Question

Suppose x₁ and x₂ are perfect substitutes with the utility function U(x₁, x₂) = 2x₁ + 6x₂. If p₁ = 1, p₂ = 2, and income m = 10, what it the optimal bundle (x₁*, x₂*)?

Answer 1

Given,

x₁ and x₂ are perfect substitutes .

The utility function, U(x₁, x₂) = 2x₁ + 6x₂.

p₁ = 1, p₂ = 2, m = 10

As x₁ and x₂ are perfect substitutes the consumer will only consume the commodity which has the lower price.

Here  p₁ = 1 < p₂ = 2

So ,the consumer will only consume the commodity x₁ .

The budget equation is ,

p₁ x₁ + p₂ x₂=m,

x₁ +2 x₂ = 10

As thhe consumer will only consume the commodity x₁ ,  x₂ = 0. Putting  x₂ = 0 we get

x₁ = 10

So the optimal bundle (x₁*,x₂*) has (10,0).