problem sets

[RHIDIMA]

Matt lives on popcorn and seafood salads. The price of popcorn is 1 dollar per bag and the
price of seafood salads is 2 dollars each. Matt allows himself to spend no more than 13 dollars a
day on food. He also restricts his consumption to 5,500 calories per day. There are 1,000 calories
in a bag of popcorn and 500 calories in a seafood salad. If he spends his entire money budget each
day and consumes no more calories than his calorie limit:
(a) he can consume up to 3 bags of popcorn per day, but no more.
(b) he can consume up to 1 bags of popcorn per day, butno more.
(c) he can consume up to 5 seafood salads per day, but no more.
(d) he can consume up to 4 bags of popcorn per day, but no more.
(e) None of the above.

The answer to this question, why can't it be c) also. Because solving the equation-
p+2s=13 & 2p+s=11, we are getting p=3 & s=5..

[X]

Thank you,Sir. I got to know from Wolfram Alpha that the indifference curves are actually circles, and we have to consider these circles in the first quadrant of the 2d Cartesian planefor economic problems.

Am I right?

[Amit Goyal]

Yes, you are right. ICs will be the portion of the concentric circles (with (0,0) as the center) that lies in the first quadrant.

[Amit Goyal]

The question says that calorie intake can be less than 5500 but not more. And all the money should be spend on popcorn and salad.
That is, the set of solutions satisfy the following two constraints:
p + 2s = 13
&
2p + s ≤ 11

Check that the above two conditions is equivalent to
p + 2s = 13
&
p ≤ 3

OR equivalently,

p + 2s = 13
&
s ≥ 5

And hence the answer is (a) and not (c).

[Akshay Jain]

probability question
Suppose that the four inspectors at a film factory
are supposed to stamp the expiration date on each
package of film at the end of the assembly line. John,
who stamps 20% of the packages, fails to stamp the
expiration date once in every 200 packages; Tom, who
stamps 60% of the packages, fails to stamp the expiration
date once in every 100 packages; Jeff, who stamps
15% of the packages, fails to stamp the expiration date
once in every 90 packages; and Pat, who stamps 5% of
the packages, fails to stamp the expiration date once
in every 200 packages. If a customer complains that
her package of film does not show the expiration date,
what is the probability that it was inspected by John?

[XIPP]

(Bayes bless me!)

[Akshay Jain]

general equilibrium question
there are two consumers 1 and 2
consumer 1 utility function is given by U1= 1, if x+y<1 and U1= x+y, if x+y>=1 (endowment (1,0))
consumer 2 utility function is U2= x+y (endowment (0,1))
find out the competitive equilibrium allocation(s) and chek for the validiy of 1st welfare theorem
if 1st theorem is not applicable then find out the pareto efficient allocation...