Question

In a simple exchange two-good-two-individual world where there are 90 units of good x and 100 units of good y in total, two individuals are trying to maximize their own utility. Individual A’s utility function is U (x_A,y_A)=x_A^0.7y_A^0.3, while individual B is with the utility function U (x_B,y_B)= 4x_B + y_B.

Suppose that the endowment of individual A is 40 units of x and 45 units of y.

1）Individual B is endowed with （ ） units of x and （ ） units of y.  With the endowment, the MRS of Individual A is （ ） and the MRS of Individual B is （ ）. (MRS is defined as the number of y per unit of x. Please round your results to the nearest hundredth.)

2) The above calculation shows that ________Select one:

a. Individual A values x more than Individual B does.

b. Individual A values x less than Individual B does.

c. Individual A and B values good x equally.

3)The above calculation shows that ________Select one:

a. The endowment is Pareto efficient.

b. Allocating more x to A in exchange for more y to B can be a Pareto Improvement.

c. Allocating more y to A in exchange for more x to B can be a Pareto Improvement.

4) Allocation A (42,72) and B(48, 28) is Pareto Efficient. Select one:

a. True

b. False

Allocation A (42,72) and B(48, 28) is in the contract curve. Select one:

a. True

b. False

Moving from the endowment to the allocation in the previous question is a Pareto Improvement. Select one:

a. True

b. False

Answer 1

xA +xB = 90

yA+yB = 100

xA =40 and yA = 45

This implies,

xB = 90 - 40 = 50

xyB = 100 - 45 = 55

U(xA,yA) = xA^(0.7)*yA^(0.3)

MRSA = MUxA/MUyA = (7/3)*(yA/xA)

U(xB,yB)=4xB+yB

MRSB = MUxB/MUyB = 4/1=4

MRS of A at endownment (xA = 40, yA =45) = (7/3)*(45/40) = 2.625

MRS of B at endownment (xB=50, yB=55) = 4

1)

Individual B is endowed with （ 50） units of x and （55 ） units of y.

With the endowment, the MRS of Individual A is （2.63 ） and the MRS of Individual B is （ 4）.

2)

Thus, at the endowment, MRSA < MRSB, implying that the above calculation shows that- a. Individual A values x more than Individual B does

3)

Thus, at the endowment, MRSA < MRSB, implying that the above calculation shows that - b. Allocating more x to A in exchange for more y to B can be a Pareto Improvement.

4)

Allocation A (42,72) and B(48, 28) implies,

MRSA = MUxA/MUyA = (7/3)*(yA/xA)

=(7/3)*(72/42)

=4

MRSB = 4

Hence, both MRSA = MRSB. Thus, Pareto Efficient

Hence, the statement is TRUE

5)

Since, the Allocation A (42,72) and B(48, 28) is Pareto Efficient, hence, it is in the contract curve.

Hence, the statement is TRUE

6)

Moving from the endowment to the allocation in the previous question is a Pareto Improvement.

Hence, the statement is TRUE