The following exercise is to enable you to apply duality: Consider the following indirect utility function: v(p1, p2, m) = (3 ^0.75 )/4 · m/( (p1)^ 0.25*((p2)^ 0.75)) Find the expenditure function.
The following exercise is to enable you to apply duality: Consider the following indirect utility function:...
5. Consider the indirect utility function given by: m v(P1, P2, m) = P1 + P2 (a) What are the demand functions (b) What is the expenditure function? (c) What is the direct utility function?
Given the following utility function:
Where, q1 and q2 are consumer goods and the budget
constraint is given as.
With p, and p the prices of the goods and the month
the income. Find.
1. The Marshallian Demands for (q1 and 92.
2. The Indirect Utility Function, V (p1, p2, m)
3. The Hicksian Demands for q1 and q2.
4. The Expenditure Function, m (p1, p2, U)
U(992)=9, +10 log2 U(992)=9, +10 log2
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...
Tricky question: Suppose that the consumer's indirect utility function is given by: v(p, y) = y/(apı + Bp2), where P1, P2 and y are prices and income and where a, ß are positive parameters. Derive the consumer's direct utility function.
Exercise 2: Expenditure minimization We assume an individual whose preferences can be represented by the utility functions | Ưới a) = 8 * @a An expenditure-minimizing consumer would try to minimize the amount they spend on both and rach that their utility is at least as high as some set level of utility U. Mathematically, we thus have minha + P such that Ul. 22) 20 1. Please write the Lagrangan formula corresponding to this particular optimization set up oynundo...
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...
. 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...
2. 2.1 Draw the indifference curves for the utility function U(21, 22) = x1 + 3x2. 2.2 What is the marginal rate of substitution evaluated at an arbitrary consumption bundle (21, 22)? 2.3 Suppose that p1 = 5, P2 = 2, and M = 10. Find the utility-maximizing consump- tion bundle (among those that satisfy the budge constraint) for this agent. You should be able to do this without using any calculus: it should be clear from your indifference curves....
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. 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