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Given a utility function U=(x+2)(y+1) and Px = 4, Py = 6, and budget B =...
4) A consumer’s utility function is u(x, y) = min{x, 3y} (a) Find the consumer’s optimal...
4) A consumer’s utility function is u(x, y) = min{x, 3y} (a) Find the consumer’s optimal choice for x, y as functions of income I and prices px,py. (b) Sketch the demand curve for y as a function of other price px when py = 10, I = 100. Suggestion: a picture showing the budget set, optimal choice and indifference curve. (I need help with the sketching which is the second part)
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...
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...
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) = 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...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her i...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her income I = 10. (e) Draw an optimal bundle which is the result of utility maximization under given budget set. (Hint: Assume interior solution). Define corresponding expenditure minimization problem (note the elements for expenditure minimization problem are (i) objective function, (ii) constraint, (iii) what to choose). (f)Describeaboutwhatthedualityproblemis. Definemarshalliandemandfuction andhicksiandemandfunction. (Hint: identifytheinputfactorsofthesefunctions.) (g) Consider a price increase for the good x from...
S An individual has a utility function as follows subject to the budget constraint; 6r+2y 110 i) Write down the Lagrangian function for this individual. (2 marks) (6 marks) Using Cramer's rule...
S An individual has a utility function as follows subject to the budget constraint; 6r+2y 110 i) Write down the Lagrangian function for this individual. (2 marks) (6 marks) Using Cramer's rule, solve for x, y and 2. ii) Using Hessian matrix, check the second-order sufficient condition to verify that the utility of this individual is at maximum. (3 marks)
S An individual has a utility function as follows subject to the budget constraint; 6r+2y 110 i) Write down the...
Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and
Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and income effect for good x from the price change.
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
1. (5 pts.) If U X13y23, M 120, Px-2, and Py-10, find the utility-maximizing combination of...
1. (5 pts.) If U X13y23, M 120, Px-2, and Py-10, find the utility-maximizing combination of X and Y using the Lagrangian multiplier. Also find the MRS and the ratio of the prices at the utility-maximizing combination. Show your work on a separate page. a. Units of X b. Units of Y c. MRS d. Px/Py
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...
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...
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) = 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...
S An individual has a utility function as follows subject to the budget constraint; 6r+2y 110 i) Write down the Lagrangian function for this individual. (2 marks) (6 marks) Using Cramer's rule, solve for x, y and 2. ii) Using Hessian matrix, check the second-order sufficient condition to verify that the utility of this individual is at maximum. (3 marks)
S An individual has a utility function as follows subject to the budget constraint; 6r+2y 110 i) Write down the...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
1. (5 pts.) If U X13y23, M 120, Px-2, and Py-10, find the utility-maximizing combination of X and Y using the Lagrangian multiplier. Also find the MRS and the ratio of the prices at the utility-maximizing combination. Show your work on a separate page. a. Units of X b. Units of Y c. MRS d. Px/Py
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