> Automatic is sold as an expensive option here but that makes no sense to me - how can a chip be more expensive to produce than a physical gear box?
I'm not sure what you mean by "chip" here -- all cars have gear boxes (in some form -- you need to have a way of converting the engine's rotation into wheel rotation without stalling or overworking the engine) the question is how they work and what controls the gear ratio. A manual gearbox is actually very simple conceptually and mechanically, resulting in cheaper hardware (and the repair costs are quite cheap too).
Common automatics use a fluid coupling as their gearbox with a torque converter, which is a more complicated piece of machinery (with more significant repair costs in the medium-term -- a clutch replacement is $1000 while an automatic transmission rebuild is $5000). So it makes some sense that they are more expensive -- though it's not always the case that automatics are more expensive to buy (it's only really the case of cheaper cars that they're always more expensive).
The only kind of automatic I can think of that is a "chip" would be a double-clutch transmission (which might appear like an automatic to a user), but as the name suggests under the hood it is two manual transmissions with a computer trying to predict the future to know what gear is needed next). Those are even more expensive because they are ridiculously complicated, and probably require some sort of license from the manufacturer to sell.