A consumer has the following indirect utility function: u (x1, x2) = − 1/ x1 − 1 /x2 1. Compute the Walrasian demand functions. 2. Obtain the indirect utility function. 3. Obtain the expenditure function and the Hicksian demands.
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A consumer has the following indirect utility function:
u (x1, x2) = − 1/ x1 − 1 /x2
1. Compute the Walrasian
2. Obtain the indirect utility function.
3. Obtain the expenditure function and the Hicksian demands.
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- A consumer is faced with the following utility function, U(x1 x2)=(xp1 1+xp2)1/p, where 0<p<1. The consumer also faces the prices p1 and p2 and has income level m. C) derive the the corresponding expenditure function for the consumer and the hicksian demand function.Consider the indirect utility function: v(p1; p2; m) = m /(p1 + p2). What is the Hicksian demand function?Consider a three-commodity consumer setting with the expenditure function: e(p, u) = up1α p2βp3γ Find the indirect utility function Find the Walrasian demand function Verify Roy's identity Recover consumer's direct utility function
- Consider a consumer with utility function u(x1, x2) = α_1x_1^( 2) + α_2x_2^( 2) where α1 > 0 and α2 > 0. Assume that p1, p2 > 0.? (a) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (b) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utilityConsider an individual with the following utility function: Derive step-by-step both corresponding Hicksian demand functions depending on the different prices (P₁, P2) and a fixed utility level u. The equation given In picture.do This in 10 minutes.A consumer is faced with the followlling Utility Function, U( x 1 x2) = ( xp +xp ) 1/ρ, where 0<ρ<1. The consumer also faces the prices and and has income level m. 1. Set up the Lagrangian 0ptimisation function for the consumer and Compute the optimal consumption bundle for the consumer. 2. The solution in (a) represents the Marshallian demand function for and . Using the solution in (a) compute the indirect utility function. 3. Derive the corresponding expenditure function for the consumer and the Hicksian demand function.
- Assuming a linear budget constraint, consider the following utility maximization problem:U (x1, x2) = 2x10.5 + 4x20.5 1. Compute the Marshallian demand functions for goods 1 and good 2.2. Find the compensated demand function.3. Derive the expenditure function and verify that h (p, u) = ∇pe (p, u)4. Derive the indirect utility function and verify Roy's IdentitA consumer has the following utility function:u(x) = (xρ1 + xρ2)1/ρ 1. Derive the Walrasian demand function x(p, w) and compute the indirect utility function.2. Write down the expenditure minimization program.Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian demand function for good Y.
- For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x and x2 are p₁ and p₂ respectively and income is m. i) U(x1x2) = ln(x1+ x2) ii) U(x1x2) = (x1+ x2)Consider a three-commodity consumer setting with the expenditure function:e(p, u) = up1α p2βp3γ 1. Find the indirect utility function2. Find the Walrasian demand function3. Verify Roy's identity4. Recover consumer's direct utility functionSuppose a consumer’s utility from consuming the two goods x and y is given by: PHOTO a) Calculate the uncompensated (Marshallian) demand functions for x and y respectively. b) Calculate the consumer’s indirect utility function for x and y c) Compute the compensated (Hicksian) demand functions for x and y d) Determine the uncompensated own- and cross-price elasticities. e) Determine the compensated own- and cross-price elasticities.