Homework Answers
![neli tj gu optinaal Pr 2Y 5n put - 15 X 12 12 25x &2 2 ] 2 u 15 CS Scanned with CamScanner](http://img.homeworklib.com/questions/4ed19c00-ce2c-11ea-8312-7d0c5bd1f3f7.png?x-oss-process=image/resize,w_560)
Add Answer to:
6. Consider the following constrained maximization problem: 2 5 tu (х, у) x7y7 max х,у s.t...
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y...
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y = 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (b) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x, y)? Compare with the value found in (a) for the Lagrange multiplier. (C) Suppose we change the budget constraint to px + y = m, but keep the same utility...
L I L I JUNULUI! SM 4. Consider the utility maximization problem max U(x,y) = (x...
L I L I JUNULUI! SM 4. Consider the utility maximization problem max U(x,y) = (x + y s.t. x+4y= 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (1) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x,y)? Compare with the value found in (a) for the Lagrange multiplier (c) Suppose we change the budget constraint to px + 4y=m, but keep the same utility...
9. Consider the utility maximization problem max x + y s.t. px + y =m, where...
9. Consider the utility maximization problem max x + y s.t. px + y =m, where the constants p, 9, and m are positive, and the constant a € (0,1). (a) Find the demand functions, x* (p, m) and y* (p, m). (b) Find the partial derivatives of the demand functions w.r.t. p and m, and check their signs. (c) How does the optimal expenditure on the x good vary with p?8 (d) Put a = 1/2. What are the...
(5) Consider how a consumer decides how much of two goods, x and y, to consume...
(5) Consider how a consumer decides how much of two goods, x and y, to consume but races amb constraint. The consumer maximizes the following utility function s.t. the budget constraint U(x, y) = (x - rayß subject to Pxx + p,Y = 1 Where x and y stand for the two goods, Px, and Py stand for the prices of the goods X and Y, respectively, and I stands for Income (a) Write down the Lagrangian and solve for...
Consider the following integer program Max 2x+3y s.t 6x+7y23 x-y
Consider the following integer program Max 2x+3y s.t 6x+7y23 x-y<12 xy0 x,y: integer Let V1 denote the optimal objective value of the above optimization problem. Let V2 denote the optimal objective value of the optimization problem obtained by dropping "x,y: integer" constraint. Similarly, let V3 denote the optimal objective value of the optimization problem obtained by dropping "x-y<-12" constraint which one of the following statements is correct? a. V2 V1 and V3<-V1 b. V1 V2 and V1<-V3 c. V2V1 but...
8.(15 POINTS) Consider the following optimization problem: Max xi + subject to : 5xí +60192 +...
8.(15 POINTS) Consider the following optimization problem: Max xi + subject to : 5xí +60192 + 5x3 = 1 and 21 > 0,22 > 0. where 2 and 32 are choice variables. (a) Write the Lagrangean and the Kuhn-Tucker conditions. (6) State and verify the second order condition. Distinguish between sufficient and necessary condi tions. (c) Is the constraint qualification condition satisfied? Show clearly why or why not. (d) Solve the Kuhn-Tucker conditions for the optimal choice: x1, x, and...
Consider the following linear program: Max 2A + 10B s.t. 3A ≤ 15 B ≤ 6...
Consider the following linear program: Max 2A + 10B s.t. 3A ≤ 15 B ≤ 6 4A + 4B = 28 A, B ≥ 0 a. draw graph that shows the feasible region for the problem b. What are the extreme points of the feasible region c. Draw graph that shows the optimal solution for the problem
Please answer the following question. (30 pts possible) 1 Consider the following (Cobb-Douglas) utility function: And...
Please answer the following question. (30 pts possible) 1 Consider the following (Cobb-Douglas) utility function: And budget constraint: M2 PX+PY 1. *Treat P, Py, M, a, and B as positive constants. Note, a +B Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) Show that the...
Complete parts a-e. 1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint:...
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
Problem 1: Consider the following linear optimization problem: max 1 +22x;3 subject to x1 + x2...
Problem 1: Consider the following linear optimization problem: max 1 +22x;3 subject to x1 + x2 +r3 10 2x1 -r2 2-4 i20, -1,2,3 a) Bring the problem to a standard form (b) Show that the point (2,8,0)T is optimal by the optimality condition of the linear program- ming. Is it an extreme point? Provide arguments for your answers (c) Determine at least one other point different than (2,8,0)T, which is an extreme point of the constraint set 1) (d) Find...
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y = 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (b) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x, y)? Compare with the value found in (a) for the Lagrange multiplier. (C) Suppose we change the budget constraint to px + y = m, but keep the same utility...
L I L I JUNULUI! SM 4. Consider the utility maximization problem max U(x,y) = (x + y s.t. x+4y= 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (1) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x,y)? Compare with the value found in (a) for the Lagrange multiplier (c) Suppose we change the budget constraint to px + 4y=m, but keep the same utility...
9. Consider the utility maximization problem max x + y s.t. px + y =m, where the constants p, 9, and m are positive, and the constant a € (0,1). (a) Find the demand functions, x* (p, m) and y* (p, m). (b) Find the partial derivatives of the demand functions w.r.t. p and m, and check their signs. (c) How does the optimal expenditure on the x good vary with p?8 (d) Put a = 1/2. What are the...
(5) Consider how a consumer decides how much of two goods, x and y, to consume but races amb constraint. The consumer maximizes the following utility function s.t. the budget constraint U(x, y) = (x - rayß subject to Pxx + p,Y = 1 Where x and y stand for the two goods, Px, and Py stand for the prices of the goods X and Y, respectively, and I stands for Income (a) Write down the Lagrangian and solve for...
Consider the following integer program Max 2x+3y s.t 6x+7y23 x-y<12 xy0 x,y: integer Let V1 denote the optimal objective value of the above optimization problem. Let V2 denote the optimal objective value of the optimization problem obtained by dropping "x,y: integer" constraint. Similarly, let V3 denote the optimal objective value of the optimization problem obtained by dropping "x-y<-12" constraint which one of the following statements is correct? a. V2 V1 and V3<-V1 b. V1 V2 and V1<-V3 c. V2V1 but...
8.(15 POINTS) Consider the following optimization problem: Max xi + subject to : 5xí +60192 + 5x3 = 1 and 21 > 0,22 > 0. where 2 and 32 are choice variables. (a) Write the Lagrangean and the Kuhn-Tucker conditions. (6) State and verify the second order condition. Distinguish between sufficient and necessary condi tions. (c) Is the constraint qualification condition satisfied? Show clearly why or why not. (d) Solve the Kuhn-Tucker conditions for the optimal choice: x1, x, and...
Please answer the following question. (30 pts possible) 1 Consider the following (Cobb-Douglas) utility function: And budget constraint: M2 PX+PY 1. *Treat P, Py, M, a, and B as positive constants. Note, a +B Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) Show that the...
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
Problem 1: Consider the following linear optimization problem: max 1 +22x;3 subject to x1 + x2 +r3 10 2x1 -r2 2-4 i20, -1,2,3 a) Bring the problem to a standard form (b) Show that the point (2,8,0)T is optimal by the optimality condition of the linear program- ming. Is it an extreme point? Provide arguments for your answers (c) Determine at least one other point different than (2,8,0)T, which is an extreme point of the constraint set 1) (d) Find...
Most questions answered within 3 hours.
-
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 41 minutes ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 2 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 2 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 4 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 4 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 4 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 4 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 5 hours ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 4 hours ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 4 hours ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 5 hours ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 4 hours ago