Question

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 (T), the equivalent lump sum tax (L), and the dead weight loss (DWL). (Hint: Expenditure minimization at the final level of utility.)

(c) Is good x a normal good? Does law of demand hold for good x? Are good x and good y substitutes or complements?

Answer #1

4. 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: ( Hint:
You need to find the initial, final, and hypothetical optimal
consumption bundles, their corresponding maximized utility levels
and/or minimized expenditure and compare. )...

Jane’s utility function has the following form: U(x,y)=x^2
+2xy
The prices of x and y are px and py respectively. Jane’s income
is I.
(a) Find the Marshallian demands for x and y and the indirect
utility function.
(b) Without solving the cost minimization problem, recover the
Hicksian demands for x and y and the expenditure function from the
Marshallian demands and the indirect utility function.
(c) Write down the Slutsky equation determining the effect of a
change in px...

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.

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?

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...

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...

Consider a consumer whose utility function is
u(x, y) = x + y (perfect substitutes)
a. Assume the consumer has income $120 and initially faces the
prices px = $1 and py = $2. How much x and y would they buy?
b. Next, suppose the price of x were to increase to $4. How
much would they buy now?
c. Decompose the total effect of the price change on demand
for x into the substitution effect and the...

Emily's preferences can be represented by u(x,y)=x^1/4 y^3/4 .
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: $ ____________

1.
The lump sum principle says...?
All taxes make a consumer equally unhappy
A tax on one good make a consumer happier than an equivalent
revenue lump sum tax.
A tax on one good make a consumer less happy than an equivalent
revenue lump sum tax.
Tax revenues should only be used as a lump sum, not split up among
many projects
A tax on one good should be kept small.
2.
For normal goods…?
A change in income causes...

Complete parts 1 and 2:
Part 1:
Suppose the consumer believes that goods X and Y are perfect
substitutes with 5 units of X equivalent to 1 unit of Y. Which of
the following is correct?
Group of answer choices
the marginal rate of substitution is not well defined when
(X,Y)=(5,1)
the marginal utility of X is 5 and the marginal utility of Y is
1
the utility function is U(X,Y)=X+5Y
the utility function is U(X,Y)=5X+Y
Part 2:
Suppose the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 16 minutes ago

asked 22 minutes ago

asked 26 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago