Given:

Utility Function:

U(x₁, x₂) = - 1/x₁- 1/x₂

Budget Constraint:

P₁x₁ + P₂x₂= y

Where: x₁, x₂= Quantities of Goods Consumed

P₁ = Price of Good x₁

P₂ = Price of Good x₂

y = Consumer Income

Course Hero Expert Answer:

For Utility Maximization, we have the following LaGrangian Function:

Z = U(x₁, x₂) + (y - P₁x₁ - P₂x₂)

Z = - 1/x₁- 1/x₂+ (y - P₁x₁- P₂x₂) (1)

For the First Order Condition, we partially differentiate equation w.r.t. x₁, x₂& , then make them equal to zero.

Z/x₁²- P₁= 0

or

1/x₁² - P₁= 0

P₁= 1/x₁²

= 1/P₁x₁²

= 1/ P₁x₁² (2)

Z/x₂ = 1/x₂²- P₂= 0

P₂ = 1/x₂²

P₂= 1/x₂²

= 1/P₂x₂² (3)

Z/ = y - P₁x₁ - P₂x₂ = 0

y = P₁x₁ + P₂x₂ (4)

This is the First Order Condition for Utility Maximization.

1. Suppose a consumer seeks to maximize the utility function U (2 1, 202 ) = 0 2 subject to the budget constraint P121 + P2 2 = Y, where a, and *2 represent the quantities of goods consumed, p, and p2 are the prices of the two goods and Y' represents the consumer's income. (e) (10) What is the interpretation of this value of the Lagrangian multiplier in this