Posted by
Amit Goyal on
Feb 25, 2009; 8:10am
URL: http://discussion-forum.276.s1.nabble.com/Daily-Question-solutions-tp2382507.html
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.
Ans. Marginal Utility from both goods is 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)
Ans. Slutsky: (150,75) ---> (112.5, 112.5)---> (75, 75); Hicks: (150,75) ---> (75√2, 75√2)---> (75, 75)
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?
Ans. Yes
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.
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?
Ans. champion-father-champion
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.
Ans. (15, 7)
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?
Ans. mp/(mp+(1-p))
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?
Ans. 10
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?
Ans. 1/3, 0
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 it 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?
Ans. 121/256