Question

Assume there are only two goods, X and Y. Prove that quasi-concave utility U(X,Y) is

identical to dMRX/dX < 0

Answer 1

Utiltiy is the representation of Continuous, Locally non satiated and atleast twice differentiable preferences.

U(X,Y) is the function of two variables then U(.) is called as quasi concave if g(.) is the increasing fucntion then function f is defined as f(x)=g(U(x)) for all x is quasi concave same for all y

then we know that for increasing function second oreder condition always yield negative value i.e. less than zero

dU(X,Y)/dX=MRx

If we differentitate MRx again with X we should get dMRx/dX must be less than zero

hence proved dMRx/dX<0