i. Write down the Lagrangian form and solve the utility maximization problem.ii. Assume that the income increases from 100 to $101. What is the increase in the optimal value of u(x,y)? Suppose that Jack has the utility function u (x, y) = /x + y. The price per unit%3Dof x is $1 and the price per unit of y is $4. He receives $100 that all has to be spent ontwo commodities x and y.

i. u(x,y)=x+y x+4y=100 α=max u(x,y) st x+4y=100α=x+y+λ(100-x-4y)dαdx=12x-λ=012x=λ…

Suppose that Jack has the utility function u (x, y) = Vx + y. The price per unit %3D of x is $1 and the price per unit of y is $4. He receives $100 that all has to be spent on two commodities x and y.

Suppose that Jack has the utility function u (x, y) = Vx + y. The price per unit %3D of x is $1 and the price per unit of y is $4. He receives $100 that all has to be spent on two commodities x and y.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

i. Write down the Lagrangian form and solve the utility maximization problem.

ii. Assume that the income increases from 100 to $101. What is the increase in the optimal value of u(x,y)?

Suppose that Jack has the utility function u (x, y) = /x + y. The price per unit
%3D
of x is $1 and the price per unit of y is $4. He receives $100 that all has to be spent on
two commodities x and y.

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