Question
In: Math
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility function given by Ux,y=x+y-0.05x2-0.05y2 subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two goods are, respectively, 2 and 5. Assuming marginal utilities Ux, Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
Solutions
milcah answered 2 years agoRelated Solutions
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
A consumes two goods, x and y. A ’s utility function is given by u(x, y)...
A consumes two goods, x and y. A ’s utility function is given
by u(x, y) = x 1/2y 1/2
The price of x is p and the price of y is 1. A has an income
of M.
(a) Derive A ’s demand functions for x and y.
(b) Suppose M = 72 and p falls from 9 to 4. Calculate the
income and substitution effects of the price change.
(c) Calculate the compensating variation of the price
change....
You are a consumer who consumes goods X (education) and goods Y (recreation), where the price...
You are a consumer who consumes goods X (education) and goods Y
(recreation), where the price of good X is PX and the price of Y is
Py. Your income that can be allocated to purchase these two items
is M.
Questions
a. What happens if the price of education rises? Describe the
substitution effect and the income effect.
b. Derive the demand curve for education.
You are a consumer who consumes goods X (education) and goods Y (recreation), where the price...
You are a consumer who consumes goods X (education) and goods Y
(recreation), where the price of good X is PX and the price of Y is
Py. Your income that can be allocated to purchase these two items
is M.
Question
a. What happens if the price of education rises? Describe the
substitution effect and the income effect.
b. Derive the demand curve for education.
You are a consumer who consumes goods X (education) and goods Y (recreation), where the price...
You are a consumer who consumes goods X (education) and goods Y
(recreation), where the price of good X is PX and the price of Y is
Py. Your income that can be allocated to purchase these two items
is M.
Questions
a. What happens if the price of education rises? Describe the
substitution effect and the income effect.
b. Derive the demand curve for education.
A utility-maximizing consumer believes two goods are Perfect Substitutes u(x, y) = 3x + 4y. She...
A utility-maximizing consumer believes two goods are Perfect
Substitutes u(x, y) = 3x + 4y. She pays pY = 2 and
pX = 1. Her income is m = 24. Next month the price of
good x will rise to pX = 3. Round your final answers to
3 decimal places.
What is the EV, CV and Approximate ΔCS?
A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...
A consumer purchases two goods, x and y and has utility
function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x
and MUy = 3. The price of x is px = 4 and the price of y is py = 2.
The consumer has M units of income to spend on the two goods and
wishes to maximize utility, given the budget.
Draw the budget line for this consumer when M=50 and the budget
line when...
13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y)...
13. Pip consumes two goods, x and y. Pip’s utility function is
given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of
y is 1. Pip has an income of M.
(a) Derive Pip’s demand functions for x and y. [5 marks]
(b) Suppose M = 72 and p falls from 9 to 4. Calculate the income
and substitution effects of the price change. [5 marks]
(c) Calculate the compensating variation of...
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