Let’s say I sell widgets on the market for a retail price of x. Factor in their cost to me - in this case, I mark them up by 25% of their original cost so that my base cost could be represented as 0.8x. But it could be whatever.
So now Joe Big Client comes along and wants to buy 5000 of my widgets, but of course he is expecting some sort of volume discount. How do I know what unit price to offer him such that he’ll feel he’s getting a good deal but I’m still maximizing my profits?
There is no magic formula for your question. The answer is a function of your competition and any discounts they are offering, balancing the amount in profit you’ll lose per unit against the minimum discount it will take to get the business, and the nature of the widget and business itself. That is, is the widget otherwise flying off the shelf at normal prices? And is it a perishable item that spoils such that you risk losing some inventory to spoilage or obsolescence? That might factor into your discount decision as well.
Another factor is, is this a new product? If so, perhaps having a high volume ‘reference customer’ will actually make others buy more because they’ll see your product as ‘proven’ based on the fact this customer has purchased a large amount. Or it could attract investors which may be worth it to you even to the point of offering the widget at close to cost or even a loss. Doubly so if the customer is huge (like Walmart or Costco) where starting that relationship could get them to buy others of your products in high volumes, or result in multiple large purchases down the road.
One software company charges K*n^(3/4) for n licenses. That’s their magic formula.
There are entire courses taught in business school about pricing. I have a whole book on this topic shelved away somewhere. So it’s not trivial, and there is no single formula.
**Yarster **hits on important points. The answer comes from analysis of the market, which includes supply and demand curves, and elasticity, which is the response of demand to a change in price.
In your case you also need to consider what are your fixed costs and marginal costs to produce a widget, and how much profit you need to make. If you have high fixed costs and low marginal costs, then maybe you are willing to make the same $ profit on a large-volume transaction than a small one so you discount to make that number. This might be true for making a plastic toy where you have to pay for a factory, dies, etc., but each toy costs like $0.05 to make. But if you have high marginal costs then you can’t offer much for a volume discount, something labor intensive like hand-wired guitar amplifiers.
You can give him a couple prices quotes, ask him how much he’ll buy at each price point, construct your own demand curve, and then set price to maximize profit 
Ahhh… if only it were that easy.