Question

4. Anne's utility function is given by u(xi,x2) Michael's utility function is given by u(xı, x2)' = x1x2. She has two friends, Michael and Peter 1 and Peter's is given by u(x1, X2) = = 1042 1 Τ) -x12. Who has the same preferences as Anne? And who has indifference curves with similar shape as Anne's indifference curves? Explain.

Answer 1

The Preferences of Anne given by the utility function u(x₁,x₂) = x₁x₂ looks like a rectangular hyperbola. It is imperative to note at this juncture that when either x₁ or x₂ or both rises then utility of Anne rises. However in Michael's utility function x1x2 is in denominator along with the coefficient 2 with a positive sign before it. This means that whenx₁ orx₂ or both rises in Michael's utility function then 1/(10 + 2 x₁x₂) falls. But along with the negative sign before the expression1/(10 + 2 x₁x₂) , that is, -(1/(10 + 2 x₁x₂)) rises as x₁ orx₂ or both rises. Thus Michael has same preferences as Anne. On the other hand the preferences of Peter are just opposite of Anne's because of the negative sign beforex₁x_2. However the shape of indifference curves are similar in appearance for Peter as for Anne just that they are mirror reflections of one another.