A consumer has the utility function over goods X and Y, U(X; Y) = X1/3Y1/2 Let...
A consumer has the utility function over goods X and Y, U(X; Y) = X1/3Y1/2
Let the price of good x be given by Px, let the price of good y be given by Py,
and let income be given by I.
- Derive the consumer’s generalized demand function for good X.
- Solve for the Marshallian Demand for X and Y using Px, and Py (there are no numbers—use the notation).
- c. Is good Y normal or inferior? Explain precisely.
Homework Answers
Add Answer to:
A consumer has the utility function over goods X and Y, U(X; Y)
= X1/3Y1/2
Let...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y}...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
1. Suppose a consumer has the utility function over goods x and y u(x, y) =...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
7. A consumer has the following utility function for goods X and Y: U(X,Y) 5XY3 +10...
7. A consumer has the following utility function for goods X and Y: U(X,Y) 5XY3 +10 The consumer faces prices of goods X and Y given by px and py and has an income given by I. (5 marks) Solve for the Demand Equations, X (px,py,I) and Y*(px,py,I) a. b. (5 marks) Calculate the income, own-price and cross-price elasticities of demand for X and Y
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the...
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the consumer's Marshallian demand functions. (2) Find the consumer's compensated demand functions. (3) Suppose the price of good y is Py = $1 per unit and the consumer's income is 1 = $20. Find the total effects on good x and good y when the price of good x increases from px - $1 per unit to p} = $2 per unit.
A consumer buys two goods, good X and a composite good Y. The utility function is...
A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X, Y) = 2X1/2+Y. The demand function for good X is X = (Py/Px)2. (Edit: The price of X is Px, the price of Y is Py.) Suppose that initially Px=$0.5 and then it falls and becomes Px=$0.2 Calculate the substitution effect, income effect, and the price effect and show the answer graphically.
A consumer buys two goods, good X and a composite good Y. The utility function is...
A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X,Y) = In3XY. The price of X is Py, the price of Y is Py and Income is I. 1) Derive the demand equation for good X. ( 5 marks) 2) Are the two goods X and Y complements or substitutes? Why? ( 5 marks) 3) Suppose that I=$10 and suppose that initially the Px = $1 and subsequently Px falls and...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗ = m/Px (a/a+b) where m is income and Px is the price of good x. Using this demand function, find the formula for this consumer’s price elasticity of demand. Interpret it in words.
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $180...
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $180 to spend, and the price of X, PX = 4.50, and the price of Y, PY = 2 a. How much X and Y should the consumer purchase in order to maximize her utility? b. How much total utility does the consumer receive? c. Now suppose PX decreases to 2. What is the new bundle of X and Y that the consumer will demand?...
(a) A representative consumer has a utility function U (x, y) = xy. A representative firm makes good x and has a product...
(a) A representative consumer has a utility function U (x, y) = xy. A representative firm makes good x and has a production function x = f(k, l) = (kl)0.25and an unavoidable fixed cost equal to A. There are 100 consumers and, initially, 100 firms. Prices are w = v = Py = 1 and Px is determined in a competitive market. Representative consumer income is I = 2. (a) Find the representative individual’s Marshallian demand for good x?
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
7. A consumer has the following utility function for goods X and Y: U(X,Y) 5XY3 +10 The consumer faces prices of goods X and Y given by px and py and has an income given by I. (5 marks) Solve for the Demand Equations, X (px,py,I) and Y*(px,py,I) a. b. (5 marks) Calculate the income, own-price and cross-price elasticities of demand for X and Y
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the consumer's Marshallian demand functions. (2) Find the consumer's compensated demand functions. (3) Suppose the price of good y is Py = $1 per unit and the consumer's income is 1 = $20. Find the total effects on good x and good y when the price of good x increases from px - $1 per unit to p} = $2 per unit.
A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X,Y) = In3XY. The price of X is Py, the price of Y is Py and Income is I. 1) Derive the demand equation for good X. ( 5 marks) 2) Are the two goods X and Y complements or substitutes? Why? ( 5 marks) 3) Suppose that I=$10 and suppose that initially the Px = $1 and subsequently Px falls and...
Most questions answered within 3 hours.
-
When UV light of wavelength 288 nm falls on a metal surface, the
maximum kinetic energy...
asked 1 minute from now -
Your company has just brought in a new line of products... And
they are pieces of...
asked 2 minutes ago -
in three paragraphs or more discuss the role of the U.S.
Children’s Bureau in dealing with...
asked 1 minute ago -
Place the following salts in order of increasing water
solubility:
i. Fe(OH)2 Ksp = 7.9 ×...
asked 4 minutes ago -
If inflation is increasing at 2.6 percent per year, and your
salary increases at the same...
asked 5 minutes ago -
An aspirin dose of 5.0mg per kg of body weight has been
prescribed to reduce the...
asked 11 minutes ago -
The AASB Conceptual Framework (2.12-2.19) refers to ‘faithful
representation’ as being necessary for financial information to...
asked 16 minutes ago -
A U.S. corporation with net receivables in euro could hedge by
_________________.
A. buying euro forward...
asked 18 minutes ago -
Consider the following reversible reaction: CO2 +
H2O <--> H2CO3.In which
direction (right or left) will...
asked 21 minutes ago -
Which of the following probabilities indicates a relationship
that is not statistically significant?
Group of answer...
asked 22 minutes ago -
QUESTION 8
Which layer of the TCP/IP hierarchy presents incoming messages
to the computer user?
a....
asked 29 minutes ago -
A solenoid a cross-sectional area of 5.4x10^-4 m^2, consists of
540 turns per meter, and carries...
asked 40 minutes ago