Is it permissible to run a business that sells on credit with a price markup for deferred payment?

Yes — the majority and mainstream position across contemporary Islamic finance is that charging a higher, clearly stated price for deferred/credit payment than for immediate cash payment is permissible, provided the price is fixed and agreed at the time of the sale contract itself and does not increase further if the payment is later delayed beyond the agreed date. This is, in fact, the basis of murabaha and bai muajjal, the sale-based financing structures that most Islamic banks use instead of interest-based lending.

The key distinction scholars draw is between this and riba: a sale with one agreed, fixed total price (even if that price is higher than the cash price, and even if paid in installments) is a trade transaction, not a loan, and trade is explicitly permitted in the Quran alongside the prohibition of riba. What would make it problematic is any structure where the amount owed keeps increasing the longer payment is delayed (that reintroduces a time-value-of-money mechanism identical to interest) — some scholars have historically been more cautious about credit-price markups specifically because of how easily this line can blur in practice, which is why the fixed-price-at-contract condition is treated as non-negotiable.

Source: Quran 2:275 ("Allah has permitted trade and forbidden riba"); mainstream contemporary Islamic finance practice around murabaha and bai muajjal — see IslamQA.info answer 13973 on raising the price for installment payment.