Question

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 answer fully and state any assumptions that you
make.]*

d) Neatly sketch two indifference curves based on the utility
function above. *[Ensure that you label the graph carefully, and
depict three points on each curve.]*

Answer #1

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...

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 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?

Jen’s utility function is U (X, Y ) = (X + 2)(Y + 1), where X is
her consumption of good X and Y is her consumption of good Y .
a. Write an equation for Jen’s indifference curve that goes
through the point (X, Y ) = (2, 8). On the axes below, sketch Jen’s
indifference curve for U = 36
b. Suppose that the price of each good is 1 and that Jen has an
income of 11....

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 there are 2 consumers, A and B. The utility functions of
each consumer are given by:UA(X, Y) =X^1/2 Y^1/2 UA(X, Y) = 3X+
2Y
The initial endowments are:W X/A= 10, W Y/A= 10, W X/B= 6, W
Y/B= 6
a) Using 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.
b) (4 points) What is the marginal rate...

For the utility function U(X,Y) = XY^3, find the marginal rate
of substitution and discuss how MRS XY changes as the consumer
substitutes X for Y along an indifference curve.

2. Suppose you can describe your preferences by the utility
function U =
2qS0.8qM0.2.
(a) Which good, ski lift tickets or meals out, provides you with
greater marginal utility when you have equal quantities of
each?
(b) Provide a formula for the slope of any indifference curve
(the Marginal Rate of Substitution) between ski lift tickets and
meals out.
(c) What happens to your Marginal Rate of Substitution as the
number of ski lift tickets you purchase increases (i.e., does...

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?

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.

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