dse 2010

[Monika]

a consumer has a utility function u(x,y)=xy. suppose consumer demands bundle (X, Y). now suppose the seller of the good x offers- buy 1 get 1 free scheme: for each unit of x puchaded, consumer gets another unit of x for free. given this scheme suppose the consumer buys (xd, yd) and gets xd for free. which is true-

a) xd>X, yd>Y
b) xd>X, y=Y
c) xd>X, y<yd
d) xd=X, yd=Y

[Ram]

its option 4....if we read the question carefully it mentioned that consumer buys (xd,yd) and gets additional xd as free. here nothing is mentioned regarding prices so I assumed prices as constant as we all know that if price of one commodity decreases the quantity demanded of that commodity will increase(am assuming it as normal good). here consider that price of x is halved ( am just assuming ) the budget line will have same intercept on y-axis ( i.e. commodity y) and the intercept on x-axis will change that means x will get doubled. but here nothing has mentioned regarding prices we can say that (xd,yd) are same as (x,y) because they mentioned that consumer buys (xd,yd) and gets additional xd as free. if they mentioned there as consumer got (xd,yd) then it is option 2.... Correct me if am wrong or If I would have made it complicated :)

[Monika]

since the prices of good x get halfed, shouldn't he consume more of good x? since he spends his entire income, he'll be left with some money if he still buys the previous bundle??

[Manvendra]

Monika wrote

since the prices of good x get halfed, shouldn't he consume more of good x? since he spends his entire income, he'll be left with some money if he still buys the previous bundle??

Hey,in the question it says that the consumer will get an extra X units over his purchased
(optimum) bundle . Here, X will be equal to the amount consumed when the purchaser is trying to maximize his utility.
So,the optimum bundle remains the same i.e. Xd , Yd ( because neither the price nor the utility has changed ).But his actual consumption of good X will go on to become:
Xd + Xd = 2 Xd .

[anon_econ]

if u r thinking of it in terms of halving of the price, then yes, quantity purchased would be doubled. but then this is the quantity purchased at half the price, that is, it includes the free goods. so if xd is the quantity actually bought (excluding the free units), then it wud be the same as the initial bundle.

[Monika]

but i cant understand y wont income or substituion effect cum in??

[Monika]

all rite..i have understood it now..thanx a lot..i was going terribly wrong sumwer :/