DIFFERENTIAL INPUT STAGE
Q1 and Q2 are your basic differential amplifier (long tail pair). The tail RE, sets the DC collector bias current for both transistors
Ic1 = Ic2 = Ie / 2 = (VCC - Vbe) / RE · 1/2
Ic1 sets Q1's gain (or transconductance - voltage in, current out) for an AC signal.
gm1 = Ic1 / VT
where VT = 26 mV. This gives Q1's output current of
ic1 = vin · 1/2 · gm1
Why the factor of 1/2? The input vin = (vin+ - vin-) divides equally between vbe1 and vbe2.
Finally, why include RC1? For DC bias purposes, RC1 helps set Ic1 equal to Ic2. Your first guess at this value is RC1 = vbe3 / Ic1. For example, if the desired Ic1 = 0.5 mA, then RC1 = 0.7V / 0.5 mA = 1.4 k. You might have to tweak this value to get Ic1 ~ Ic2. Although RC1 is our friend in balancing collector currents, it also robs us of signal gain by diverting some of ic1 away from the base of Q3.