What I tried to show using numbers was that a business must advertise and the coupon discount given is not a reduction of profit, it is a re-allocation of advertising cost. So, by training your customers to wait for your coupon, you are training them to wait for YOU, and come to YOU when you have a coupon out - rather than think of trying some other business because they haven't been trained to wait for your coupon.

In my example, customers from both advertising methods cost the same, so my profit would be the same on the lower couponed price as the regular price from the radio ad.

Radio ad - cost of new customer - $50 - item sold $200 - less ad cost = $150 revenue.
Coupon ad - cost of new customer - $10 - item sold $160 ($200 less coupon $40) = $150 revenue.

The gain (if it so transpires for your business) is the repeat customer, not the price markup on a single sale. A customer who comes to you once a week is going to be more profitable than one who shares his weekly business between you and another business. If you can train them to come to you, you have a winner.

The initial gain or loss is never the final result for your business. You must follow the money through your entire pricing/cost process to determine the final outcome.