![1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R. Suppose the agents wealth w is large enough that good 3 is demanded in non-zero quantities. Do not normalize the price of good 3 for this problem 1. Find the agents Hicksian demand for each good. (Hint: first use the fact that goods 1 and 2 are optimally demanded in the same quantity. Then use the fact that bang for the buck for the combined good 1+2 must be equal to 1. The utility guarantee should appear only in the Hicksian demand for good 3.) 2. Which goods are complements? Which are substitutes?](http://img.homeworklib.com/questions/c73b2390-5f3a-11eb-b6ee-c96c8a4e27a2.png?x-oss-process=image/resize,w_560)
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1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R....
Suppose that an individual has the following quasilinear utility function: ?(?1, ?2) = ln(?1) + ?2...
Suppose that an individual has the following quasilinear utility function: ?(?1, ?2) = ln(?1) + ?2 Show graphically the total effect, substitution effect and income effect when the price of good ?1 decreases (assuming there is an interior solution). Then derive Hicksian demand curves for ?1.(the sign in the utility function is positive)
. 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...
answer e and f only please Exercise 3. Slutsky (Quasilinear) The utility function is u =...
answer e and f only please
Exercise 3. Slutsky (Quasilinear) The utility function is u = x + xy, and the budget constraint is m=P,X, + P2XZ. a) Derive the optimal demand curve for good 1, x,(PP2), and good 2, x2(m, PP.). b) Looking at the cross price effects (@x_/ôp, and Ox_/ôp.) are goods x, and X, substitutes or complements? Looking at income effects (@x,lôm and Ox_lām) are goods x, and X, inferior, normal or neither? c) Assume m=100, =0.5...
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...
1. Consider the following utility function over goods 1 and 2, (a) [15 points] Derive the...
1. Consider the following utility function over goods 1 and 2, (a) [15 points] Derive the Marshallian demand functions and the indirect utility (b) [15 points] Using the indirect utility function that you obtained in part (a), () [10 points] Using the functions you have derived in the above, show that function derive the expenditure function from it and then derive the Hicksian demand function for good 1. iihi İ. the indirect utility function is homogeneous of degree zero in...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where I and y are the two goods she consumes. The price of good r is p ,. The price of good y is Py. Her income is m. (a) Write her maximization problem and find her demand functions for the two goods. Is it always possible to have an interior solution? Justify your answer. (b) Are the two goods ordinary or giffen? Are the...
2 Perfect substitutes Consider an agent with perfectly substitutable utility over R The agent has total...
2 Perfect substitutes Consider an agent with perfectly substitutable utility over R The agent has total wealth w>0 1. Suppose the agent faces linear prices and that P1くPi for every i > 1, what is the agent's optimal consumption bundle? What fraction of her wealth does she spend on each good? Show that the tangency conditions for optimality are satisfed for the bundle you've found. 2. Suppose instead she faces the same linear price for every good. Describe the set...
This question explores some features of the quasilinear utility function. Avi’s utility function is ?(?, ?)...
This question explores some features of the quasilinear utility function. Avi’s utility function is ?(?, ?) = 4?1/2 + ?. Barry’s utility function is ?(?, ?) = ? + 3?1/3. Derive Avi’s demand functions for goods x and y. What must be true of Px for her to be at a corner solution? Which good would not be consumed under this condition? (10 points) Now assume an interior solution and graph Avi’s income consumption curve. (3 points) Derive Barry’s demand...
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...
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15...
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? consumption goods normal goods? (b) [ 15 points Derive the Hicksian demand functions. Does the icksian demand increase with price?
. 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...
answer e and f only please
Exercise 3. Slutsky (Quasilinear) The utility function is u = x + xy, and the budget constraint is m=P,X, + P2XZ. a) Derive the optimal demand curve for good 1, x,(PP2), and good 2, x2(m, PP.). b) Looking at the cross price effects (@x_/ôp, and Ox_/ôp.) are goods x, and X, substitutes or complements? Looking at income effects (@x,lôm and Ox_lām) are goods x, and X, inferior, normal or neither? c) Assume m=100, =0.5...
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...
1. Consider the following utility function over goods 1 and 2, (a) [15 points] Derive the Marshallian demand functions and the indirect utility (b) [15 points] Using the indirect utility function that you obtained in part (a), () [10 points] Using the functions you have derived in the above, show that function derive the expenditure function from it and then derive the Hicksian demand function for good 1. iihi İ. the indirect utility function is homogeneous of degree zero in...
2 Perfect substitutes Consider an agent with perfectly substitutable utility over R The agent has total wealth w>0 1. Suppose the agent faces linear prices and that P1くPi for every i > 1, what is the agent's optimal consumption bundle? What fraction of her wealth does she spend on each good? Show that the tangency conditions for optimality are satisfed for the bundle you've found. 2. Suppose instead she faces the same linear price for every good. Describe the set...
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...
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? consumption goods normal goods? (b) [ 15 points Derive the Hicksian demand functions. Does the icksian demand increase with price?
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