Homework Answers
In this question first we setup lagrangian and maximize the equation with and find out the optimal value of x and y. answer above question is explained below
in part b we show how solution we get from lagrangian is not optial because utility of consumer is negative from the consumption of both goods.
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4. Suppose there is a consumer that is trying to solve the following optimization problem: -...
please answer both (a) and (b) thank you 3. Suppose there is a consumer that is...
please answer both (a) and (b)
thank you
3. Suppose there is a consumer that is trying to solve the following optimization problem: Maxxy -(x-4)2-(y - 1)2 s.t. 4x +2y < 20 (a) Use the Lagrangian method to solve the above utility maximization problem. That is, jump straight to setting up the Lagrangian and solving. (11 points) ve 2 1. xy (b) Are the demands you solved for in part a the utility maximizing values for x and y? If...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1 u(x,y) = 2x+2y C2 u(x,y) = x^3/4y^1/4 C3 u(x,y) = min(x,y) C4 u(x,y) = min(4x,3y) On the appropriate graph, draw each consumer’s indifference curves through the following points: (2,2), (4,4), (6,6) and (8,8), AND label the utility level of each curve. Hint: Each grid should have 4 curves on it representing the same preferences but with different utility levels. 3. In the following parts,...
In each of the following constrained optimization problems, use the Lagrangian method to solve for a...
In each of the following constrained optimization problems, use the Lagrangian method to solve for a solution where possible. When the Lagrangian method fails to give the unique correct answer carefully explain why. Let f(x,y)y. Solve max(ru) f(x, y) s.t. r2 3 0 and y 1.
need help on b, c and d please. 2. Suppose a consumer has the utility function...
need help on b, c and d please.
2. Suppose a consumer has the utility function over goods x and y u(x,y) = 4x^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*(Papy,m) and y" (Px.py,m). Show all of your work...
1. Price of x is 12 and price of y is 8. Answer the following questions...
1. Price of x is 12 and price of y is 8. Answer the following questions for a consumer who earns $600 and whose preference can be represented with the utility functions U(x,y) x0.4y0.6 = a) Write down the utility maximization problem. (2 points) b) Does the utility function represent convex preference? Explain. (2 points) c) Write down the budget constraint. What is the slope of the budget line? (2 points) d) What is the slope of the indifference curve...
please help me the best you can Part 1: Optimization with inequality constraints 1. A consumer...
please help me the best you can
Part 1: Optimization with inequality constraints 1. A consumer lives on an island. Her utility function is U = (x²y)1/3. She produces two goods, x and y. She faces a production constraint and an environmental constraint: Her production possibility frontier is: x² + y2 s 300. She faces an environmental constraint given by x + y = 200. a) Set up the Lagrangian function. b) List all of the Kuhn-Tucker conditions. c) Interpret...
Problem 2 Expenditure Function: E = x + 2y Utility Constraint: 75 = Vx+ Vy (a)...
Problem 2 Expenditure Function: E = x + 2y Utility Constraint: 75 = Vx+ Vy (a) Write the Lagrangian function for this problem (b) Solve for the optimal values of x and y (Note that you DON'T have to use the Lagrangian from A)
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 U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and...
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose...
please answer both (a) and (b)
thank you
3. Suppose there is a consumer that is trying to solve the following optimization problem: Maxxy -(x-4)2-(y - 1)2 s.t. 4x +2y < 20 (a) Use the Lagrangian method to solve the above utility maximization problem. That is, jump straight to setting up the Lagrangian and solving. (11 points) ve 2 1. xy (b) Are the demands you solved for in part a the utility maximizing values for x and y? If...
In each of the following constrained optimization problems, use the Lagrangian method to solve for a solution where possible. When the Lagrangian method fails to give the unique correct answer carefully explain why. Let f(x,y)y. Solve max(ru) f(x, y) s.t. r2 3 0 and y 1.
need help on b, c and d please.
2. Suppose a consumer has the utility function over goods x and y u(x,y) = 4x^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*(Papy,m) and y" (Px.py,m). Show all of your work...
1. Price of x is 12 and price of y is 8. Answer the following questions for a consumer who earns $600 and whose preference can be represented with the utility functions U(x,y) x0.4y0.6 = a) Write down the utility maximization problem. (2 points) b) Does the utility function represent convex preference? Explain. (2 points) c) Write down the budget constraint. What is the slope of the budget line? (2 points) d) What is the slope of the indifference curve...
please help me the best you can
Part 1: Optimization with inequality constraints 1. A consumer lives on an island. Her utility function is U = (x²y)1/3. She produces two goods, x and y. She faces a production constraint and an environmental constraint: Her production possibility frontier is: x² + y2 s 300. She faces an environmental constraint given by x + y = 200. a) Set up the Lagrangian function. b) List all of the Kuhn-Tucker conditions. c) Interpret...
Problem 2 Expenditure Function: E = x + 2y Utility Constraint: 75 = Vx+ Vy (a) Write the Lagrangian function for this problem (b) Solve for the optimal values of x and y (Note that you DON'T have to use the Lagrangian from A)
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 U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose...
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