Question

Suppose a consumer views two goods, X and Y, as perfect complements. Her utility function is given by U = MIN [2X, Y]. Sketch the graph of the consumers indifference curve that goes through the bundle X = 5 and Y = 4. Put the amount of Y on the vertical axis, and the amount of X on the horizontal axis. Which of the three assumptions that we made about consumer preferences is violated in this case?

Answer #1

Suppose a consumer views two goods, X and Y, as perfect
complements. Her utility function is given by U = MIN [2X, Y].
Sketch the graph of the consumers indifference curve that goes
through the bundle X = 5 and Y = 6. Put the amount of Y on the
vertical axis, and the amount of X on the horizontal axis. Which of
the three assumptions that we made about consumer preferences is
violated in this case?

Suppose a consumer has a utility function U(X,Y) = MIN (X,Y) + X
+ Y. Using a graph, illustrate the indifference curve that goes
through the bundle X = 3, Y = 3.
I have the answer but could someone explain to me how to
approach the solution and what each part means.

Suppose the utility function for a consumer is given by U =
5XY.
X is the amount of Good X and Y is the amount of Good Y.
a) Neatly sketch the utility function. [Ensure that you
label the graph carefully and state any assumptions that you make
in sketching the curve.]
b) Does this utility function exhibit diminishing marginal
utility? [Ensure that you explain your answer fully.]
c) Calculate the marginal rate of substitution. [Ensure that
you explain your...

Consider a consumer whose preferences over the goods are
represented by the utility function U(x,y) = xy^2. Recall that for
this function the marginal utilities are given by MUx(x, y) = y^2
and MUy(x, y) = 2xy.
(a) What are the formulas for the indifference curves
corresponding to utility levels of u ̄ = 1, u ̄ = 4, and u ̄ = 9?
Draw these three indifference curves in one graph.
(b) What is the marginal rate of substitution...

Suppose a consumer has the utility function u(x, y) = x + y.
a) In a well-labeled diagram, illustrate the indifference curve
which yields a utility level of 1.
(b) If the consumer has income M and faces the prices px and py
for x and y, respectively, derive the demand functions for the two
goods.
(c) What types of preferences are associated with such a utility
function?

1.Suppose there are two consumers, A and B.
The utility functions of each consumer are given by:
UA(X,Y) = X^1/2*Y^1/2
UB(X,Y) = 3X + 2Y
The initial endowments are:
A: X = 4; Y = 4
B: X = 4; Y = 12
a) (10 points) Using an Edgeworth Box, graph the initial
allocation (label it "W") and draw the
indifference curve for each consumer that runs through the
initial allocation. Be sure to label your graph
carefully and accurately....

Suppose Marwa considers blueberry kombucha (B) and green juice
(G) to be perfect complements. Marwa always mixes 2 bottles of
blueberry kombucha with one bottle of green juice. Marwa has $30 to
spend on these beverages. The price of blueberry kombucha is $5 per
bottle and the price of green juice is $6 per bottle. On a graph,
draw Marwa's budget constraint, identify Marwa's optimal bundle,
and draw the indifference curve that goes through that bundle.
Please put the quantity...

Consider the utility function U(x, y) =
x0.4y0.6, with MUx = 0.4
(y0.6/x0.6) and MUy = 0.6
(x0.4/y0.4).
a) Is the assumption that more is better satisfied for both
goods?
b) Does the marginal utility of x diminish, remain constant, or
increase as the consumer buys more x? Explain.
c) What is MRSx, y?
d) Is MRSx, y diminishing, constant, or increasing as the consumer
substitutes x for y along an indifference curve?
e) On a graph with x on...

. Suppose utility is given by the following function:
u(x, y) = min(2x, 3y) Suppose Px = 4, Py =
6, and m = 24.
Use this information to answer the following questions:
(a) What is the no-waste condition for this individual?
(b) Draw a map of indifference curves for these preferences. Be
sure to label your axes, include the no-waste line, and draw at
least three indifference curves.
(c) Given prices and income, what is the utility-maximizing
bundle of...

7.
Suppose you have the following utility function for two
goods:
u(x1, x2) = x
1/3
1 x
2/3
2
. Suppose your initial income is I, and prices are p1 and
p2.
(a) Suppose I = 400, p1 = 2.5, and p2 = 5. Solve for the
optimal bundle. Graph the budget
constraint with x1 on the horizontal axis, and the
indifference curve for that bundle.
Label all relevant points
(b) Suppose I = 600, p1 = 2.5, and...

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