Common Emitter Stage BJT Amplifier with Early Effect Inclusion

Some guidance only for homeworks:

Early effect (=the effective width of the base shrinks as reverse Vcb increases) can be seen as current gain increase as Vcb (and Vce) increases. That can be seen as AC conductance between C and E. If you have the curves Ic vs Vce at different base currents you see how Ic grows as Vce increases. As a simplest linearization you can insert in gain calculations to the AC model a leakakge resistor Va/Ic between C and E, where Va is the Early voltage and Ic is the operating point collector current.

I guess you are expected to use a large signal model and derive by yourself the linearized equations because you have the needed parameters such as VT and Is. Hopefully you can calculate partial derivatives to derive the linearized quantities such as Gm.

Here's a small screenshot taken from Early effect article in Wikipedia:

Gm is the partial derivative of Ic when the variable is Vbe. You must calculate the numerical value in the operating point.