ISI

[s]

Murthy takes only idli and vara.his preferences are U=f(sqrootq1 + sqrootq2), f'>0..q1 q2 are number of idli and vara respectively.
at food shop prices are Rs1 and Rs 2 per piece of idli and vara respectively. fractional units not sold.
i) one day he ordered and ate 6 pieces of each item. do you think his order was optimal? if not what is optimal given that he spends no more than in the above order?
ii) next day shop revised prices Rs 1.50 per piece for both items. he now decides to have previous day's optimal satisfaction level and spend no more than what he did the day before. what should he order?

in i) his order is not optimal as optimal order is q1=12 q2=3 (please confirm answers)
in ii) previous day optimal utility level U*=f(3sqreroot3) ....and his new budget constraint is 18=1.5(q1+q2)....
so i got two equations sqrootq1 + sqrootq2=3sqreroot3 and 18=1.5(q1+q2)....but i am getting complex values for q1 q2....

please help ....

[s]

2)A vickery auction is an auction in which each bidder submits a seaed bid(a bid that is revealed only after all bids are submitted). the highest bidder wins auction, but the winning bidder pays not what he bids but the second highest bids. suppose you are participating in the auction for an object worth Rs.20,000 to you how much will you bid for the object:
i)Rs.19600
ii)Rs 19998
iii)20000
Iv)20002

3)a firm sold Rs 50000 worth of its products and carried over stock of Rs 7000 of unsold products to the next year in the first year of its operation. in the same year it bought the products of other firms worth Rs. 30000 for use as raw materials of which it carried over a stock of unused products worth Rs 2000 to next year. the value added in its production in the year:
i)20000
ii)25000
iii)27000
1v)29000
is it 29000?

4) a farmer produces 100 units of rice.he keeps a part of his output for self conspn and sells the rest inthe market to buy vegetables. if price of rice goes up with price of vegetables remaining unchanged, his budget line:
i)shifts out with same intrcpt on rice axis
ii)shifts out with same intercept on vegetable axis
iii)doesnt change
iv)shifts in with the same intercept on rice axis

[ritu]

HI S ....HOW DID U FIND OUT THE OPTIMAL VALUES IN PART 1...???

[ritu]

for fourth question i think it should be part 1....ie....BL shifts out with same intercept on rice axis....my idea was this
your budget line is.....
Pr.R+Pv.V=100Pr
income here is 100 Pr coz he produces rice and then sells it...so revenue  from rice production is his income..
now intercept on vegetable axis,put R=o u get V=100Pr/Pv
intercept on rice axis is ,put V=0,R=100Pr/Pr=100
ur rice intercept is independent of rice or veggie price...so increase in price of rice  doesnt affect BL....but it leads to rise in value of veggie intercept coz its in numerator...so it shifts out with no change in rice intercept.....pls confirm

[ritu]

for question 3,,,,my answer is 27,000


pls confirm

[s]

hey,
for Q1, i maximised Lagrangean= f(sqrootq1+sqrootq2)+lamda(M-q1-q2)
solving i got q1=4q2...and thus q1=2M/3, q2=M/6...one day he ate 6 pieces of each so wat i considered was he spent entire income on the goods(ths is an assumption iv made ie 6,6 is on the budget line b not optimal, i cnt figure out any other way to find M))that way at given prices  M=1x6+2x6=18...then q1=12, q2=3 ..so 6,6 not optimal..

for 3,i did
 value of output=50000
+inventory inv=7000
-intermediate purchase=30000
+unused raw material(also like inventory)=2000

=27000

[s]

oops sorry that was 29000 not 27000