[emodendroket]

For this analogy to work the ridesharing services would need to give taxi companies a lot more than a nickel a ride.

[jwallaceparker]

The specific value of the subsidy is completely irrelevant to the analogy.

[emodendroket]

If the fishing rod let your friend catch 105% as much as he needed to eat you probably need to keep fishing yourself.

[jwallaceparker]

Yes, you would. But with your remaining time you'd build shelter or firewood, just not as much.

The same principle applies. You still both improved your standard of living. The extent of the improvement depends on the productivity increase afforded by the fishing rod.