U=x^2y^2+xy Derive the Marshallian demands and indirect utility function
U=x^2y^2+xy
Derive the Marshallian demands and indirect utility function
Homework Answers
Marshallian Demand
Indirect Utility Function V(P, M)
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U=x^2y^2+xy
Derive the Marshallian demands and indirect utility function
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What...
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What restrictions does a Cobb-Douglas lity function (preferences) impose on demand functions? Explain your answer. marks) 1/4 Maximize u = x;"/4x2 4x, + 2x, = 100 Subject to - Use the information in above to derive the consumer's indirect utility anction (value function) and then prove Roy's identity (10 marks)
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min...
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold =...
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold = 1, Py = 1, and I = 8. a. Solve for the Marshallian demand functions of x and y (your answer should have numbers, not variables. You should round your answers to three decimal places): * old 4 y = 4 b. What is the utility associated with these demands, prices, and income? u = 16 c. Suppose the price of x rises to...
3. Consider the following utility function, u(x1;x2)=min[xa1; bxa2]; 00 (a) [15 points] Derive the Marshallian demand...
3. Consider the following
utility function, u(x1;x2)=min[xa1; bxa2]; 00 (a) [15 points]
Derive the Marshallian demand functions. (Explain your derivation
in details.) Does the Marshallian demand increase with price? Are
the two consumption goods normal goods? (b) [15 points] Derive the
Hicksian demand functions. Does the Hicksian demand increase with
price?
3. Consider the following utility function, (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two...
how to find indirect utility function here? Jeanette has the following utility function: U-ain(x) + b*In(y), where...
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
2. Jane's utility function has the following form: U (1,y) = 3x2 +2.ry The prices of...
2. Jane's utility function has the following form: U (1,y) = 3x2 +2.ry The prices of cand y are p, and Py respectively. Jane's income is I. (a) Find the Marshallian demands for and y and the indirect utility function. (b) Without solving the cost minimization problem, recover the Hicksian de mands for x and y and the expenditure function from the Marshallian demands and the indirect utility function. (c) Write down the Slutsky equation determining the effect of a...
. Consider the following utility function over goods 1 and 2, u (ri, 2)- In a...
. Consider the following utility function over goods 1 and 2, u (ri, 2)- In a 3 ln r2. (a) [15 points] Derive the Marshallian demand functions and the indirect utility function (b) [15 points] Using the indirect utility function that you obtained in part (a), derive the expenditure function from it and then derive the Hicksian demand function for good 1. (c) [10 points] Using the functions you have derived in the above, show that i. the indirect utility...
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is...
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
Consider the following utility function over goods 1 and 2, plnx1 +3lnx2: (a) [15 points] Derive...
Consider the following utility function over goods 1 and 2,
plnx1 +3lnx2: (a) [15 points] Derive the
Marshallian demand functions and the indirect utility function. (b)
[15 points] Using the indirect utility function that you obtained
in part (a), derive the expenditure function from it and then
derive the Hicksian demand function for good 1. (c) [10 points]
Using the functions you have derived in the above, show that i. the
indirect utility function is homogeneous of degree zero in...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What restrictions does a Cobb-Douglas lity function (preferences) impose on demand functions? Explain your answer. marks) 1/4 Maximize u = x;"/4x2 4x, + 2x, = 100 Subject to - Use the information in above to derive the consumer's indirect utility anction (value function) and then prove Roy's identity (10 marks)
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold = 1, Py = 1, and I = 8. a. Solve for the Marshallian demand functions of x and y (your answer should have numbers, not variables. You should round your answers to three decimal places): * old 4 y = 4 b. What is the utility associated with these demands, prices, and income? u = 16 c. Suppose the price of x rises to...
3. Consider the following
utility function, u(x1;x2)=min[xa1; bxa2]; 00 (a) [15 points]
Derive the Marshallian demand functions. (Explain your derivation
in details.) Does the Marshallian demand increase with price? Are
the two consumption goods normal goods? (b) [15 points] Derive the
Hicksian demand functions. Does the Hicksian demand increase with
price?
3. Consider the following utility function, (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two...
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
2. Jane's utility function has the following form: U (1,y) = 3x2 +2.ry The prices of cand y are p, and Py respectively. Jane's income is I. (a) Find the Marshallian demands for and y and the indirect utility function. (b) Without solving the cost minimization problem, recover the Hicksian de mands for x and y and the expenditure function from the Marshallian demands and the indirect utility function. (c) Write down the Slutsky equation determining the effect of a...
. Consider the following utility function over goods 1 and 2, u (ri, 2)- In a 3 ln r2. (a) [15 points] Derive the Marshallian demand functions and the indirect utility function (b) [15 points] Using the indirect utility function that you obtained in part (a), derive the expenditure function from it and then derive the Hicksian demand function for good 1. (c) [10 points] Using the functions you have derived in the above, show that i. the indirect utility...
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
Consider the following utility function over goods 1 and 2,
plnx1 +3lnx2: (a) [15 points] Derive the
Marshallian demand functions and the indirect utility function. (b)
[15 points] Using the indirect utility function that you obtained
in part (a), derive the expenditure function from it and then
derive the Hicksian demand function for good 1. (c) [10 points]
Using the functions you have derived in the above, show that i. the
indirect utility function is homogeneous of degree zero in...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
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