### Properties of the equilibrium price for a demand function

The demand function for a certain good is D(p,m) and the supply function is S(p). For a given m, the equilibrium price p* is given by p* = f(m). a) Show that f'(m) = [dD(p*,m)/dm] / [S'(p*) - dD(p*,m)/dp*] b) Verify this result when S(p) = 2p and D(p,m) = 6m^2p^(-1) + m c) By using the implicit function rule, or oth