For which of the following utility functions can we use the Lagrange method to solve the...
For which of the following utility functions can we use the Lagrange method to solve the utility maximisation problem? Explain
W(x1,x2)=X1X2(1/2) OR Z(x1x2) =X1(1/2)+X2(1/2)
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Ans.
For all the function we have given, we can use Lagrange method to solve the utility maximisation problem. Because for the all the functions we can find local maxima and minima for the equality constraint ( budget line in this case)
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For which of the following utility functions can we use the
Lagrange method to solve the...
For the following utility functions, a. Find the marginal rate of substitution. b. Derive the equation...
For the following utility functions, a. Find the marginal rate of substitution. b. Derive the equation for the indifference curve where utility is equal to a value of 100. c. Plot the indifference curve where utility is equal to a value of 100. (1) u(x1, x2) = x1x2; (2) u(x1, x2) = x1x2 + 10x2; (3) u(x1, x2) = x12 + x2
Do the following utility functions represent the same preferences? Please provide your reasoning (a) u(X1; XY)...
Do the following utility functions represent the same
preferences? Please provide your reasoning
(a) u(X1; XY) = X1 X2, V(X; X2) = 3(x] X2)2 +6 (b) u(x]; X») = X1X2, V(X]; X2) =-3(x1x2)2 +6 (c) u(x1,x2)=X]X2,v(x1,x2)=lnx1 +lnx2 (d) u(x]; X) = X1 X2, V(X1; X2) = x1 + x2
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3...
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do not check the second order sufficiency conditions) b) If the right side of the above constraint (1) is changed to 3.4, using sensitivity analysis find the approximate new minimum value of fX).
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
1. Consider a utility-maximizing price-taking consumer in a two good world. Denote her budget constraint by...
1. Consider a utility-maximizing price-taking consumer in a two good world. Denote her budget constraint by p1x1 + p2x2 = w, p1,p2,w > 0,x1,x2 ≥ 0 (1) and suppose her utility function is u(x1,x2) = 2x1/2 1 + x2. (2) Since her budget set is compact and her utility function is continuous, the Extreme Value Theorem tells us there is at least one solution to this optimization problem. In fact, demand functions, xi(p1,p2,w),i = 1,2, exist for this example. (i)...
Find the optimal bundle for the following utility functions and for budget line (P1X1+P2X2=m) a) U(X1,X2)=X1X2...
Find the optimal bundle for the following utility functions and for budget line (P1X1+P2X2=m) a) U(X1,X2)=X1X2 b) U(X1,X2)=X1^2X2^3 c) U(X1,X2)=X1^2+2X2 d)U(X1,X2)= ln (x1^3X2^4) e) U(X1,X2)= 2X1+X2 f) U(X1,X2)= min (2X1,X2)
please answer step by step Solve the following problem using Lagrange multiplier method: Maximize f(x.y,z) =...
please answer step by step
Solve the following problem using Lagrange multiplier method: Maximize f(x.y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2-1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above changed to: (3) (4) constraints are 2x-0.9y-z 2 x2+y2-0.9.
Solve the...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9.
Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9
Solve the following problem using Lagrange...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 co...
Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 comma x subscript 2 right parenthesis equals x subscript 1 cubed x subscript 2 squared (a) What is your optimal choice for x1 and x2 (as functions of p1 and p2 and I) ? Use the Lagrange Method. (b) Given prices p1...
Do the following utility functions represent the same
preferences? Please provide your reasoning
(a) u(X1; XY) = X1 X2, V(X; X2) = 3(x] X2)2 +6 (b) u(x]; X») = X1X2, V(X]; X2) =-3(x1x2)2 +6 (c) u(x1,x2)=X]X2,v(x1,x2)=lnx1 +lnx2 (d) u(x]; X) = X1 X2, V(X1; X2) = x1 + x2
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do not check the second order sufficiency conditions) b) If the right side of the above constraint (1) is changed to 3.4, using sensitivity analysis find the approximate new minimum value of fX).
a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
please answer step by step
Solve the following problem using Lagrange multiplier method: Maximize f(x.y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2-1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above changed to: (3) (4) constraints are 2x-0.9y-z 2 x2+y2-0.9.
Solve the...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9.
Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9
Solve the following problem using Lagrange...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
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