Question

Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 8 units of X and a TOTAL of 8 units of Y. The consumers’ utility functions are given by:

UA(X,Y) = 4X + Y

UB(X,Y) = X*Y

For each of the following allocations, write TRUE if it is Pareto Efficient and FALSE if it is not:

i) Consumer A gets 6 units of X and 2 units of Y, and Consumer B gets 2 units of X and 6 units of Y.

ii) Consumer A gets 4 units of X and 6 units of Y, and Consumer B gets 4 units of X and 2 units of Y.

iii) Consumer A gets 7 units of X and 0 units of Y, and Consumer B gets 1 unit of X and 8 units of Y.

iv) Consumer A gets 4 units of X and 0 units of Y, and Consumer B gets 4 units of X and 8 units of Y.

Answer #1

Suppose there are two consumers, A and B, and two goods, X and
Y. Consumer A is given an initial endowment of 4 units of good X
and 4 units of good Y. Consumer B is given an initial endowment of
4 units of good X and 4 units of good Y. Consumer A’s utility
function is given by:
UA(X,Y) = X*Y4,
and consumer B’s utility function is given by
UB(X,Y) = X*Y.
Therefore, consumer A’s marginal utilities for each...

Suppose there are two consumers, A and B, and two goods, X and
Y. The consumers have the following initial endowments and utility
functions:
W X A = 2 W Y A = 9 U A ( X , Y ) = X 1 3 Y 2 3 W X B = 6 W Y B
= 2 U B ( X , Y ) = 3 X + 4 Y
Suppose the price of X is PX=2 and the...

For two agents, a and b, with the following
utility functions over goods x and y (6)
ua= ua(xa,ya)=xa^1/4 ya^3/4
ub=ub (xb,yb) = xb^1/2 yb^1/2
Calculate the utility level before and after trading.
initial endowments ωa=(4,5) and wb=(3,2)

1. Suppose there are two consumers, A and B. The utility
functions of each consumer are given by: UA(X,Y) = X*Y UB(X,Y) =
X*Y3 Therefore: • For consumer A: MUX = Y; MUY = X • For consumer
B: MUX = Y3; MUY = 3XY2 The initial endowments are: A: X = 10; Y =
6 B: X = 14; Y = 19 a) (40 points) Suppose the price of Y, PY = 1.
Calculate the price of X, PX...

) For two agents, a and b, with the following
utility functions over goods x and y (6)
ua= ua(xa,ya)=xa^1/4 ya^3/4
ub=ub (xb,yb) = xb^1/2 yb^1/2
Determine the slope of the contract curve in the interior of an
Edgeworth box that would show this two-person two-goods
situation.

2) For two agents, a and b, with the following
utility functions over goods x and y (6)
ua=ua(xa,ya)=xaya
ub=ub(xb,yb)=xbyb
a) Determine the slope of the contract curve in the interior of
an Edgeworth box that would show this two-person two-goods
situation.
b) For initial endowments ωa=(12,7) and ωb=(9,10), what is the
Walras allocation between the two agents a and b?
(Remember that it is the relative price of the goods that matters
in this consideration. Also remember that all...

Consider a pure exchange economy with two consumers, Ann (A) and
Bob (B), and two commodities, 1 and 2, denoted by (x^A_1, x^A_2)
and (x^B_1, x^B_2). Ann’s initial endowment consists of 20 units of
good 1 and 5 units of good 2. Bob’s initial endowment consists of 0
unit of good 1 and 5 units of good 2. The consumers’ preferences
are represented by the following Cobb-Douglas utility
functions:U^A(x^A_1, x^A_2) = (x^A_1)^2(x^A_2)^2 and
U^B=√x&B1√x^B2. Denote by p1 and p2 the...

Cali and David both collect stamps (x) and fancy spoons (y).
They have the following preferences and endowments.
Uc (x, y) =
xc.yc2
ωc = (10, 5.2)
UD (x, y) = xD.
yD
ωD = (14, 6.8)
Write down the resource constraints and draw an Edgeworth box
that shows the set of feasible allocations.
Label the current allocation inside the box. How much utility
does each person have?
Show that the current allocation of stamps and fancy spoons is
not...

ua (xa) = min
(2x1a,x2a,x3a)
endowment (2,2,2) ub (xb) =
min (x1b,
2x2b,
x3b) endowment (2,2,2)
uc (xc) = min
(x1c,x2c,
2x3c) endowmwnt (2,2,2) (note
2x1 means 2 times good x1)
consider the following exchange economy with three consumers (a
b c) and the following goods (1, 2 and 3) (a)
calculate each consumers level of utility at the autarkic
allocation (b) show that the autarkic allocation is
NOT pareto efficient by identifying another FEASIBLE allocation...

In the economy of Ricardia, two consumer goods, X and Y, are
produced from a single factor input, labor, according to the
production functions:
Y = 3Ly and X = 3Lx
where Ly and Lx are the quantities of labor used in the
production of Y and X respectively. The total amount of labor
available is 66 units.
(a) Derive the equation for the economy's production possibility
frontier. Confirm that the marginal rate of transformation is equal
to MPLy/MPLx.
(b)...

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