2) For two agents, a and b, with the following
utility functions over goods x and...
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...
For two agents, a and b, with the following
utility functions over goods x and y...
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)
Cali and David both collect stamps (x) and fancy spoons (y).
They have the following preferences...
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...
Alice (A) and Bob (B) have an endowment of goods xx and yy, with
Alice's endowment...
Alice (A) and Bob (B) have an endowment of goods xx and yy, with
Alice's endowment being (ωxA,ωyA)=(3,6)(ωAx,ωAy)=(3,6) and Bob's
endowment
equals (ωxB,ωyB)=(3,9)(ωBx,ωBy)=(3,9). Alice's
utility is given by uA(xA,yA)=x2AyAuA(xA,yA)=xA2yA, while Bob's
utility is uB(xB,yB)=xBy2BuB(xB,yB)=xByB2. Find the competitive
equilibrium.
Select one:
a. xA=26/7,yA=13/3,xB=16/7,yB=32/3,px/py=14/6xA=26/7,yA=13/3,xB=16/7,yB=32/3,px/py=14/6
b. xA=16/7,yA=13/3,xB=26/7,yB=32/3,px/py=3/7xA=16/7,yA=13/3,xB=26/7,yB=32/3,px/py=3/7
c. xA=16/7,yA=32/3,xB=26/7,yB=13/3,px/py=7/3xA=16/7,yA=32/3,xB=26/7,yB=13/3,px/py=7/3
d. xA=26/7,yA=13/3,xB=16/7,yB=32/3,px/py=3/7
Please solve all the parts.Thank you.
A consumer can spend her income on two products, good...
Please solve all the parts.Thank you.
A consumer can spend her income on two products, good X and good
Y . The consumer’s tastes are represented by the utility function
U(x, y) = xy.
a. Suppose that Px = 4 and Py = 1, and I = 16.
Draw the budget line and mark it as BL1. Initial optimum is at A.
Find the optimal amounts, xA and yA and locate A on the graph. Find
the initial level of...
A consumer’s preferences are represented by the following
utility function: u(x, y) = lnx + 1/2...
A consumer’s preferences are represented by the following
utility function: u(x, y) = lnx + 1/2 lny
1. Recall that for any two bundles A and B the following
equivalence then holds
A ≽ B ⇔ u(A) ≥ u (B)
Which of the two bundles (xA,yA) = (1,9) or (xB,yB) = (9,1) does
the consumer prefer?
Take as given for now that this utility function represents a
consumer with convex preferences. Also remember that preferences ≽
are convex when for...
UA = ?^1/2?^1/4 and (??x, ??y) = (90,30)
UB = ?1/2?^1/4 and (??x, ??y) = (10,50)...
UA = ?^1/2?^1/4 and (??x, ??y) = (90,30)
UB = ?1/2?^1/4 and (??x, ??y) = (10,50)
For each of the above economies
a) Derive the contract curve.
b) Find the competitive equilibrium price ratio and
allocation.
c) Use an Edgeworth box to illustrate the competitive
equilibrium
Consider the following utility functions over goods X and Y for
two individuals:
Daves utility function...
Consider the following utility functions over goods X and Y for
two individuals:
Daves utility function : Ud(x,y) = 6min(x,y)
Jess's Utility function is Uj (x,y) = 6x + 3Y
Draw Daves indifference curve map for two specific utility
levels: U= 6 and U = 12
Draw Jess indifference curve map for two seperate utility
levels: U=6 and U=12
Explain the preferences between the two
What is the MRS for Dave? and for Jess?
Let Ella’s preferences for goods x and y are represented by
the utility function ?(E) (?,...
Let Ella’s preferences for goods x and y are represented by
the utility function ?(E) (?, ?) = 2? + ?,
whereas Louis’ utility function is ?(L) (?, ?) = ? + ?
The initial endowments of Ella and Louis include 8 units of x
and 4 units of y each (i.e., there are
a total of 16 units of x and 8 units of y in this
economy).
a. (2 points) What are the marginal rates of substitution for...
4: There is an exchange economy with two agents, A, B, and two
goods, x, y. A's...
4: There is an exchange economy with two agents, A, B, and two
goods, x, y. A's endowment is
x = 6, y = 4, and B's endowment is x =
4, y = 6.
(a) A has the utility function u(x,
y) = x + y and B
u(x, y) = xy. Find a
competitive equilibrium allocation (CEA) and associated equilibrium
prices. What difference would it make if A's endowment is
x = 3, y = 1, and B's endowment is x...