A consumer has the following utility function: U(x.y)=x(y+1), where x and y are quantities of two consumption goods whose prices are Px and Py, respectively. The consumer also has a budget of B. Therefore, the Lagrangian for this consumer is x(y + 1) + X(B – Prx – Py) (a) Verify that this is a maximum by checking the second-order conditions. By substituting x* and y* into the utility function, find an expression for the indirect utility function U* = U(Pr, Py, B) and derive an expression for the expenditure function E = E(Pr, Py, U*) (b) This problem could be recast as the following dual problem Min Prx + Pyy Subject to æ(y + 1) = U* Find the values of x and y that solve this minimization problem and show that the values ofx and y are equal to the partial derivatives of the expenditure function, dE/ðP, and ðE/@P, respectively.

A consumer has the following utility function: U(x.y)=x(y+1), where x and y are quantities of two consumption goods whose prices are Px and Py, respectively. The consumer also has a budget of B. Therefore, the Lagrangian for this consumer is x(y + 1) + X(B – Prx – Py) (a) Verify that this is a maximum by checking the second-order conditions. By substituting x* and y* into the utility function, find an expression for the indirect utility function U* = U(Pr, Py, B) and derive an expression for the expenditure function E = E(Pr, Py, U) (b) This problem could be recast as the following dual problem Min Prx + Pyy Subject to æ(y + 1) = U Find the values of x and y that solve this minimization problem and show that the values ofx and y are equal to the partial derivatives of the expenditure function, dE/ðP, and ðE/@P, respectively.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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