Question
In: Economics
Cleopatra spends all her money on bags (B) and shoes (S). Her utility function is U(B,...
Cleopatra spends all her money on bags (B) and shoes (S). Her utility function is U(B, S) = 2B^0.5S^0.5 . Her income is $150. Price of shoes is pS = 2. Price of bags depends on the number of bags purchased. Bags cost $5 each if she purchases between 1 and 8 bags. If she purchases more than 8 bags, the price falls to $2 for all subsequent books. (a) Draw Kleopatra's budget constraint where bag is on the horizontal axis. (10 Points) (b) Solve for Cleopatra's optimal bundle. (15 Points) (c) Suppose Cleopatra's utility function is U(B, S) = 0.5ln(B) + 0.5ln(S). What is her optimal bundle? (10 Points) (Hint: Compare the MRS for both utility functions.)
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
Cleopatra spends all her money on bags (B) and shoes (S). Her utility function is U(B,...
Cleopatra spends all her money on bags (B) and shoes (S). Her
utility function is U(B, S) = 2B0.5S
0.5
. Her income is
$150. Price of shoes is pS = 2. Price of bags depends on the number
of bags purchased. Bags cost $5 each if she purchases
between 1 and 8 bags. If she purchases more than 8 bags, the price
falls to $2 for all subsequent books.
(a) Draw Kleopatra's budget constraint where bag is on the...
Jessica spends all her money on bags(B) and shoes(S). Her utility function is U(B,S) = 2...
Jessica spends all her money on bags(B) and shoes(S). Her
utility function is U(B,S) = 2 * B^0.5 * S^0.5 . Her income is
150$. Price of shoes is Ps = 2. Price of bags depends on the number
of bags purchased. Bags cost $5 each if she purchases between 1 and
8 bags. If she purchases more than 8 bags, the price falls to $2
for all subsequent bags.
a) Draw Jessica's budget constraint where bag is on the...
Lin spends her income on green goods (G) and born goods (B). Her utility function is Her...
Lin spends her income on green goods (G) and born goods
(B). Her utility function is
Her marginal utility for green goods is
Her marginal utility for brown goods is
Find Lin's demand for brown goods expressed in terms of
exogenous parameters
An investor's utility function for money (Bernoulli utility function) is the square root of money: u(x)=√x....
An investor's utility function for money (Bernoulli utility
function) is the square root of money: u(x)=√x. Her decision making
can be modeled by assuming that she maximizes her expected utility.
Her current wealth is 100. (All quantities are in hundreds of
dollars.)
She has the opportunity to buy a security that either pays 8
(the "good outcome") or loses 1 (the "bad outcome"). She can buy as
many units as she wishes. For example, if she buys 5 units, she...
An investor's utility function for money (Bernoulli utility function) is the square root of money: u(x)=√x....
An investor's utility function for money (Bernoulli utility
function) is the square root of money: u(x)=√x. Her
decision making can be modeled by assuming that she maximizes her
expected utility. Her current wealth is 100. (All quantities are in
hundreds of dollars.)
She has the opportunity to buy a security that either pays 8
(the "good outcome") or loses 1 (the "bad outcome"). She can buy as
many units as she wishes. For example, if she buys 5 units, she...
Derek spends all his income on Coke and chips. Derek's utility function is U(x, y) =...
Derek spends all his income on Coke and
chips.
Derek's utility function is U(x, y) = min(4x, 2x + y),
where x is his consumption of Coke
(in cans) and y is his consumption of chips (in
packets). Derek is consuming 15 cans
Of Coke and 10 packets of chips. The price of Coke is
$10 per can.
a. Graph the indifference curve for Derek that passes
through the point (15,10). What is
the marginal rate of substitution at
(15,10)?...
Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes,...
Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S, T) = 2ST, so MUs=2T and MUT = 2S. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on clothing and dancing. (Hint: See Q&A 4.3.) a. What is the equation for her budget line? Draw...
Leah loves buying shoes and going out to dance. Her utility function for pairs of shoes,...
Leah loves buying shoes and going out to dance. Her utility
function for pairs of shoes, X, and the number of times she goes
dancing per month, Y, is given by
U(x,y)=20XY2+100U(x,y)=20XY2+100
Now suppose that a pair of shoes sells for $10 and it costs Leah
$5 to spend an evening out dancing. And assume that she has $90 to
spend on clothing and dancing. You are now asked to derive consumer
equilibrium.
a. What is the equation for her...
Margaret spends all of her income on t-shirts (x1) and shoes (x2). Her preferences can be...
Margaret spends all of her income on t-shirts (x1) and shoes
(x2). Her preferences can be represented by the utility function u
(x1, x2) = 2√x1x2.
(a) Derive the demand functions for t-shirts and shoes in terms
of the price of t-shirts (p1), the price of shoes (p2), and income
(m). Show your result on a graph.
(b) Draw the Income Offer Curve and Engel Curves (one for each
good).
(c) Draw the Price Offer Curve and Demand Curves.
(d)...
Margaret spends all of her income on t-shirts (x1) and shoes (x2). Her preferences can be...
Margaret spends all of her income on t-shirts (x1) and shoes
(x2). Her preferences can be represented by the utility function u
(x1, x2) = 2√x1x2
(a) [15 Points] Derive the demand functions for t-shirts and
shoes in terms of the price of t-shirts (p1), the price of shoes
(p2), and income (m). Show your result on a graph.
(b) [10 Points] Draw the Income Offer Curve and Engel Curves
(one for each good).
(c) [10 Points] Draw the Price...
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