The Cobb-Douglas function is widely used in Economics to represent the relationship between the inputs and outputs of a firm. Ittakes the form Y = ALa KB, where Y representsthe outputs, L the work and K the capital. This formulation can be applied to utility and takesthe form u(x) = xal ...xan, where the exponentsare positive and add up to 1. Consider the problem of maximizing utility:max xay1-aS.a p1x+p2y=wx, y≥0Where p1, p2 > 0 are the prices and w > 0 the budget.A) Write the conditions of KKT and find a solution of them, depending on p1, p2,w and a.B) Can it be said that this solution is optimal for the original problem? Justify.C) Find the multiplier 1, depending on p1, p2, w and a. La función de Cobb-Douglas es muy utilizada en Economía para representar la relación entrelos inputs y los outputs de una firma. Toma la forma Y = AL KB, donde Y representa losoutputs, L el trabajo y Kel capital. Esta formulación puede ser aplicada a la utilidad y toma laforma u(x) = x01...xan, donde los exponentes son positivos y suman 1. Considere el problemade maximización de la utilidad:α 1-amáx.ray-S.a pix P2y = wx, y ≥0donde P1, P20 son los precios y w > 0 el presupuesto.a) Escriba las condiciones de KKT y encuentre una solución de ellas, en función dep1, P2,y a.b) Se puede decir que esta solución es óptima para el problema original? Justifique.c) Encuentre el multiplicadorλ, en función de p1, p2, w ya.พ

Answered: La función de Cobb-Douglas es muy…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter8: Cost Analysis

Section: Chapter Questions

Problem 9E

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The Cobb-Douglas function is widely used in Economics to represent the relationship between the inputs and outputs of a firm. It takes the form Y = ALa KB, where Y represents the outputs, L the work and K the capital. This formulation can be applied to utility and takes the form u(x) = xal ...xan, where the exponents are positive and add up to 1. Consider the problem of maximizing utility: max xay1-a S.a p1x+p2y=w x, y≥0 Where p1, p2 > 0 are the prices and w > 0 the budget. A) Write the conditions of KKT and find a solution of them, depending on p1, p2,w and a. B) Can it be said that this solution is optimal for the original problem? Justify. C) Find the multiplier 1, depending on p1, p2, w and a.