Hydrology - Depression cone VS transmissivity
Based on the Theis equation, increasing the transmissivity will increase the radius of influence and decrease the total drawdown.  Drawdown is directly proportional to the pumping rate and inversely proportional to aquifer transmissivity and storativity.

$$s = \frac{Q}{4T\pi}\int_u^\infty \frac{e^{-y}}y dy$$
and $$u = \frac{r^{2}s}{4Tt}$$
Where s is drawdown, r is radius from well, t is time, T is transmissivity, Q is pumping rate, and u is the well function.

Applying this equation, you can produce plots like this:

for these plots, I used Q = 500, S = 0.01, and t = 4