Trades: will they occur...?

Question

Suppose there is an island with only 2 people on it, Pamela and Quentin. They have endowment of only 2 goods: bananas and fish. Bananas = good 1, fish =good2

endowment vectors for Pamela & Quentin:

(Wp1, Wp2) = (10,5)

(Wq1, Wq2) = (5,20)

utility fncs for Pamela & Quentin:

Up(Xp1, Xp2) = Xp1Xp2

Uq(Xq1, Xq2) = Xq1Xq2

Is it possible for trade to occur in this economy? why or why not?... (how would i shade in the area indicating all possible final allocations after trade?)

Consider the following trades+ show analysis whether will/won't trade:

1. Pamela trades 5 of her bananas for 2 fish from Quentin

2. Q trades 1 banana for 2 fish from P.

3. Q trades 1 banana for 5 fish from P.

4. P trades 2 bananas for 5 fish from Q.

(find the allocations after trade and then use utility fnc)

how would i do this? i'm supposed to plug in these #s to the utility fnc right? but i don't really understand the process or why... please help!! thank you!!!

Answer 1

MRS for each of them is X2/X1

see if they are equal:

5/10=/=20/5

since they are not equal, it is not pareto efficient, and there are possible trades that could make both of them better off.  When you graph it, their indifference curves should intersect (not tangent) and the area between the curves is the possible final allocations after trade, if that makes any sense.

Utility before trade:

Pamela: 10*5=50

Quentin: 5*20=100

1. New allocation: A(p) = (5, 7) U(P)=5*7=35

her utility is lower than before, so she will not accept it.

2. A(Q) = (4, 22) U(Q)=4*22=88

his utility is lower than before, so he will not accept it.

3. A(Q)=(4, 25) U(Q)=4*25=100

he is as well off, so he will accept it

A(P)= (11, 0) U(P) = 11*0=0

she is worse off, so she will not accept it

4. A(P) = (8, 10) U(Q) = 8*10=80

she is better off, so she will accept it

A(Q) = (7, 15) U(Q) = 17*5=105

he is better off, so he will accept it