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A consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the
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- A consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Obtain the consumers demand functions X1 and X2 as well as the indirect utility function of the consumerA consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Show that the consumers indirect utility function is homogeneous of degree zero in both prices and incomeA 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. (A) Set up a Lagrangian optimisation function for the consumer and compute the optimal consumption bundle for the consumer B)the solution in (a) represents the mashallian demand function for x1and x2. using the solution in (a) compute the indirect utility function
- 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. Set up a Lagrangian optimisation function for the consumer and compute the optimal consumption bundle for the consumerA 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. (A) Set up a Lagrangian optimisation function for the consumer and compute the optimal consumption bundle for the consumer B)the solution in (a) represents the mashallian demand function for x1and x2. usuing the solution in (a) compute the indirect utility functionFor 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)
- 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.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. (A) Set up a Lagrangian optimisation function for the consumer and compute the optimal consumption bundle for the consumer B)the solution in (a) represents the mashallian demand function for x1and x2. usuing the solution in (a) compute the indirect utility function. C) derive the the corresponding expenditure function for the consumer and the hicksian demand function. D) using your knowledge on classical demand theory, explain under what circumstances the expenditure minimisation problem and the utility maximization problem would yield the same results.For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x1 and x2 are p1 and p2 respectively and income is m. U(x1 x2) = In (x1 + x2) U(x1 x2) = x1 + x2
- A consumer’s utility function is given by: U(X1,X2)= X(α),X(1-α) where A>0, 0<α<1 The consumer also faces the prices P1 and P2 has income level m. a.) Obtain the consumer’s demand functions for and as well as the indirect utility function of the consumer b.) Show that the consumer’s indirect utility function is homogenous of degree zero in both prices and income. c.) Set up the expenditure minimization problem and find the expenditure function E(p,u)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.Consider the utility function u(x) =√x1+ √x2 ; and a standard budget constraint: p1x1+p2x2=I. a.Are the preferences convex? b. Are the preferences represented by this function homothetic? c. Verify that the demand function is homogeneous of degree 0 in prices and income.