2. Consider the following utility function, (a) [15 pointsl) Derive the Hicksian demand functions and the...
2. Consider the following utility function, (a) 15 points] Derive the Hicksian demand functions and the expenditure function. (b) [15 points] Derive the indirect utility functions
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...
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 consumption goods normal goods? (b) 15 points] Derive the Hicksian demand functions. Does the Hicksian demand ncrease 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...
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...
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, u(x1;x2) = min [sqrt (x1); sqrt(ax2)]; where a > 0 a)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)Show two different ways to derive the Hicksian demand functions. Does the Hicksian demand increase with price?
Find the Hicksian demand function and the expenditure functions for the agent who has following utility functions: • u(x1,x2)=x1 +2x2• u(x1,x2)=min{x1,4x2} • u ( x 1 , x 2 ) = x α1 x β2
2.Optional Question on duality for those who welcome a challenge Consider the same utility function as given by: U(X, Y) = X-Y For the primal problem, find the Marshallian uncompensated demand functions, X(Px Ру and y(Rs Py, by maximizing utility subject to budget constraint Px. X + Ру.Y - I. After obtaining the optimal consumption choices, write down the indirect utility function. Give a simple diagrammatic and economic interpretation. Illustrate the use of the indirect utility function by plugging in...