Question

Paul considers goods 1 and 2 as perfect complements: ?(?1, ?2 ) = ???{?1, ?2 }. At the moment Paul is optimally consuming the bundle (?1 = 10, ?2 = 10). Suppose that prices change, so that (?1 = 6, ?2 = 8). What is the minimal amount of income Paul would need to maintain the same utility level after the price change?

a. ? = 100;

b. ? = 80;

c. ? = 140;

d. ? = 180;

Answer 1

U = min{x₁,x₂}

Initially x₁ = 10 and x₂ = 10 => U = min{10,10} = 10

So, Now We have to minimize : m = 6x₁ + 8x₂ subject to : U = min{x₁,x₂} = 10  

In order to minimize expenditure for such a function, a consumer consumes at a point where kink of an indifference curve will occur.

Here kink will occur x₁ = x₂ => U = min{x₁,x₂} = min{x1,x₁} = 10 => x₁ = 10 and x₂ = x₁ = 10

=> m = 6*10 + 8*10 = 140

Hence Minimal amount of income Paul will require = 140.

Hence, the correct answer is (c) m = 140