Resistors in volume in China cost about 0.1 cent US.
Electrolytic capacitors cost around 1 cent up to around 33 uF.
Some selected ICs cost as little as 2 cents 0 eg TL431, a dual opamp such as LM358 may be 5 cents.
An NE567 would do your job but is a bit rare and may cost 10 - 20 cents.
I had altogether too much to do with these in another lifetime. They work quite well.
- The NJM567 tone and frequency decoder is a highly stable phase
locked loop with synchronous AM lock detection and power output
circuitry. Its primary function is to drive a load whenever a sustained
frequency within its detection band is present at the self-biased input.
The bandwidth cebter frequency, and output delay are independently
determined by means of four external components.
A CD4046 digital PLL would do your job - pricing here and datasheet here - TI and here -Fairchild
Price from Digikey is $US12.8 at 50,000 quantity so Asian price may be 5 cents.
Circuit diagram in real world use is not much more than shown below. Phase comparator two is just an XOR gate but works like magic. The circuit shown below would probably cost under 10 cents in 10,000 + volume in China but PCB cost and manufacturing costs will about double that.
This circuit will work superbly with minimal noise and quite well in modestly noisy circumstances. In very noisy environments a 5th order active filter can be added at a cost of 2 transistors and RC glue - but good quality R's and 's needed for a stable filter - say an additional $0.10.