Question

Bee's utility function is given as U(x₁, x₂) = x₁² + x₂ ². His budget constraint is P₁x₁ + P₂x₂ = m. His demand for x₁ is: A. m/2P₁ B. mP₁/P₂²+P₂² C. m/P₁+P₂ D. m/P₁ if P₁ < P₂ and 0 if P₂ < P₁

Answer 1

To find Bee's demand for x₁, we need to maximize his utility function subject to the budget constraint. We can use the method of Lagrange multipliers to solve the problem.

The Lagrangian function is:

L = x₁² + x₂² + λ(m - P₁x₁ - P₂x₂)

Taking the partial derivative of L with respect to x₁, x₂, and λ, and setting them equal to zero, we get:

• ∂L/∂x₁ = 2x₁ - λP₁ = 0
• ∂L/∂x₂ = 2x₂ - λP₂ = 0
• ∂L/∂λ = m - P₁x₁ - P₂x₂ = 0

Solving these equations simultaneously, we get:

• x₁ = m/2P₁
• x₂ = m/2P₂

Substituting these values of x₁ and x₂ into the budget constraint, we get:

• P₁(m/2P₁) + P₂(m/2P₂) = m
• m/2 + m/2 = m

Therefore, the demand for x₁ is:

• x₁ = m/2P₁

So the correct answer is A. m/2P₁.