Question

1. Suppose utility for a consumer over food(x) and clothing(y) is represented by u(x,y) = 915xy. Find the optimal values of x and y as a function of the prices px and py with an income level m. px and py are the prices of good x and y respectively.

2. Consider a utility function that represents preferences: u(x,y) = min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m.

3. Consider a utility function u(x1, x2) = ax1+bx2 and a budget line p1x1+p2x2=m If the absolute value of the slope of the indifference curve, a/b, is greater than the absolute value of the slope of the budget line, p1/p2 find the optimal consumption bundle.

4. Juliana's optimal consumption of movie tickets is given by the function x1=(3m)/(5p1), where m is her income and p1 is the price of a movie ticket. According to Juliana's preferences, movie tickets are inferior, neutral or normal good? Assuming her income (m=400.00) increases by $100.00 and the price of a movie ticket is p1=2, by how many units does her consumption of movie tickets change?

5. Douglas consumes two goods, x and y. His utility function is u(x,y) = √� + � Let the price of good x be $2 and the price of good y be $2. Furthermore, assume that Douglas has $420.00 to spend on these two goods. Find the demand for good x and y. Now suppose that the price of good x decreases to $1.00. What is the income effect and substitution effect of this price change on the demand for x?

Answer #2

answered by: anonymous

An agent has preferences for goods X and Y represented by the
utility function U(X,Y) = X +3Y
the price of good X is Px= 20, the price of good Y is
Py= 40, and her income isI = 400
Choose the quantities of X and Y which, for the given prices and
income, maximize her utility.

Suppose a consumer has the utility function U (x, y) = xy + x +
y. Recall that for this function the marginal utilities are given
by MUx(x,y) = y+1 and MUy(x,y) = x+1.
(a) What is the marginal rate of substitution MRSxy?
(b)If the prices for the goods are px =$2 and py =$4,and if the
income of the consumer is M = $18, then what is the consumer’s
optimal affordable bundle?
(c) What if instead the prices are...

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?

Sam's is interested in two goods, X and Y. His indirect utility
function is
U* = M px-.6 py-4.
( same as U* = M /(px.6
py0.4 ) )
where
M is Sam's income, and px and
py denote respectively the price of good X and the price
of good Y.
Sam's market demand functions are X*=0.6M/px and Y* =
0.4M/py .
Find the absolute value of the change in Sam's consumers surplus
if the price of good X...

Emily's preferences can be represented by u(x,y)=x1/4
y3/4 . Emily faces prices (px,py)
= (2,1) and her income is $120.
Her optimal consumption bundle is: _______
(write in the form of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same
Her new optimal consumption bundle
is:_______ (write in the form of (x,y) with no
space)
Her Equivalent Variation is:
$__________

A consumer has utility function U(x, y) = x + 4y1/2 .
What is the consumer’s demand function for good x as a function of
prices px and py, and of income m, assuming a
corner solution?
Group of answer choices
a.x = (m – 3px)/px
b.x = m/px – 4px/py
c.x = m/px
d.x = 0

Emily's preferences can be represented by u(x,y)=x1/4
y3/4 . Emily faces prices (px,py)
= (2,1) and her income is $120.
a) Her optimal consumption bundle is:________
(write in the form of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same
b) Her new optimal consumption bundle
is:_______ (write in the form of (x,y) with no
space)
c) Her Equivalent Variation
is: $________

Consider the utility function U(x,y) = xy Income is I=400, and
prices are initially
px =10 and py =10.
(a) Find the optimal consumption choices of x and y.
(b) The price of x changes, to px =40, while the price of y remains
the same. What are
the new optimal consumption choices for x and y?
(c) What is the substitution effect?
(d) What is the income effect?

Emily's preferences can be represented by u(x,y) =
x1/2 y1/2 . Emily faces prices
(px,py) = (2,1) and her income is $60. (some
formulas in chapter 5 might help)
Her optimal consumption bundle is:
______________ (write in the form of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same
Her new optimal consumption bundle is:
______________ (write in the form of (x,y) with
no space)
Her Equivalent Variation is:
$_______________
Her...

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

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