How should you respond to customers who press us for a lower price?

This depends upon your position with the company. In most cases, customers are asking people to do things that they are not authorized to do. If you do not set the prices and are not authorized to negotiate prices, then there is nothing you can do for such customers. You can tell them that this is the price, you cannot change it, and they are free either to buy it at the price for which it is being sold, or not to buy it if they don't want to pay that much. Those are the choices.

If, however, you do have authority to change prices and to make deals, then it is up to you to decide whether it is beneficial to your business to make such deals and to lower your prices. You are under no obligation to give in to customer demands, but in some circumstances, maybe the goodwill of the customer is valuable enough to justify the lower price. If the customer expects you to sell your product at a loss, then you really have to say no. Otherwise, you will shortly be bankrupt and out of business. But who knows, perhaps your prices actually are very high, and you can lower them and still make a profit.