Dse Micro Doubt

[The Villain]

Two consumers A and B. Two goods x and y. A and B each owns 100 units of y and A owns 12 units of x and B owns 3 units of x. U1= y + 60x -2x2 and U2= y + 30x – x2 . A proposes that he will trade one unit of good x to B in exchange for some units of y. How many units of y, B should give to A, so that they both are better off?
a) Any payment between 16 ≤ t ≤ 22
b) Any payment between 12 ≤ t ≤ 24
c) Both of the above
d) None of the above

[RajEco]

mine is coming out to be  15 ≤ t ≤ 22.

[Atika Gupta]

Answer is b.
MRSxy for A = 60-4x
At endowment point MRSxy= dy/dx for A = 12. This implies that if A sacrifices I unit of X then to remain at the same IC (so that his utility does not fall) he requires 12 units of Y. Therefore, B should give at least 12 units of Y to A.

MRSxy for B=30-2x which at endowment point = 24. This implies that for an additional unit of x, B can sacrifice 24 units of Y without any decline in utility. Hence, maximum units of Y that B can give is 12.
Hence, For any amount of Y traded between 12 and 24 both A and B will be better off.

[RajEco]

hey atika

I just tried your answer to find out the utilities of B
Initially when he was having the bundle (100,3) his utility was Ub= 181,.
After say transfer of 24 units of y to A and getting 1 unit of x in return, his utility when he is now consuming bundle (100-24, 3+1)= (76,4) is 180. So why will he make the exchange.?

[The Villain]

ans is a