Suppose an individual has a preference represented by the utility function U(X, X) = X +...

 

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Suppose an individual has a preference represented by the utility function U(X₁, X₂) = X₁ + InX₂. The individual consumes two goods, X, and X₂ and faces the prices P, and P2. Consumption is constrained by income level M. 5. Now, suppose the expenditure function is approximated by: log c(u, p)= a(p) + ub(p) 1 m where: a(p) = a + Σalog p₁ + Zlog pilog P Pi 2 k-1 j-i 22 b(p) = P.P i v(M, p) = a. Using Shepherd's lemma derive an expression for the share equations (i.e., take derivative with respect to prices to generate Hicksian demand functions) b. Assume that the indirect utility function and a(p) can be expressed as: 22 log M-a(p) b(p) a(p) = log P Solve for the Marshallian demand equations (note that this will be the expression for the AIDS model) Suppose an individual has a preference represented by the utility function U(X₁, X₂) = X₁ + InX₂. The individual consumes two goods, X, and X₂ and faces the prices P, and P2. Consumption is constrained by income level M. 5. Now, suppose the expenditure function is approximated by: log c(u, p)= a(p) + ub(p) 1 m where: a(p) = a + Σalog p₁ + Zlog pilog P Pi 2 k-1 j-i 22 b(p) = P.P i v(M, p) = a. Using Shepherd's lemma derive an expression for the share equations (i.e., take derivative with respect to prices to generate Hicksian demand functions) b. Assume that the indirect utility function and a(p) can be expressed as: 22 log M-a(p) b(p) a(p) = log P Solve for the Marshallian demand equations (note that this will be the expression for the AIDS model)