Question

Bob’s preferences over biscuits (x) and other goods (y) are
given by . His income is 10. a. Find Bob’s demand for x when the
price of y is 2 b. When the price of x increases from 1 to 3,
calculate the change in consumer surplus. Draw a graph to
illustrate.

Bob’s preferences over biscuits (x) and other goods (y) are given
by U(x,y)=xy. His income is 10.

Answer #1

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...

Consider a consumer with Cobb-Douglas preferences over two
goods, x and y described by the utility function u(x, y) = 1/3ln(x)
+ 2/3n(y) 1. Assume the prices of the two goods are initially both
$10, and her income is $1000. Obtain the consumer’s demands for x
and y.
2. If the price of good x increases to $20, what is the impact
on her demand for good x?
3. Decompose this change into the substitution effect, and the
income effect....

Consider a student who purchases education (x) and other goods
(y). The student has preferences over these goods given by u(x, y)
= ln(x) + 3ln(y). The prices of education and other goods are,
respectively, px = 10 and py = 5, and the student’s income is I =
20.
A. Graph the budget constraint, IEP, optimal bundle (x ∗ , y∗ ),
and the indifference curve passing through the optimal consumption
bundle. Label all curves, axes, slopes, and intercepts....

An individual has preferences over housing, x (measured in
square metres), and other goods, y, represented by utility function
u(x,y) = x4y. Her disposable income is $75000, and the price of
housing is $1000/m2, while that of other goods is py = $1.
c) [10 marks] Find the compensating variation (CV) value of this
policy’s effect on welfare, and provide an interpretation for
it.

Consider a student who purchases education (x) and
other goods (y). The student has preferences over these
goods given by u(x,y) = ln(x) +
3ln(y). The prices of education and other goods
are, respectively, px = 10 and
py = 5, and the student’s income is I
= 20.
1. What do limMUx(x,y) and
limMUy(x,y) tell you about the optimal
consumption x→0 y→0 bundle? (2 points)
2. Find an expression for the slope of the indifference curve
through the point...

Suppose a consumer's preferences are given by U(X,Y) = X*Y.
Therefore the MUX = Y and MUY = X. Suppose
the price of good Y is $1 and the consumer has $80 to spend (M =
80). Sketch the price-consumption curve for the
values
PX = $1
PX = $2
PX = $4
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...

Zhixiu has the following linear preferences over coffee (x) and
candy (y): u(x,y)=2x+5y
d. Solve the utility maximization problem for x* and y* when
m=150 and px=10.
e. Graph Zhixiu's demand function for candy y* as py changes
when her income is m=150 and the price of candy is px=10. Be sure
to label any kink points in your graph.
f. Set up the expenditure minimization problem for Zhixiu.
g. Solve the expenditure minimization problem for x^c and y^c
when...

A consumer has preferences given by U(x, y) = min[x, y].
(a) Calculate the equilibrium quantities of x and y when px = $2,
py = $3
and I = 12.
(b) Suppose px increases to $3 when a per unit tax of $1 is placed
on x.
What is the new value of x and how much tax revenue is
raised?
(c) Suppose that the same tax revenue is raised by an income tax
as
opposed to a per...

Consider an individual making choices over two goods, x and y
with prices px = 3 and py = 4, and who has income I = 120 and her
preferences can be represented by the utility function U(x,y) =
x2y2. Suppose the government imposes a sales tax of $1 per unit on
good x:
(a) Calculate the substitution effect and Income effect (on good
x) after the price change. Also Illustrate on a graph.
(b) Find the government tax revenues...

A consumer has an income of $120 to buy two goods (X, Y). the
price of X is $2 and the price of Y is $4. The consumer utility
function is given by ?(?, ?) = ? 2/3 ∗ ? 1/3 You are also told that
his marginal utilities are ??? = 2 3 ( ? ? ) 1/3 ??? = 1 3 ( ? ? )
2/3
1. Find the slope of the budget constrain. (1 point)
2. Calculate...

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