no mate they chose a supercharger becuase the supercharged 1.8 is readily available unit from toyota and used in existing cars, nothing to do with power delivery. More to do with the fact they already have a deal with toyota to use there engines.
No sir the supercharger is developed by Lotus Engineering. Toyota has nothing to do with it
Turbo v supercharging
There’s no doubting that a supercharger gives a more even spread of power and, unlike a turbo, it keeps on going. Lotus has had plenty of experience with small capacity turbos with the Vauxhall VXR220 Turbo. Like many blown cars it makes rapid progress but in a series of surges. It’s not so noticeable on the road but on the track the turbo does its stuff and then just goes flat. It feels very odd.
Lotus has employed a Rootes-type Eaton M62 supercharger. It would be simplistic to say that it just bolts onto the standard Toyota engine but in fact it’s not actually far from the truth. The engine really is unmodified, save for a thorough reworking of the Lotus T4 engine management system which takes care of fuelling and ignition and the now lower rpm switching of the cam profiles. Like turbos, superchargers like to gorge on fresh air and a massive intercooler sits on top of the engine fed by the roof mounted air-scoop.
Whereas a turbo tends to boost the mid-range before running out of puff at the top end, a supercharger gives you both mid and top end. The 240R produces its 243bhp at a heady 8,000rpm compared to the standard Exige’s 192bhp at 7,800rpm. Peak torque with supercharger propulsion is 174lb-ft at 7,000rpm against 133lb-ft at 6,800rpm for atmo.
However follow the curves down and the supercharger is doing its thing right across the rev range and it’s a much flatter curve too. The standard engine has a very noticeable dip in the torque curve between 5,000rpm and 7,000rpm, which is where the cam switch takes place. The 240R engine suffers none of this: its torque curve virtually flat from 5,000rpm all the way to 7,000rpm. That gives an incredibly flexible and useable power band that can be dipped in and out of without having to rev the gonads off the thing. That it will continue charging round to 8,500rpm is a bonus should you need to hang onto a gear on track.
Source=Google