I want to draw your attention about customer care . Some customers are arrogent by nature . Its very difficult to convince them. My experience below..

In any service industry, you will find such customers.

What you did was very good, but as Mr. Ibrahim said, you cannot continue giving money from your pocket because you will have no money left at the end of the month.

1. Sometimes its good not to have such customer.
2. Get your supervisor/manger involve because they are the ones who can make the final decisions
3. Ask customer to check prices at other stores

Thanks for sharing your situation 

I do agree with Ibrahim specially that this is a regular Customer and in your Manager capacity there will be more tools to resolve the issue in a win win situation. 

Sometimes an angry regular Customer satisfaction is a key for increasing loyalty and business 

Cheers

What you did is very nice, but if you keep doing it, at the end of the month you will notice that you've been working for free.

Your manager must have some authority to give special discounts. Get your manager involved, either he will arrange a discount or will help you with the convincing process.

Experiences are bad or take you away from challenges . How do you project your company gives you a seat to sit. How do you project your boss gives you a place to discuss. How do you rate your product gives you confidence in convincing the customer . Try the customer as god & convince him / her . If still she/he does not understand to your bound guidelines & company structure than politely get up & say sorry you are trying for a sky which is not in my reach .

It is normal to meet customers having strange requests and strange personalities. Customer service is about taking care of the customer and satisfying his/her needs within the company policy. What you did it is a "personal" action to make customer happy but you worked against the company rule. If you face such situations in future it is better to explain nicely your limits to the customer and if he/she still insists you can direct them to your manager. Also if you notice that some complaints happen frequently you should discuss that with your manager.

where's your land lord

and

where's the police