3. Consider the consumer optimization problem subject to max a In(x) + 3 ln(y) P₂x +Pyy ≤w. r, y> 0. (a) Write the Lagrangean for the problem noting that the non-negativity con- straint cannot bind since z, y> 0 and write the Kuhn-Tucker conditions for the problem. subject to (b) Argue that the budget constraint is binding and solve the problem. (c) Add a third good to the model so that the new problem becomes: max a ln(x + 2) + 3 ln(y +2) z.y. P₂x +Pyy + P₂² ≤w, x, y, z ≥ 0, where you can define In(0) =-∞o. Argue that if := 0 at optimum, then a > 0 and y> 0. (d) Is it possible to have at optimum z>0, y > 0, z > 0? (e) When is z = 0 at optimum?

3. Consider the consumer optimization problem subject to max a In(x) + 3 ln(y) P₂x +Pyy ≤w. r, y> 0. (a) Write the Lagrangean for the problem noting that the non-negativity con- straint cannot bind since z, y> 0 and write the Kuhn-Tucker conditions for the problem. subject to (b) Argue that the budget constraint is binding and solve the problem. (c) Add a third good to the model so that the new problem becomes: max a ln(x + 2) + 3 ln(y +2) z.y. P₂x +Pyy + P₂² ≤w, x, y, z ≥ 0, where you can define In(0) =-∞o. Argue that if := 0 at optimum, then a > 0 and y> 0. (d) Is it possible to have at optimum z>0, y > 0, z > 0? (e) When is z = 0 at optimum?

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 3SQP

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