Question
In: Economics
Sandra has the following preferences over cookies (x) and tea (y) u(x, y) = min(4x, 2y)...
Sandra has the following preferences over cookies (x) and tea (y) u(x, y) = min(4x, 2y)
(a) Are Sandra’s preferences complete, transitive, and continuous? Explain/Prove your answer and state the definitions for completeness, transitivity, and continuity. (6 points) 4
(b) Are Sandra’s preferences monotone? If yes, are they strongly monotone or weakly monotone? Define weak and strong monotonicity and then prove your answer. (5 points)
(c) Are Sandra’s preferences strictly convex? Prove your answer (3 points) 5
(d) Graph Sandra’s indifference curves that go through points (2,2), (4,4), (6,6), (8,8). Be sure to label the axis and the utility levels of the indifference curves. (Hint: You should be graphing 4 indifference curves) (5 points)
Solutions
Rahul Sunny answered 2 hours agoRelated Solutions
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1) Draw the indifference curves where U=6 and U=12.
2) Draw Amy's typical demand curve for good x.
A consumer has his preferences represented by the utility function U(x,y) = min {5x + 4y,...
A consumer has his preferences represented by the utility
function U(x,y) = min {5x + 4y, 4x + 7y} if x is on the horizontal
axis and y is on the vertical axis, what is the slope of his
indifference curve at the point (10,10)
a. -4/7
b. -5/4
c. -4/5
d. -7/4
e. -5/7
Suppose a consumer has preferences given by U(X,Y) = MIN[2X,Y]. Suppose PX = 1 and PY...
Suppose a consumer has preferences given by U(X,Y) = MIN[2X,Y].
Suppose PX = 1 and PY = 2. Draw the Income Consumption Curve for
this consumer for income values
• M = 100
• M = 200
• M = 300
To do this, carefully draw the budget constraints associated
with each of the prices for good X, and indicate the bundle that
the consumer chooses in each case. Also, be sure to label your
graph accurately.
Ella’s preferences can be represented by the utility function u(x,y) = min{5x, y}. If the price...
Ella’s preferences can be represented by the utility
function u(x,y) = min{5x, y}. If the price of x is
$10 and the price of y is $15, how much money would she need
to be able to purchase a bundle that she likes as well as the
bundle (10, 25).
Select one:
a. $475.
b. $85.
c. $425.
d. $209.
e. $440.
preferences are represented by U(x;y)= x^2y^3. Her income is $1,000, the price of x is $5,...
preferences are represented by U(x;y)= x^2y^3. Her income is
$1,000, the price of x is $5, and the price of y is $20. If
the price of x falls to $4, calculate the (a) slutsky
substitution (b) Income and (c) total effect of the price decrease
on the
demand of x. Set up the Lagrange to find all the demands.
Using the change of variables u=x^2y and v=y/x, integrate f(x,y) =x^2y^2 over the region bordered by...
Using the change of variables u=x^2y and v=y/x, integrate f(x,y)
=x^2y^2 over the region bordered by y= 1/x^2,y= 3/x^2, y=x and y=
2x.
Brianna’s preferences can be represented by the utility function u(x,y) = min{x,y}. Initially she faces prices...
Brianna’s preferences can be
represented by the utility function u(x,y) = min{x,y}.
Initially she faces prices ($2,$1) and her income is $12. If prices
change to ($3,$1) then the compensating variation
Select one:
a. There is not enough information to
determine which variation is greater.
b. is $2 more than the equivalent
variation.
c. is $1 less than the equivalent
variation.
d. equals the equivalent variation.
e. is $1 more than the equivalent
variation.
(a) If your utility is represented by u(x; y) = min(x+2y; 2x+y);what do your indi¤erence curves...
(a) If your utility is represented by u(x; y) = min(x+2y;
2x+y);what
do your indi¤erence curves look like?
(b) Given your answer in (a), obtain the MRS (marginal rates of
sub-
stitution).
(c) Suppose the prices of x and y are px = $3 and px = $1 and
you
have 100 dollars. What would you choose?
(d) If px decreases to $1; what would you choose?
(e) Use the Slutsky decomposition to decompose the total price
e¤ect
into the...
(a) If your utility is represented by u(x; y) = min(x+2y; 2x+y);what do your indi¤erence curves...
(a) If your utility is represented by u(x; y) = min(x+2y;
2x+y);what do your indi¤erence curves look like?
(b) Given your answer in (a), obtain the MRS (marginal rates of
sub- stitution).
(c) Suppose the prices of x and y are px = $3 and px = $1 and
you have 100 dollars. What would you choose?
(d) If px decreases to $1; what would you choose? (e) Use the
Slutsky decomposition to decompose the total price e¤ect into the...
Find the average value of f(x,y)= 4x+2y over region bounded by coordinate axis and lines x+y=4...
Find the average value of f(x,y)= 4x+2y over region bounded by
coordinate axis and lines x+y=4 and x+y=8
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