Question

A consumer with convex, monotonic preferences consumes non-negative amounts of x1 and x2

Given u(x1,x2)=x1^a . x2^(.5-a) represents said preferences

What restrictions must you place on a? Explain.

Answer #1

Suppose that a consumer has preferences over bundles of
non-negative amounts of each two goods, x1 and x2, that can be
represented by a quasi-linear utility
function of the form
U(x1,x2)=x1 +√x2.
The consumer is a price taker who faces a price per unit of good
one that is equal to $p1 and a price per unit of good two that is
equal to $p2. An- swer each of the following questions. To keep
things relatively simple, focus only on...

Suppose that a consumer has perfect complements, or Leontief,
preferences over bundles of non-negative amounts of each of two
commodities. The consumer’s consumption set is R^2(positive). The
consumer’s preferences can be represented by a utility function of
the form U(x1, x2) = min(x1, x2).
1. Illustrate the consumer’s weak preference set for an
arbitrary (but fixed) utility level U.
2. Illustrate a representative iso-expenditure line for the
consumer.
3. Illustrate the consumer’s utility-constrained expenditure
minimisation problem.
4. Illustrate the derivation...

2. Assume a consumer has as preference relation represented by
u(x1; x2) = ax1 + bx2 with x 2 C = R2 +; and a; b > 0: Answer
the following: a. Show the preference relation this consumer is
convex and strictly monotonic. b. Graph the indiference curves for
this consumer c. Compute the MRS between good 1 and good 2, and
explain why it coincides with the slope of an indiference curve. d.
Characterize the demand functions/correspondences for this...

Consider a consumer who consumes two goods and has utility
function
u(x1,x2)=x2 +√x1.
The price of good 2 is 1, the price of good 1 is p, and income is
m.
(1) Show that a) both goods are normal, b) good 1 is an ordinary
good, c) good 2 is a gross substitute for good 1.

Consider a consumer that has preferences defined over bundles
of non-negative amounts of each of two commodities. The consumer’s
consumption set is R2+. Suppose that the consumer’s preferences can
be represented by a utility func- tion, U(x1,x2). We could imagine
a three dimensional graph in which the “base” axes are the quantity
of commodity one available to the consumer (q1) and the quantity of
commodity two available to the consumer (q2) respec- tively. The
third axis will be the “height”...

1. A consumer has an utility function given by U(x1, x2) = ?
log(x1) + (1 ? ?) log(x2), with0<?<1.
HerincomeisgivenbyM,andthepricesshefacesarep1 andp2, respectively.
What is the optimal choice of x1 and x2? Follow the steps outlined
in the math refresher notes. How does this result compare to the
one in the notes? Explain.

1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21 +
2x1x2 + x22
. Al’s wife, El Einstein, has a utility function v(x1,
x2) = x2 + x1.
(a) Calculate Al’s marginal rate of substitution between
x1 and x2.
(b) What is El’s marginal rate of substitution between
x1 and x2?
(c) Do Al’s and El’s utility functions u(x1,
x2) and v(x1, x2) represent the
same preferences?
(d) Is El’s utility function a...

What is the generating function for the number of non-negative
integer solutions to
x1 + x2 + x3 + x4 + x5 = 50
if:
1.) There are no restrictions
2.) xi >= 2 for all i
3.) x1 <= 10
4.) xi <= 12 for all i
5.) if x1 is even

Bundes preferences are given by the utility function
u(x1+x2)=x1+x2. Suppose p2=3 and m=24. Show all working and plot
this consumers PCC when p1 drops continuously from 6 to 2.

The utility function U(x1, x2) = lnx1 ^5 + lnx2^2 represents
Cobb- Douglas preferences. Show if it is true or false. (without
using graph)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 11 minutes ago

asked 13 minutes ago

asked 21 minutes ago

asked 22 minutes ago

asked 22 minutes ago

asked 28 minutes ago

asked 35 minutes ago

asked 38 minutes ago

asked 43 minutes ago

asked 44 minutes ago

asked 1 hour ago