Calculating gain, input and output resistances of a current amplifier circuit
I don't see how you get Iin = VxGd from the 2nd equation. I agree with you that the two node voltages are proportional from the 1st eqn, but when I solve for Iin in the 2nd eqn (eliminating Vx via your first equation) I get a term   -gds(gds-g)/(gds+GD), a partial current, that must be flowing through the independent Vgs source. Applying KCL at the botttom node, then seems to contradict your later statement that Iin = Iout.