series should Elmer choose?

[Amit Goyal]

Suppose Asha's preferences between two commodities x and y can be represented by u(x,y)=min{x-5,y+3}. Given an income of Rs.73 and px=3 and py=4. Find Asha's optimal consumption bundle.

[Khushboo]

 Asha's optimal consumption bundle is [ 15,7 ].

[Kanika]

Asha 's optimal cinsumtion is(15,7)

[Amit Goyal]

(by deepti)

the optimal bundle 4 asha is-(15,7)

[Amit Goyal]

BY DEEPTI


suppose prob of winning 4m champion is p and prob orf winning 4m father is q.

also p<q

now if he chooses  champion  father chmpion series den prob of winning  atlst 2 cnsecutive games is-  pq(2-p)

if he chooses father champion father series den prob of winning atlesat 2 cnscutv games is-

pq(2-q)

therefr he wld choose chmpn fathr chmpn series..

[Amit Goyal]

BY DEEPTI

both d goods hv pstv marginal utility...

slutsky se = ie=37.5


hicks se=43.94
        ie=31.06

[ankita]

1) since the mu for both goods is positive ic curves are downward sloping.

2) slutsky: te:75, ie=se=37.5

hicks, te:75, se=43.93, ie=remaining

[ankita]

optimal consumption bundle is (15, 7)

[ankita]

he should be choosin the father champion father series..a guess...

[Amit Goyal]

Feb 17-20, 2009

In answering a question on a multiple choice test a student either knows the answer or he guesses. Let p be the probability that he knows the answer and 1-p the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability 1/m, where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer to a question given that he answered it correctly?

A miner is trapped in a mine containing three doors. The first door leads to a tunnel which takes him to safety after two hours' travel. The second door leads to a tunnel which returns him to the mine after three hours' travel. The third door leads to a tunnel which returns him to the mine after five hours' travel. Assuming that the miner is at all times equally likely to choose any one of the doors, what is the expected length of time until the miner reaches safety?

A family has two children. What is the conditional probability that both are boys given that at least one of them is a boy? Assume that the sample space S is given by S = {(b,b),(b,g),(g,b),(g,g)}, and all outcomes are equally likely. ((b,g) means for instance that the older child is a boy and the younger child a girl.)
Also find the conditional probability that both are boys given that at least one of them is a girl?

Two people share a room in a hospital.On any given day a person independently picks up an infection with probability 1/4.An individual who contracts its on a day will definitely pass it on to the other person (in the room) the next day.Once contracted the infection stays for two days.What is the probability that at the end of 2 days both patients have the infection?