Question
In: Economics
Suppose that an individual has a utility function of the form U = Y½ where U...
Suppose that an individual has a utility function of the form U = Y½ where U is utility and Y is income.
a) Calculate the utility level for Y values of $10,000, $40,000, $90,000, $160,000, and $250,000 and then plot the individual’s total utility function.
b) This individual is currently earning $90,000 but has a 50-50 chance of earning either $40,000 or $160,000 in a new job.
i) Calculate the expected income and utility from the new job.
ii) Calculate and illustrate the risk premium .
iii) Calculate the standard deviation.
PLEASE SHOW YOUR WORK ON HOW YOU GOT EACH ANSWER (INCLUDING STEP-BY-STEP CALCULATIONS)!
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
1. Suppose that an individual has the following utility function, ? = ?^0.5?.?, where U stands...
1. Suppose that an individual has the following utility
function, ? = ?^0.5?.?, where U stands for utility and W for
Wealth. The individual currently has a net wealth of $400,000. The
individual believes there is a 5% chance they will get into a car
accident this year. It is expected that a car accident would cost
them $100,000 (dropping their overall wealth to $300,000).
a) How much would it cost to purchase an actuarially fair
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Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...
Suppose that the utility function of a consumer is U(x,y) = x
¼y ¾, where x and y are the quantities of the
good X and good Y consumed, respectively. The consumer's income is
400.
(a) What is the demanded bundle when the price of good X is 10
and the price of good Y is 10?
(b) Redo part (a) when the price of good X is doubled?
(c) Redo part (a) when the price of good Y is...
Consider an individual with utility of the form: U(x,y) = xayb where (a+b)=1. The price of...
Consider an individual with utility of the form: U(x,y) =
xayb where (a+b)=1. The price of good x is
px and the price of good y is py. The
individual faces a budget constraint of I (or income).
A. Find the demand functions for the individual in question.
B. Suppose the price of each good increases by a factor of T
(therefore the price of good x is (1+T)px and the price
of good y is (1+T)py). Prove that the...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x,
y) = −4(x − 5.5)^2 − 2(y − 3.5)^2 Further assume that the price of
good x, px = $6, the price of good y, py = $8, and the individual
has an income m = $65
a) Draw an indifference curve (one IC is enough) that represents
this person’s preferences. Please label the graph properly
including values for x and y.
b) Intuitively, and without formally solving, can you guess...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x,
y) = −4(x − 5.5)^2 − 2(y − 3.5)^2
Further assume that the price of good x, px = $6, the price of
good y, py = $8, and the individual has an income m = $65
a) Draw an indifference curve (one IC is enough) that represents
this person’s preferences. Please label the graph properly
including values for x and y.
b) Intuitively, and without formally solving, can you guess...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x,
y) = −4(x − 5.5)^2 − 2(y − 3.5)^2
Further assume that the price of good x, px = $6, the price of
good y, py = $8, and the individual has an income m = $65
a) Draw an indifference curve (one IC is enough) that represents
this person’s preferences. Please label the graph properly
including values for x and y.
b) Intuitively, and without formally solving, can you guess...
An individual has the utility function: U(x,y)=xyx = $ spent on educationy = $...
An individual has the utility function: U(x,y)=xyx = $ spent on educationy = $ spent on other goodsThe individual receives a voucher that pays $S for education or
a lump-sum subsidy of $S.1. What is the optimal bundle with the voucher?2. What is the optimal bundle with the lump-sum subsidy?3. With which option is she strictly better off?
Suppose an individual has the following utility function: U(X,Y) = 2XY. Draw the budget constraint when...
Suppose an individual has the following utility function: U(X,Y)
= 2XY. Draw the budget constraint when the price of each unit of X
and Y are 5 and 4, and income is 120. Find the choice that
maximizes utility.
Suppose that an individual has wealth of $20,000 and utility function U(W) = ln(W), where ln(W)...
Suppose that an individual has wealth of $20,000 and utility
function U(W) = ln(W), where ln(W) indicates the natural logarithm
of wealth. What is the maximum amount this individual would pay for
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An individual has the utility function u = min (x, y). His income is $ 12....
An individual has the utility function u = min (x, y). His
income is $ 12.
Initially, the prices were px = 4 and py = 1, and the individual
consumed the basket x = y = 2.4.
Then, px increases to $ 6 (py does not change), and the individual
now consumes the basket
x = y = 1.71.
a) Calculate the compensatory variation of this price change.
b) Calculate the equivalent variation of this price change.
c) On...
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