A simple ESP8266 module from AliExpress is less than $4 (an ESP12F module - which is the FCC certified one with most I/O ports available - is $2), can be programmed with Arduino, has WiFi and that is more than enough for wireless home automation peripherals that are not supposed to do lots of processing (it will still easilly fit a REST interface for automated control and even a web interface for user control alongside it).

That said, in order to power it unless you can somehow draw 3.3v from the device it's attached to, you actually need more parts and that'll add up to more than $4 unless you're doing it with batteries (and design and assemble your own voltage regulator circuit which is not that hard and is cheap, or maybe get a slightly more expensive ESP module that comes with voltage regulation) - this works fine if your device sleeps most of the time and just wakes up once in a while to check some data from a server holding instructions for it. For an always one device, best IMHO to use a 3.3V wall power adaptor, which will cost at least $6 from AliExpress.

The power considerations apply exactly the same for ESP32s.