Mathematics for Economists

Liquidity modelling

Assume that there is some ordering costc. In this case

J(S)=cS+h
E



(SD)+



+p
E



(DS)+



.

Calculating the derivative

c+hF(S)p( 1 F(S))= 0.

Solving the equation

cp+F(S)(h+p)= 0 , F(S)=pp+ch.