a) ANSWER : Only good y is consumed. Optimal consumption of X= 0 . Optimal consumption of Y= I/Py
b) ANSWER: only good x is consumed. Optimal consumption of X= I/Px . Optimal consumption of Y = 0
only answer C.
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a) ANSWER : Only good y is consumed. Optimal consumption
of X= 0 . Optimal consumption...
Intuition. Consider this problem. ma U = x + y e need to relax the usual...
Intuition. Consider this problem.
ma U = x + y e need to relax the usual two conditions we assume for an optimal solution (tangency and binding constraint) because this problem will yield corner solutions. Tha Lagrangian method will not be helpful, so use your intuition and graphs. anglan methd wil na Suppose Px-1 and Py-2. What is the optimal consumption of X and Y? Suppose Px 2 and Py-1. What is the optimal consumption of X and Y? Does...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4)...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
U 1 3 x 3 y 4 = Suppose the price of x is given by...
U 1 3 x 3 y 4 = Suppose the price of x is given by px and the price of y is given by Py and the budget income of the consumer is given by 1. Price of x, Price of y and Income are always strictly positive. Assume interior solution. a) Write the statement of the problem (1 point) b) Compute the parametric expressions of the equilibrium quantity of x & y purchased and the maximized utility. You...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B)...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that is not the optimal bundle. C) Suppose U=X∙Y5. Find X* and Y*. D) Suppose U = 5∙X + 2∙Y and I=12, Px=2 and Py=1. Find X* and Y*.
Optimal Consumption of good x and good y: Maximization Rule - Maximization of Utility given a...
Optimal Consumption of good x and good y: Maximization Rule - Maximization of Utility given a Budget Constraint = Marginal Utility of good x/Price of good x = Marginal Utility of good y/Price of y Calculate Consumption Bundle using the following information: Price of Good x = $5, Price of Good y = $16 and Income = $100 / 0 Quantity Consumed Total Utility Quantity Consumed Total Utility Calculate: a.) Price Elasticity of Demand =% Change in Quantity Demanded/%Change in...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that is not the optimal bundle. C) Suppose U=X∙Y5. Find X* and Y*. D) Suppose U = 5∙X + 2∙Y and I=12, Px=2 and Py=1. Find X* and Y*.
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed...
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed when income falls if x and y are normal goods? Draw a budget constraint (before the income decrease) and a convex utility curve that corresponds to the optimal consumption bundle. Draw a new budget constraint (after income falls) and a new convex utility curve that corresponds to the optimal consumption bundle. Has the amount of x and y consumed increased or decreased due to...
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...
Intuition. Consider this problem.
ma U = x + y e need to relax the usual two conditions we assume for an optimal solution (tangency and binding constraint) because this problem will yield corner solutions. Tha Lagrangian method will not be helpful, so use your intuition and graphs. anglan methd wil na Suppose Px-1 and Py-2. What is the optimal consumption of X and Y? Suppose Px 2 and Py-1. What is the optimal consumption of X and Y? Does...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
U 1 3 x 3 y 4 = Suppose the price of x is given by px and the price of y is given by Py and the budget income of the consumer is given by 1. Price of x, Price of y and Income are always strictly positive. Assume interior solution. a) Write the statement of the problem (1 point) b) Compute the parametric expressions of the equilibrium quantity of x & y purchased and the maximized utility. You...
Optimal Consumption of good x and good y: Maximization Rule - Maximization of Utility given a Budget Constraint = Marginal Utility of good x/Price of good x = Marginal Utility of good y/Price of y Calculate Consumption Bundle using the following information: Price of Good x = $5, Price of Good y = $16 and Income = $100 / 0 Quantity Consumed Total Utility Quantity Consumed Total Utility Calculate: a.) Price Elasticity of Demand =% Change in Quantity Demanded/%Change in...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed when income falls if x and y are normal goods? Draw a budget constraint (before the income decrease) and a convex utility curve that corresponds to the optimal consumption bundle. Draw a new budget constraint (after income falls) and a new convex utility curve that corresponds to the optimal consumption bundle. Has the amount of x and y consumed increased or decreased due to...
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...
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